Instructions¶

WebAssembly computation is performed by executing individual instructions.

Parametric Instructions¶

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}}$¶

Do nothing.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}$¶

Trap.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}}$¶

Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~{({t^\ast})^?}$¶

Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}_2$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}_1$ from the stack.
If $c \neq 0$, then:
1. Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}_1$ to the stack.
Else:
1. Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}_2$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}_1~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}_2~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~{({t^\ast})^?}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}_1 & \quad \mbox{if}~ c \neq 0 \\ & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}_1~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}_2~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~{({t^\ast})^?}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}_2 & \quad \mbox{if}~ c = 0 \\ \end{array}\end{split}\]

Note

In future versions of WebAssembly, $\mathsf{select}$ may allow more than one value per choice.

Numeric Instructions¶

Numeric instructions are defined in terms of the generic numeric operators. The mapping of numeric instructions to their underlying operators is expressed by the following definition:

\[\begin{split}\begin{array}{lll@{\qquad}l} \mathit{op}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}\scriptstyle\kern-0.1emN}}(i_1,\dots,i_k) &=& \href{../Step_pure/numerics.html#int-ops}{\mathrm{i}\mathit{op}}_N(i_1,\dots,i_k) \\ \mathit{op}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{f}\scriptstyle\kern-0.1emN}}(z_1,\dots,z_k) &=& \href{../Step_pure/numerics.html#float-ops}{\mathrm{f}\mathit{op}}_N(z_1,\dots,z_k) \\ \end{array}\end{split}\]

And for conversion operators:

\[\begin{split}\begin{array}{lll@{\qquad}l} \href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?}_{t_1,t_2}(c) &=& \href{../Step_pure/numerics.html#convert-ops}{\mathit{cvtop}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}^?}_{|t_1|,|t_2|}(c) \\ \end{array}\end{split}\]

Where the underlying operators are partial, the corresponding instruction will trap when the result is not defined. Where the underlying operators are non-deterministic, because they may return one of multiple possible NaN values, so are the corresponding instructions.

Note

For example, the result of instruction $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}$ applied to operands $i_1, i_2$ invokes $\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}}(i_1, i_2)$, which maps to the generic $\href{../exec/numerics.html#op-iadd}{\mathrm{iadd}}_{32}(i_1, i_2)$ via the above definition. Similarly, $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle64}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}\mathsf{\_}\href{../syntax/types.html#syntax-numtype}{\mathsf{f\scriptstyle32}}\mathsf{\_s}$ applied to $z$ invokes $\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{trunc}}^{\mathsf{s}}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{f\scriptstyle32}},\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle64}}}(z)$, which maps to the generic $\href{../exec/numerics.html#op-trunc}{\mathrm{trunc}^{\mathsf{s}}}_{32,64}(z)$.

$t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c$¶

Push the value $t.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c$ to the stack.

Note

No formal reduction rule is required for this instruction, since $\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}$ instructions already are values.

${\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}}$¶

Assert: Due to validation, a value of number type ${\mathit{nt}}$ is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
If ${{\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}}}{{}_{{\mathit{nt}}}(c_1)}$ is empty, then:
1. Trap.
Let $c$ be an element of ${{\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}}}{{}_{{\mathit{nt}}}(c_1)}$.
Push the value $({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c \in {{\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}}}{{}_{{\mathit{nt}}}(c_1)} \\ & ({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ {{\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}}}{{}_{{\mathit{nt}}}(c_1)} = \epsilon \\ \end{array}\end{split}\]

${\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}}$¶

Assert: Due to validation, a value of number type ${\mathit{nt}}$ is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
If ${{\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}}}{{}_{{\mathit{nt}}}(c_1, c_2)}$ is empty, then:
1. Trap.
Let $c$ be an element of ${{\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}}}{{}_{{\mathit{nt}}}(c_1, c_2)}$.
Push the value $({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c \in {{\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}}}{{}_{{\mathit{nt}}}(c_1, c_2)} \\ & ({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ {{\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}}}{{}_{{\mathit{nt}}}(c_1, c_2)} = \epsilon \\ \end{array}\end{split}\]

${\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-testop}{\mathit{testop}}}$¶

Assert: Due to validation, a value of number type ${\mathit{nt}}$ is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{\href{../syntax/instructions.html#syntax-testop}{\mathit{testop}}}}{{}_{{\mathit{nt}}}(c_1)}$.
Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-testop}{\mathit{testop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {{\href{../syntax/instructions.html#syntax-testop}{\mathit{testop}}}}{{}_{{\mathit{nt}}}(c_1)} \\ \end{array}\end{split}\]

${\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-relop}{\mathit{relop}}}$¶

Assert: Due to validation, a value of number type ${\mathit{nt}}$ is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{\href{../syntax/instructions.html#syntax-relop}{\mathit{relop}}}}{{}_{{\mathit{nt}}}(c_1, c_2)}$.
Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-relop}{\mathit{relop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {{\href{../syntax/instructions.html#syntax-relop}{\mathit{relop}}}}{{}_{{\mathit{nt}}}(c_1, c_2)} \\ \end{array}\end{split}\]

${\mathit{nt}}_2 {.} {{\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}}}{\mathsf{\_}}{{\mathit{nt}}_1}$¶

Assert: Due to validation, a value of number type ${\mathit{nt}}_1$ is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
If ${{\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}}}{{}_{{\mathit{nt}}_1, {\mathit{nt}}_2}(c_1)}$ is empty, then:
1. Trap.
Let $c$ be an element of ${{\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}}}{{}_{{\mathit{nt}}_1, {\mathit{nt}}_2}(c_1)}$.
Push the value $({\mathit{nt}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({\mathit{nt}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{nt}}_2 {.} {{\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}}}{\mathsf{\_}}{{\mathit{nt}}_1}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({\mathit{nt}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c \in {{\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}}}{{}_{{\mathit{nt}}_1, {\mathit{nt}}_2}(c_1)} \\ & ({\mathit{nt}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{nt}}_2 {.} {{\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}}}{\mathsf{\_}}{{\mathit{nt}}_1}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ {{\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}}}{{}_{{\mathit{nt}}_1, {\mathit{nt}}_2}(c_1)} = \epsilon \\ \end{array}\end{split}\]

Reference Instructions¶

$\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~x$¶

Let $F$ be the current frame.
Assert: due to validation, the defined type $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}[x]$ exists.
Let $\href{../valid/conventions.html#syntax-deftype}{\mathit{deftype}}$ be the defined type $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{types}}[x]$.
Push the value $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~\href{../valid/conventions.html#syntax-deftype}{\mathit{deftype}}$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]) \\ \end{array}\end{split}\]

Note

No formal reduction rule is required for the case $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ $\href{../syntax/types.html#syntax-absheaptype}{\mathit{absheaptype}}$, since the instruction form is already a value.

$\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, $x < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{module}}{.}\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcs}}|}$.
Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{module}}{.}\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcs}}{}[x])$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{module}}{.}\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcs}}{}[x]) \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}}$¶

Assert: Due to validation, a reference value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1)$ to the stack.
Else:
1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1) & \quad \mbox{if}~ {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} = (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}}) \\ & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0) & \quad \mbox{otherwise} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}as\_non\_null}}$¶

Assert: Due to validation, a reference value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
Push the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}as\_non\_null}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} = (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}}) \\ & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}as\_non\_null}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} & \quad \mbox{otherwise} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}eq}}$¶

Assert: Due to validation, a reference value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_2$ from the stack.
Assert: Due to validation, a reference value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_1$ from the stack.
If ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_1$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. If ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_2$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
  1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1)$ to the stack.
2. Else if ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_1 = {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_2$, then:
  1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1)$ to the stack.
3. Else:
  1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)$ to the stack.
Else if ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_1 = {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_2$, then:
1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1)$ to the stack.
Else:
1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_1~{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_2~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}eq}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1) & \quad \mbox{if}~ {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_1 = (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}}_1) \land {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_2 = (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}}_2) \\ & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_1~{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_2~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}eq}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1) & \quad \mbox{otherwise, if}~ {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_1 = {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_2 \\ & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_1~{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}_2~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}eq}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0) & \quad \mbox{otherwise} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}test}}~{\mathit{rt}}$¶

Let F be the topmost $\mathsf{frame}$.
Assert: Due to validation, a reference value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ from the stack.
Let ${\mathit{rt}'}$ be the type of ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$.
If ${\mathit{rt}'}$ matches ${{\href{../exec/types.html#type-inst}{\mathrm{clos}}}}_{f{.}\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}({\mathit{rt}})$, then:
1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1)$ to the stack.
Else:
1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0)$ to the stack.

Todo

(9) Need to handle RulePr s |- ref : rt properly in prose instead of $ref_type_of below is the official specification

Let $F$ be the current frame.
Let $\mathit{rt}_1$ be the reference type $\href{../exec/types.html#type-inst}{\mathrm{clos}}_{F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}(\mathit{rt})$.
Assert: due to validation, $\mathit{rt}_1$ is closed.
Assert: due to validation, a reference value is on the top of the stack.
Pop the value $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$ from the stack.
Assert: due to validation, the reference value is valid with some reference type.
Let $\mathit{rt}_2$ be the reference type of $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$.
If the reference type $\mathit{rt}_2$ matches $\mathit{rt}_1$, then:
1. Push the value $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1$ to the stack.
Else:
1. Push the value $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & s ; f ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}test}}~{\mathit{rt}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~1) & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ s \href{../exec/values.html#valid-ref}{\vdash} {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} : {\mathit{rt}'} \\ {\land}~ \{ \begin{array}[t]{@{}l@{}} \}\end{array} \href{../valid/matching.html#match-reftype}{\vdash} {\mathit{rt}'} \href{../valid/matching.html#match-reftype}{\leq} {{\href{../exec/types.html#type-inst}{\mathrm{clos}}}}_{f{.}\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}({\mathit{rt}}) \\ \end{array} \\ & s ; f ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}test}}~{\mathit{rt}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~0) & \quad \mbox{otherwise} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}cast}}~{\mathit{rt}}$¶

Let F be the topmost $\mathsf{frame}$.
Assert: Due to validation, a reference value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ from the stack.
Let ${\mathit{rt}'}$ be the type of ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$.
If ${\mathit{rt}'}$ does not match ${{\href{../exec/types.html#type-inst}{\mathrm{clos}}}}_{f{.}\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}({\mathit{rt}})$, then:
1. Trap.
Push the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ to the stack.

Todo

(9) Need to handle RulePr s |- ref : rt properly in prose instead of $ref_type_of below is the official specification

Let $F$ be the current frame.
Let $\mathit{rt}_1$ be the reference type $\href{../exec/types.html#type-inst}{\mathrm{clos}}_{F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}(\mathit{rt})$.
Assert: due to validation, $\mathit{rt}_1$ is closed.
Assert: due to validation, a reference value is on the top of the stack.
Pop the value $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$ from the stack.
Assert: due to validation, the reference value is valid with some reference type.
Let $\mathit{rt}_2$ be the reference type of $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$.
If the reference type $\mathit{rt}_2$ matches $\mathit{rt}_1$, then:
1. Push the value $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$ back to the stack.
Else:
1. Trap.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & s ; f ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}cast}}~{\mathit{rt}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ s \href{../exec/values.html#valid-ref}{\vdash} {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} : {\mathit{rt}'} \\ {\land}~ \{ \begin{array}[t]{@{}l@{}} \}\end{array} \href{../valid/matching.html#match-reftype}{\vdash} {\mathit{rt}'} \href{../valid/matching.html#match-reftype}{\leq} {{\href{../exec/types.html#type-inst}{\mathrm{clos}}}}_{f{.}\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}({\mathit{rt}}) \\ \end{array} \\ & s ; f ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}cast}}~{\mathit{rt}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{otherwise} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-i31}{\mathsf{ref{.}i\scriptstyle31}}$¶

Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}i\scriptstyle31}}~{{\href{../exec/numerics.html#op-wrap}{\mathrm{wrap}}}}_{32, 31}(i))$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~\href{../syntax/instructions.html#syntax-instr-i31}{\mathsf{ref{.}i\scriptstyle31}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}i\scriptstyle31}}~{{\href{../exec/numerics.html#op-wrap}{\mathrm{wrap}}}}_{32, 31}(i)) \\ \end{array}\end{split}\]

${\href{../syntax/instructions.html#syntax-instr-i31}{\mathsf{i{\scriptstyle31}{.}get}}}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}$¶

Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}i\scriptstyle31}}$ ${\href{../syntax/values.html#syntax-int}{\mathit{u\scriptstyle\kern-0.1em31}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}i\scriptstyle31}}~i)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$.
2. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{{{\href{../exec/numerics.html#op-extend}{\mathrm{extend}}}}_{31, 32}^{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}}{(i)})$ to the stack.

Todo

(4) Guarantees from validation can help simplify the prose. below is the official specification

Assert: due to validation, a value of type $(\href{../syntax/types.html#syntax-reftype}{\mathsf{ref}}~\href{../syntax/types.html#syntax-reftype}{\mathsf{null}}~\href{../syntax/types.html#syntax-heaptype}{\mathsf{i\scriptstyle31}})$ is on the top of the stack.
Pop the value $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$ from the stack.
If $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$ is $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~t$, then:
1. Trap.
Assert: due to validation, a $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$ is a scalar reference.
Let $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}i\scriptstyle31}}~i$ be the reference value $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$.
Let $j$ be the result of computing $\href{../exec/numerics.html#op-extend}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{31,32}(i)$.
Push the value $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~({\href{../syntax/instructions.html#syntax-instr-i31}{\mathsf{i{\scriptstyle31}{.}get}}}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}i\scriptstyle31}}~i)~({\href{../syntax/instructions.html#syntax-instr-i31}{\mathsf{i{\scriptstyle31}{.}get}}}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{{{\href{../exec/numerics.html#op-extend}{\mathrm{extend}}}}_{31, 32}^{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}}{(i)}) \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}new}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}$ ${\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}$.
Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}~{\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$.
Let ${({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})^{n}}$ be ${\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}_0$.
Let $a$ be the length of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{structs}}$.
Assert: Due to validation, there are at least $n$ values on the top of the stack.
Pop the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ from the stack.
Let ${\mathit{si}}$ be the structure instance $\{ \begin{array}[t]{@{}l@{}}\href{../exec/runtime.html#syntax-structinst}{\mathsf{type}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x],\; \href{../exec/runtime.html#syntax-structinst}{\mathsf{fields}}~{{{\href{../exec/runtime.html#aux-packfield}{\mathrm{pack}}}}_{{\mathit{zt}}}({\href{../exec/runtime.html#syntax-val}{\mathit{val}}})^{n}} \}\end{array}$.
Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}struct}}~a)$ to the stack.
Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{structs}} \mathrel{{=}{\oplus}} {\mathit{si}}]$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~(\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}new}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{structs}} \mathrel{{=}{\oplus}} {\mathit{si}}] ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}struct}}~a) & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}~{({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})^{n}} \\ {\land}~ a = {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{structs}}|} \\ {\land}~ {\mathit{si}} = \{ \begin{array}[t]{@{}l@{}} \href{../exec/runtime.html#syntax-structinst}{\mathsf{type}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x],\; \href{../exec/runtime.html#syntax-structinst}{\mathsf{fields}}~{({{\href{../exec/runtime.html#aux-packfield}{\mathrm{pack}}}}_{{\mathit{zt}}}({\href{../exec/runtime.html#syntax-val}{\mathit{val}}}))^{n}} \}\end{array} \\ \end{array} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}new\_default}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}$ ${\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}$.
Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}~{\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$.
Let ${({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})^\ast}$ be ${\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}_0$.
Assert: Due to validation, for all ${\mathit{zt}}$ in ${{\mathit{zt}}^\ast}$, ${{\href{../exec/runtime.html#aux-default}{\mathrm{default}}}}_{{\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\mathit{zt}})}$ is defined.
Let ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ be ${{{\href{../exec/runtime.html#aux-default}{\mathrm{default}}}}_{{\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\mathit{zt}})}^\ast}$.
Assert: Due to validation, ${|{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}|} = {|{{\mathit{zt}}^\ast}|}$.
Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ to the stack.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}new}}~x)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}new\_default}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}new}}~x) & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}~{({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})^\ast} \\ {\land}~ ({{\href{../exec/runtime.html#aux-default}{\mathrm{default}}}}_{{\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\mathit{zt}})} = {\href{../exec/runtime.html#syntax-val}{\mathit{val}}})^\ast \\ \end{array} \\ \end{array}\end{split}\]

${\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x~i$¶

Let $z$ be the current state.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}struct}}$ ${\href{../exec/runtime.html#syntax-structaddr}{\mathit{structaddr}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}struct}}~a)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$.
2. If $i < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{structs}}{}[a]{.}\href{../exec/runtime.html#syntax-structinst}{\mathsf{fields}}|}$ and $a < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{structs}}|}$, then:
  1. Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}$ ${\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}$.
  2. Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}~{\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$.
  3. Let ${({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})^\ast}$ be ${\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}_0$.
  4. If $i < {|{{\mathit{zt}}^\ast}|}$, then:
    1. Push the value ${{{{\href{../exec/runtime.html#aux-unpackfield}{\mathrm{unpack}}}}_{{{\mathit{zt}}^\ast}{}[i]}^{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}}}{(z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{structs}}{}[a]{.}\href{../exec/runtime.html#syntax-structinst}{\mathsf{fields}}{}[i])}$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~({\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x~i) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}struct}}~a)~({\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x~i) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{{{\href{../exec/runtime.html#aux-unpackfield}{\mathrm{unpack}}}}_{{{\mathit{zt}}^\ast}{}[i]}^{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}}}{(z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{structs}}{}[a]{.}\href{../exec/runtime.html#syntax-structinst}{\mathsf{fields}}{}[i])} & \quad \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}~{({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})^\ast} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}set}}~x~i$¶

Let $z$ be the current state.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}struct}}$ ${\href{../exec/runtime.html#syntax-structaddr}{\mathit{structaddr}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}struct}}~a)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$.
2. Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}$ ${\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}$.
3. Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}~{\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$.
4. Let ${({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})^\ast}$ be ${\href{../syntax/types.html#syntax-structtype}{\mathit{structtype}}}_0$.
5. If $i < {|{{\mathit{zt}}^\ast}|}$, then:
  1. Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{structs}}{}[a]{.}\href{../exec/runtime.html#syntax-structinst}{\mathsf{fields}}{}[i] = {{\href{../exec/runtime.html#aux-packfield}{\mathrm{pack}}}}_{{{\mathit{zt}}^\ast}{}[i]}({\href{../exec/runtime.html#syntax-val}{\mathit{val}}})]$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}set}}~x~i) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z ; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}struct}}~a)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}set}}~x~i) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{structs}}{}[a]{.}\href{../exec/runtime.html#syntax-structinst}{\mathsf{fields}}{}[i] = {{\href{../exec/runtime.html#aux-packfield}{\mathrm{pack}}}}_{{{\mathit{zt}}^\ast}{}[i]}({\href{../exec/runtime.html#syntax-val}{\mathit{val}}})] ; \epsilon & \quad \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}~{({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})^\ast} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new}}~x$¶

Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ to the stack.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n) \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_default}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}$ ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}$.
Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~{\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$.
Let $({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})$ be the destructuring of ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0$.
Assert: Due to validation, ${{\href{../exec/runtime.html#aux-default}{\mathrm{default}}}}_{{\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\mathit{zt}})}$ is defined.
Let ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ be ${{\href{../exec/runtime.html#aux-default}{\mathrm{default}}}}_{{\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\mathit{zt}})}$.
Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ to the stack.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_default}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n) & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}) \\ {\land}~ {{\href{../exec/runtime.html#aux-default}{\mathrm{default}}}}_{{\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\mathit{zt}})} = {\href{../exec/runtime.html#syntax-val}{\mathit{val}}} \\ \end{array} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n$¶

Let $z$ be the current state.
Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}$ ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}$.
Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~{\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$.
Let $({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})$ be the destructuring of ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0$.
Let $a$ be the length of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}$.
Assert: Due to validation, there are at least $n$ values on the top of the stack.
Pop the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ from the stack.
Let ${\mathit{ai}}$ be the array instance $\{ \begin{array}[t]{@{}l@{}}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{type}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x],\; \href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}~{{{\href{../exec/runtime.html#aux-packfield}{\mathrm{pack}}}}_{{\mathit{zt}}}({\href{../exec/runtime.html#syntax-val}{\mathit{val}}})^{n}} \}\end{array}$.
Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ to the stack.
Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}} \mathrel{{=}{\oplus}} {\mathit{ai}}]$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}} \mathrel{{=}{\oplus}} {\mathit{ai}}] ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}) \\ {\land}~ a = {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}|} \land {\mathit{ai}} = \{ \begin{array}[t]{@{}l@{}} \href{../exec/runtime.html#syntax-arrayinst}{\mathsf{type}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x],\; \href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}~{({{\href{../exec/runtime.html#aux-packfield}{\mathrm{pack}}}}_{{\mathit{zt}}}({\href{../exec/runtime.html#syntax-val}{\mathit{val}}}))^{n}} \}\end{array} \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_data}}~x~y$¶

Let $z$ be the current state.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}$ ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}$.
Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~{\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$.
Let $({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})$ be the destructuring of ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0$.
If $i + n \cdot {|{\mathit{zt}}|} / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}|}$, then:
1. Trap.
Let ${{{\href{../syntax/values.html#syntax-byte}{\mathit{byte}}}^\ast}^\ast}$ be the result for which each ${{\href{../syntax/values.html#syntax-byte}{\mathit{byte}}}^\ast}$ has length ${|{\mathit{zt}}|} / 8$, and the concatenation of ${{{\href{../syntax/values.html#syntax-byte}{\mathit{byte}}}^\ast}^\ast}$ is $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}{}[i : n \cdot {|{\mathit{zt}}|} / 8]$.
Let ${c^{n}}$ be the result for which ${({{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\mathit{zt}}}({c^{n}}) = {{\href{../syntax/values.html#syntax-byte}{\mathit{byte}}}^\ast})^\ast}$.
Push the values ${{\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\mathit{zt}}){.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{\href{../exec/numerics.html#aux-unpacknum}{\mathrm{unpack}}}}_{{\mathit{zt}}}(c)^{n}}$ to the stack.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_data}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}) \\ {\land}~ i + n \cdot {|{\mathit{zt}}|} / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}|} \\ \end{array} } \\ & z ; (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_data}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {({\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\mathit{zt}}){.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{\href{../exec/numerics.html#aux-unpacknum}{\mathrm{unpack}}}}_{{\mathit{zt}}}(c))^{n}}~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}) \\ {\land}~ {\href{../syntax/conventions.html#notation-concat}{\bigoplus}}\, {{{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\mathit{zt}}}(c)^{n}} = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}{}[i : n \cdot {|{\mathit{zt}}|} / 8] \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_elem}}~x~y$¶

Let $z$ be the current state.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
If $i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}|}$, then:
1. Trap.
Let ${{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}^{n}}$ be $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}{}[i : n]$.
Push the values ${{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}^{n}}$ to the stack.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_elem}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}|} \\ & z ; (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_elem}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}^{n}}~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ {{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}^{n}} = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}{}[i : n] } \\ \end{array}\end{split}\]

${\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}$ ${\href{../exec/runtime.html#syntax-arrayaddr}{\mathit{arrayaddr}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$.
2. If $a < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}|}$ and $i \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|}$, then:
  1. Trap.
3. If $i < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|}$ and $a < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}|}$, then:
  1. Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}$ ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}$.
  2. Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~{\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$.
  3. Let $({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})$ be the destructuring of ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0$.
  4. Push the value ${{{{\href{../exec/runtime.html#aux-unpackfield}{\mathrm{unpack}}}}_{{\mathit{zt}}}^{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}}}{(z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}{}[i])}$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{{{\href{../exec/runtime.html#aux-unpackfield}{\mathrm{unpack}}}}_{{\mathit{zt}}}^{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}}}{(z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}{}[i])} & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}) } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}$ ${\href{../exec/runtime.html#syntax-arrayaddr}{\mathit{arrayaddr}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$.
2. If $a < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}|}$ and $i \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|}$, then:
  1. Trap.
3. Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}$ ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}$.
4. Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~{\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$.
5. Let $({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})$ be the destructuring of ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0$.
6. Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}{}[i] = {{\href{../exec/runtime.html#aux-packfield}{\mathrm{pack}}}}_{{\mathit{zt}}}({\href{../exec/runtime.html#syntax-val}{\mathit{val}}})]$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z ; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z ; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}{}[i] = {{\href{../exec/runtime.html#aux-packfield}{\mathrm{pack}}}}_{{\mathit{zt}}}({\href{../exec/runtime.html#syntax-val}{\mathit{val}}})] ; \epsilon & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}) } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}len}}$¶

Let $z$ be the current state.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}$ ${\href{../exec/runtime.html#syntax-arrayaddr}{\mathit{arrayaddr}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$.
2. If $a < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}|}$, then:
  1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|})$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}len}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}len}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|}) \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}fill}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}$ ${\href{../exec/runtime.html#syntax-arrayaddr}{\mathit{arrayaddr}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$.
2. If $a \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}|}$, then:
  1. Do nothing.
3. Else if $i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|}$, then:
  1. Trap.
4. If $n = 0$, then:
  1. Do nothing.
5. Else:
  1. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ to the stack.
  2. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ to the stack.
  3. Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.
  4. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x)$.
  5. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ to the stack.
  6. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)$ to the stack.
  7. Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.
  8. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)$ to the stack.
  9. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}fill}}~x)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}fill}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}fill}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}fill}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \quad \mbox{otherwise, if}~ n = 0 \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}fill}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x) \\ (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}fill}}~x) \end{array} & \quad \mbox{otherwise} \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2$¶

Let $z$ be the current state.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$ and ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is reference value, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$ and ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is reference value, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}$ ${\href{../exec/runtime.html#syntax-arrayaddr}{\mathit{arrayaddr}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$.
2. If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}$ ${\href{../exec/runtime.html#syntax-arrayaddr}{\mathit{arrayaddr}}}$, then:
  1. If $a_1 < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}|}$ and $i_1 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a_1]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|}$, then:
    1. Trap.
  2. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$.
  3. If $a_2 \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}|}$, then:
    1. Do nothing.
  4. Else if $i_2 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a_2]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|}$, then:
    1. Trap.
  5. If $n = 0$, then:
    1. Do nothing.
  6. Else:
    1. Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x_2]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}$ ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}$.
    2. Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~{\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x_2]$.
    3. Let $({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}_2)$ be the destructuring of ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0$.
    4. Let ${{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}$ be ${\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}({\mathit{zt}}_2)$.
    5. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)$ to the stack.
    6. If $i_1 \leq i_2$, then:
      1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)$ to the stack.
      2. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)$ to the stack.
      3. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)$ to the stack.
      4. Execute the instruction $({\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x_2)$.
      5. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x_1)$.
      6. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)$ to the stack.
      7. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + 1)$ to the stack.
      8. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)$ to the stack.
      9. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + 1)$ to the stack.
    7. Else:
      1. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + n - 1)$ to the stack.
      2. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)$ to the stack.
      3. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + n - 1)$ to the stack.
      4. Execute the instruction $({\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x_2)$.
      5. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x_1)$.
      6. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)$ to the stack.
      7. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)$ to the stack.
      8. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)$ to the stack.
      9. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)$ to the stack.
    8. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)$ to the stack.
    9. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}}_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}}_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{if}~ i_1 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a_1]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|} } \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{if}~ i_2 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a_2]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|} } \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{otherwise, if}~ n = 0 } \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1) \\ (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2) \\ ({\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x_2)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x_1) \\ (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + 1)~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + 1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2) \end{array} & & \\ \multicolumn{3}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}} \quad \begin{array}[t]{@{}l@{}} \mbox{otherwise, if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x_2] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}_2) \\ {\land}~ i_1 \leq i_2 \land {{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?} = {\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}({\mathit{zt}}_2) \\ \end{array} \\ \end{array} } \\ \end{array} } \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + n - 1) \\ (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + n - 1) \\ ({\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x_2)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x_1) \\ (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2) \end{array} & & \\ \multicolumn{3}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}} \quad \begin{array}[t]{@{}l@{}} \mbox{otherwise, if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x_2] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}_2) \\ {\land}~ {{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?} = {\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}({\mathit{zt}}_2) \\ \end{array} \\ \end{array} } \\ \end{array} } \\ \end{array}\end{split}\]

Where:

\[\begin{split}\begin{array}[t]{@{}lcl@{}l@{}} {\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}({\href{../syntax/types.html#syntax-consttype}{\mathit{consttype}}}) & = & \epsilon \\ {\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}({\href{../syntax/types.html#syntax-packtype}{\mathit{packtype}}}) & = & \href{../syntax/instructions.html#syntax-sx}{\mathsf{s}} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_data}}~x~y$¶

Let $z$ be the current state.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}$ ${\href{../exec/runtime.html#syntax-arrayaddr}{\mathit{arrayaddr}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$.
2. If $a < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}|}$ and $i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|}$, then:
  1. Trap.
3. If the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}$ ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}$, then:
  1. Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~{\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x]$.
  2. Let $({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}})$ be the destructuring of ${\href{../syntax/types.html#syntax-arraytype}{\mathit{arraytype}}}_0$.
  3. If $j + n \cdot {|{\mathit{zt}}|} / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}|}$, then:
    1. Trap.
  4. If $n = 0$, then:
    1. Do nothing.
  5. Else:
    1. Let $c$ be the result for which ${{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\mathit{zt}}}(c)$ $=$ $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}{}[j : {|{\mathit{zt}}|} / 8]$.
    2. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ to the stack.
    3. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ to the stack.
    4. Push the value ${\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\mathit{zt}}){.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{\href{../exec/numerics.html#aux-unpacknum}{\mathrm{unpack}}}}_{{\mathit{zt}}}(c)$ to the stack.
    5. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x)$.
    6. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ to the stack.
    7. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)$ to the stack.
    8. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j + {|{\mathit{zt}}|} / 8)$ to the stack.
    9. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)$ to the stack.
    10. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_data}}~x~y)$.
4. Else if $n = 0$, then:
  1. Do nothing.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_data}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_data}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{if}~ i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|} } \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_data}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}) \\ {\land}~ j + n \cdot {|{\mathit{zt}}|} / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}|} \\ \end{array} } \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_data}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{otherwise, if}~ n = 0 } \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_data}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\mathit{zt}}){.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{\href{../exec/numerics.html#aux-unpacknum}{\mathrm{unpack}}}}_{{\mathit{zt}}}(c))~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x) \\ (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j + {|{\mathit{zt}}|} / 8)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_data}}~x~y) \end{array} & & \\ \multicolumn{3}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}} \quad \begin{array}[t]{@{}l@{}} \mbox{otherwise, if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{types}}{}[x] \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~({\href{../syntax/types.html#syntax-mut}{\mathsf{mut}}^?}~{\mathit{zt}}) \\ {\land}~ {{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\mathit{zt}}}(c) = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}{}[j : {|{\mathit{zt}}|} / 8] \\ \end{array} \\ \end{array} } \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_elem}}~x~y$¶

Let $z$ be the current state.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}$ ${\href{../exec/runtime.html#syntax-arrayaddr}{\mathit{arrayaddr}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$.
2. If $a < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}|}$ and $i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|}$, then:
  1. Trap.
3. If $j + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}|}$, then:
  1. Trap.
4. If $n = 0$, then:
  1. Do nothing.
5. Else if $j < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}|}$, then:
  1. Let ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ be the reference value $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}{}[j]$.
  2. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ to the stack.
  3. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ to the stack.
  4. Push the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ to the stack.
  5. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x)$.
  6. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)$ to the stack.
  7. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)$ to the stack.
  8. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j + 1)$ to the stack.
  9. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)$ to the stack.
  10. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_elem}}~x~y)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_elem}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_elem}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{if}~ i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{arrays}}{}[a]{.}\href{../exec/runtime.html#syntax-arrayinst}{\mathsf{fields}}|} } \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_elem}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{if}~ j + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}|} } \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_elem}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{otherwise, if}~ n = 0 } \\ & z ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_elem}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x) \\ (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}array}}~a)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j + 1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_elem}}~x~y) \end{array} & & \\ \multicolumn{3}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}} \quad \mbox{otherwise, if}~ {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}{}[j] \\ \end{array} } \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-extern}{\mathsf{any{.}convert\_extern}}$¶

Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Push the value $(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~\href{../syntax/types.html#syntax-heaptype}{\mathsf{any}})$ to the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}extern}}$ ${\href{../exec/runtime.html#syntax-addrref}{\mathit{addrref}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}extern}}~{\href{../exec/runtime.html#syntax-addrref}{\mathit{addrref}}})$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$.
2. Push the value ${\href{../exec/runtime.html#syntax-addrref}{\mathit{addrref}}}$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~\href{../syntax/instructions.html#syntax-instr-extern}{\mathsf{any{.}convert\_extern}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~\href{../syntax/types.html#syntax-heaptype}{\mathsf{any}}) \\ & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}extern}}~{\href{../exec/runtime.html#syntax-addrref}{\mathit{addrref}}})~\href{../syntax/instructions.html#syntax-instr-extern}{\mathsf{any{.}convert\_extern}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-addrref}{\mathit{addrref}}} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-extern}{\mathsf{extern{.}convert\_any}}$¶

Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Push the value $(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~\href{../syntax/types.html#syntax-heaptype}{\mathsf{extern}})$ to the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is address value, then:
1. Let ${\href{../exec/runtime.html#syntax-addrref}{\mathit{addrref}}}$ be the instruction ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$.
2. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}extern}}~{\href{../exec/runtime.html#syntax-addrref}{\mathit{addrref}}})$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~\href{../syntax/instructions.html#syntax-instr-extern}{\mathsf{extern{.}convert\_any}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~\href{../syntax/types.html#syntax-heaptype}{\mathsf{extern}}) \\ & {\href{../exec/runtime.html#syntax-addrref}{\mathit{addrref}}}~\href{../syntax/instructions.html#syntax-instr-extern}{\mathsf{extern{.}convert\_any}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}extern}}~{\href{../exec/runtime.html#syntax-addrref}{\mathit{addrref}}}) \\ \end{array}\end{split}\]

Vector Instructions¶

Vector instructions that operate bitwise are handled as integer operations of respective bit width.

\[\begin{split}\begin{array}{lll@{\qquad}l} \mathit{op}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v}\scriptstyle\kern-0.1emN}}(i_1,\dots,i_k) &=& \href{../Step_pure/numerics.html#int-ops}{\mathrm{i}\mathit{op}}_N(i_1,\dots,i_k) \\ \end{array}\end{split}\]

Most other vector instructions are defined in terms of numeric operators that are applied lane-wise according to the given shape.

\[\begin{split}\begin{array}{llll} \mathit{op}_{t\mathsf{x}N}(n_1,\dots,n_k) &=& \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t\mathsf{x}N}(\href{../Step_pure/instructions.html#exec-instr-numeric}{\mathit{op}}_t(i_1,\dots,i_k)^\ast) & \qquad(\mathrel{\mbox{if}} i_1^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(n_1) \land \dots \land i_k^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(n_k) \\ \end{array}\end{split}\]

Note

For example, the result of instruction $\mathsf{i32x4}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}$ applied to operands $v_1, v_2$ invokes $\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}_{\mathsf{i32x4}}(v_1, v_2)$, which maps to $\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\mathsf{i32x4}}(\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{add}}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}}(i_1, i_2)^\ast)$, where $i_1^\ast$ and $i_2^\ast$ are sequences resulting from invoking $\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\mathsf{i32x4}}(v_1)$ and $\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\mathsf{i32x4}}(v_2)$ respectively.

For non-deterministic operators this definition is generalized to sets:

\[\begin{split}\begin{array}{lll} \mathit{op}_{t\mathsf{x}N}(n_1,\dots,n_k) &=& \{ \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{t\mathsf{x}N}(i^\ast) ~|~ i^\ast \in \Large\times\href{../Step_pure/instructions.html#exec-instr-numeric}{\mathit{op}}_t(i_1,\dots,i_k)^\ast \land i_1^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(n_1) \land \dots \land i_k^\ast = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{t\mathsf{x}N}(n_k) \} \\ \end{array}\end{split}\]

where $\Large\times \{x^\ast\}^N$ transforms a sequence of $N$ sets of values into a set of sequences of $N$ values by computing the set product:

\[\begin{array}{lll} \Large\times (S_1 \dots S_N) &=& \{ x_1 \dots x_N ~|~ x_1 \in S_1 \land \dots \land x_N \in S_N \} \end{array}\]

The remaining vector operators use individual definitions.

$\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c$¶

Push the value $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c$ to the stack.

Note

No formal reduction rule is required for this instruction, since $\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}$ instructions coincide with values.

$\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} {\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Assert: Due to validation, ${|{{\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}}}}{{}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}}(c_1)}|} > 0$.
Let $c$ be an element of ${{\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}}}}{{}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}}(c_1)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} {\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c \in {{\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}}}}{{}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}}(c_1)} \\ \end{array}\end{split}\]

$\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} {\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Assert: Due to validation, ${|{{\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}}}}{{}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}}(c_1, c_2)}|} > 0$.
Let $c$ be an element of ${{\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}}}}{{}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}}(c_1, c_2)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} {\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c \in {{\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}}}}{{}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}}(c_1, c_2)} \\ \end{array}\end{split}\]

$\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} {\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_3)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Assert: Due to validation, ${|{{\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}}}}{{}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}}(c_1, c_2, c_3)}|} > 0$.
Let $c$ be an element of ${{\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}}}}{{}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}}(c_1, c_2, c_3)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_3)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} {\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ c \in {{\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}}}}{{}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}}(c_1, c_2, c_3)} } \\ \end{array}\end{split}\]

$\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{any\_true}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{\href{../exec/numerics.html#op-ine}{\mathrm{ine}}}}_{{|\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}|}}(c_1, 0)$.
Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{any\_true}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {{\href{../exec/numerics.html#op-ine}{\mathrm{ine}}}}_{{|\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}|}}(c_1, 0) \\ \end{array}\end{split}\]

${\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
If ${{\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}}}{{}_{{\mathit{sh}}}(c_1)}$ is empty, then:
1. Trap.
Let $c$ be an element of ${{\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}}}{{}_{{\mathit{sh}}}(c_1)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c \in {{\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}}}{{}_{{\mathit{sh}}}(c_1)} \\ & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ {{\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}}}{{}_{{\mathit{sh}}}(c_1)} = \epsilon \\ \end{array}\end{split}\]

${\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
If ${{\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}}}{{}_{{\mathit{sh}}}(c_1, c_2)}$ is empty, then:
1. Trap.
Let $c$ be an element of ${{\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}}}{{}_{{\mathit{sh}}}(c_1, c_2)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c \in {{\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}}}{{}_{{\mathit{sh}}}(c_1, c_2)} \\ & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ {{\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}}}{{}_{{\mathit{sh}}}(c_1, c_2)} = \epsilon \\ \end{array}\end{split}\]

${\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vternop}{\mathit{vternop}}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_3)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
If ${{\href{../syntax/instructions.html#syntax-vternop}{\mathit{vternop}}}}{{}_{{\mathit{sh}}}(c_1, c_2, c_3)}$ is empty, then:
1. Trap.
Let $c$ be an element of ${{\href{../syntax/instructions.html#syntax-vternop}{\mathit{vternop}}}}{{}_{{\mathit{sh}}}(c_1, c_2, c_3)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_3)~({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vternop}{\mathit{vternop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c \in {{\href{../syntax/instructions.html#syntax-vternop}{\mathit{vternop}}}}{{}_{{\mathit{sh}}}(c_1, c_2, c_3)} \\ & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_3)~({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vternop}{\mathit{vternop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ {{\href{../syntax/instructions.html#syntax-vternop}{\mathit{vternop}}}}{{}_{{\mathit{sh}}}(c_1, c_2, c_3)} = \epsilon \\ \end{array}\end{split}\]

${\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vtestop}}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $i$ be ${{\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vtestop}}}}{{}_{{\mathit{sh}}}(c_1)}$.
Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vtestop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i) & \quad \mbox{if}~ i = {{\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vtestop}}}}{{}_{{\mathit{sh}}}(c_1)} \\ \end{array}\end{split}\]

${\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}}}}{{}_{{\mathit{sh}}}(c_1, c_2)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {{\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}}}}{{}_{{\mathit{sh}}}(c_1, c_2)} \\ \end{array}\end{split}\]

${\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vshiftop}{\mathit{vshiftop}}}$¶

Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{\href{../syntax/instructions.html#syntax-vshiftop}{\mathit{vshiftop}}}}{{}_{{\mathit{sh}}}}{(c_1, i)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vshiftop}{\mathit{vshiftop}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {{\href{../syntax/instructions.html#syntax-vshiftop}{\mathit{vshiftop}}}}{{}_{{\mathit{sh}}}}{(c_1, i)} \\ \end{array}\end{split}\]

${\mathit{sh}}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}}{{}_{{\mathit{sh}}}(c_1)}$.
Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{sh}}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}}{{}_{{\mathit{sh}}}(c_1)} \\ \end{array}\end{split}\]

${\mathit{sh}} {.} {\mathit{swizzlop}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{\mathit{swizzlop}}}{{}_{{\mathit{sh}}}(c_1, c_2)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({\mathit{sh}} {.} {\mathit{swizzlop}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {{\mathit{swizzlop}}}{{}_{{\mathit{sh}}}(c_1, c_2)} \\ \end{array}\end{split}\]

${\mathit{sh}}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~{i^\ast}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}}{{}_{{\mathit{sh}}}({i^\ast}, c_1, c_2)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({\mathit{sh}}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~{i^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}}{{}_{{\mathit{sh}}}({i^\ast}, c_1, c_2)} \\ \end{array}\end{split}\]

${{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}$¶

Assert: Due to validation, a value is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Assert: Due to validation, ${\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0 = {\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}})$.
Let $c$ be ${{{{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}^{{-1}}}}{({{{\href{../exec/numerics.html#aux-packnum}{\mathrm{pack}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}(c_1)^{M}})}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}){.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {{{{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}^{{-1}}}}{({{{\href{../exec/numerics.html#aux-packnum}{\mathrm{pack}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}(c_1)^{M}})} \\ \end{array}\end{split}\]

${{{\href{../syntax/instructions.html#syntax-lanetype}{\mathit{lanetype}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}'}^?}}~i$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
If ${{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}'}^?}$ is not defined and ${\href{../syntax/instructions.html#syntax-lanetype}{\mathit{lanetype}}}$ is number type, then:
1. Let ${\mathit{nt}}$ be the lane type ${\href{../syntax/instructions.html#syntax-lanetype}{\mathit{lanetype}}}$.
2. If $i < {|{{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\mathit{nt}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}(c_1)|}$, then:
  1. Let $c_2$ be ${{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\mathit{nt}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}(c_1){}[i]$.
  2. Push the value $({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ to the stack.
If ${\href{../syntax/instructions.html#syntax-lanetype}{\mathit{lanetype}}}$ is packed type, then:
1. Let ${\mathit{pt}}$ be the lane type ${\href{../syntax/instructions.html#syntax-lanetype}{\mathit{lanetype}}}$.
2. If ${{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}'}^?}$ is defined, then:
  1. Let ${\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}$ be ${{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}'}^?}$.
  2. If $i < {|{{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\mathit{pt}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}(c_1)|}$, then:
    1. Let $c_2$ be ${{{{\href{../exec/numerics.html#op-extend}{\mathrm{extend}}}}_{{|{\mathit{pt}}|}, 32}^{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}}{({{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\mathit{pt}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}(c_1){}[i])}$.
    2. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({{\mathit{nt}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}~i) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2) & \quad \mbox{if}~ c_2 = {{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\mathit{nt}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}(c_1){}[i] \\ & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({{{\mathit{pt}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{extract\_lane}}}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}~i) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2) & \quad \mbox{if}~ c_2 = {{{{\href{../exec/numerics.html#op-extend}{\mathrm{extend}}}}_{{|{\mathit{pt}}|}, 32}^{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}}{({{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\mathit{pt}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}(c_1){}[i])} \\ \end{array}\end{split}\]

${{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~i$¶

Assert: Due to validation, a value is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, ${\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0 = {\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}})$.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{{{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}^{{-1}}}}{({{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}(c_1){}[{}[i] = {{\href{../exec/numerics.html#aux-packnum}{\mathrm{pack}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}(c_2)])}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\href{../syntax/types.html#aux-unpack}{\mathrm{unpack}}}({\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}){.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~i) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{if}~ c = {{{{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}^{{-1}}}}{({{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}(c_1){}[{}[i] = {{\href{../exec/numerics.html#aux-packnum}{\mathrm{pack}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}(c_2)])} } \\ \end{array}\end{split}\]

${\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vextunop}{\mathit{vextunop}}}}{\mathsf{\_}}{{\mathit{sh}}_1}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{\href{../syntax/instructions.html#syntax-vextunop}{\mathit{vextunop}}}}{{}_{{\mathit{sh}}_1, {\mathit{sh}}_2}(c_1)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vextunop}{\mathit{vextunop}}}}{\mathsf{\_}}{{\mathit{sh}}_1}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ {{\href{../syntax/instructions.html#syntax-vextunop}{\mathit{vextunop}}}}{{}_{{\mathit{sh}}_1, {\mathit{sh}}_2}(c_1)} = c \\ \end{array}\end{split}\]

${\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vextbinop}{\mathit{vextbinop}}}}{\mathsf{\_}}{{\mathit{sh}}_1}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{\href{../syntax/instructions.html#syntax-vextbinop}{\mathit{vextbinop}}}}{{}_{{\mathit{sh}}_1, {\mathit{sh}}_2}(c_1, c_2)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vextbinop}{\mathit{vextbinop}}}}{\mathsf{\_}}{{\mathit{sh}}_1}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ {{\href{../syntax/instructions.html#syntax-vextbinop}{\mathit{vextbinop}}}}{{}_{{\mathit{sh}}_1, {\mathit{sh}}_2}(c_1, c_2)} = c \\ \end{array}\end{split}\]

${\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vextternop}{\mathit{vextternop}}}}{\mathsf{\_}}{{\mathit{sh}}_1}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_3)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{\href{../syntax/instructions.html#syntax-vextternop}{\mathit{vextternop}}}}{{}_{{\mathit{sh}}_1, {\mathit{sh}}_2}(c_1, c_2, c_3)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_3)~({\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vextternop}{\mathit{vextternop}}}}{\mathsf{\_}}{{\mathit{sh}}_1}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ {{\href{../syntax/instructions.html#syntax-vextternop}{\mathit{vextternop}}}}{{}_{{\mathit{sh}}_1, {\mathit{sh}}_2}(c_1, c_2, c_3)} = c \\ \end{array}\end{split}\]

${{\mathit{sh}}_2{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}}{\mathsf{\_}}{{\mathit{sh}}_1}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)$ from the stack.
Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}}{{{}_{{\mathit{sh}}_1, {\mathit{sh}}_2}^{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}}{(c_1, c_2)}$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_2)~({{\mathit{sh}}_2{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}}{\mathsf{\_}}{{\mathit{sh}}_1}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}}{{{}_{{\mathit{sh}}_1, {\mathit{sh}}_2}^{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}}{(c_1, c_2)} \\ \end{array}\end{split}\]

${\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-zero}{\mathit{zero}}}^?}}{\mathsf{\_}}{{\mathit{sh}}_1}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-half}{\mathit{half}}}^?}}$¶

Assert: Due to validation, a value of vector type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)$ from the stack.
Let $c$ be ${{\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}}}_{{\mathit{sh}}_1, {\mathit{sh}}_2}({\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}}, {{\href{../syntax/instructions.html#syntax-half}{\mathit{half}}}^?}, {{\href{../syntax/instructions.html#syntax-zero}{\mathit{zero}}}^?}, c_1)$.
Push the value $(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-zero}{\mathit{zero}}}^?}}{\mathsf{\_}}{{\mathit{sh}}_1}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-half}{\mathit{half}}}^?}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \quad \mbox{if}~ c = {{\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}}}_{{\mathit{sh}}_1, {\mathit{sh}}_2}({\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}}, {{\href{../syntax/instructions.html#syntax-half}{\mathit{half}}}^?}, {{\href{../syntax/instructions.html#syntax-zero}{\mathit{zero}}}^?}, c_1) \\ \end{array}\end{split}\]

Variable Instructions¶

$\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}get}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{locals}}{}[x]$ is defined.
Let ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ be $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{locals}}{}[x]$.
Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}get}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}} & \quad \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{locals}}{}[x] = {\href{../exec/runtime.html#syntax-val}{\mathit{val}}} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}set}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{locals}}{}[x] = {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}]$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}set}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{locals}}{}[x] = {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}] ; \epsilon \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}tee}}~x$¶

Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.
Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}set}}~x)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}tee}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}set}}~x) \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global{.}get}}~x$¶

Let $z$ be the current state.
Let ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ be the value $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}{}[x]{.}\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}}$.
Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global{.}get}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}} & \quad \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}{}[x]{.}\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}} = {\href{../exec/runtime.html#syntax-val}{\mathit{val}}} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global{.}set}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}{}[x]{.}\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}} = {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}]$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global{.}set}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{globals}}{}[x]{.}\href{../exec/runtime.html#syntax-globalinst}{\mathsf{value}} = {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}] ; \epsilon \\ \end{array}\end{split}\]

Table Instructions¶

$\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
If $i \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|}$, then:
1. Trap.
Push the value $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}{}[i]$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|} \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}{}[i] & \quad \mbox{if}~ i < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a reference value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ from the stack.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
If $i \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|}$, then:
1. Trap.
Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}{}[i] = {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}]$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z ; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|} \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}{}[i] = {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}] ; \epsilon & \quad \mbox{if}~ i < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}size}}~x$¶

Let $z$ be the current state.
Let $({\mathit{at}}~{\mathit{lim}}~{\mathit{rt}})$ be the destructuring of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}}$.
Let $n$ be the length of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}$.
Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}size}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n) & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|} = n \\ {\land}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{type}} = {\mathit{at}}~{\mathit{lim}}~{\mathit{rt}} \\ \end{array} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}grow}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a reference value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ from the stack.
Either:
1. Let ${\mathit{ti}}$ be the table instance ${\href{../exec/modules.html#grow-table}{\mathrm{growtable}}}(z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x], n, {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}})$.
2. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|})$ to the stack.
3. Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x] = {\mathit{ti}}]$.
Or:
1. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{{{\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}}}_{{|{\mathit{at}}|}}^{{-1}}}}{({-1})})$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}grow}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x] = {\mathit{ti}}] ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|}) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ {\mathit{ti}} = {\href{../exec/modules.html#grow-table}{\mathrm{growtable}}}(z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x], n, {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}) } \\ & z ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}grow}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{{{\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}}}_{{|{\mathit{at}}|}}^{{-1}}}}{({-1})}) \\ \end{array}\end{split}\]

Note

The $\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}grow}}$ instruction is non-deterministic. It may either succeed, returning the old table size $\mathit{sz}$, or fail, returning ${-1}$. Failure must occur if the referenced table instance has a maximum size defined that would be exceeded. However, failure can occur in other cases as well. In practice, the choice depends on the resources available to the embedder.

$\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}fill}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Assert: Due to validation, a value of number type ${\mathit{at}}$ is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
If $i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|}$, then:
1. Trap.
If $n = 0$, then:
1. Do nothing.
Else:
1. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ to the stack.
2. Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.
3. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x)$.
4. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)$ to the stack.
5. Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.
6. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)$ to the stack.
7. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}fill}}~x)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}fill}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|} \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}fill}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \quad \mbox{otherwise, if}~ n = 0 \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}fill}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x) \\ ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}fill}}~x) \end{array} & \quad \mbox{otherwise} \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}copy}}~x_{1'}~x_{2'}$¶

Let $z$ be the current state.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)$ from the stack.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)$ from the stack.
Let $x_1$ be the table index $x_{1'}$.
Let $x_2$ be the table index $x_{2'}$.
If $i_1 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x_1]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|}$, then:
1. Trap.
If $i_2 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x_2]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|}$, then:
1. Trap.
If $n = 0$, then:
1. Do nothing.
Else:
1. Let $x$ be the table index $x_{1'}$.
2. Let $y$ be the table index $x_{2'}$.
3. If $i_1 \leq i_2$, then:
  1. Push the value $({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)$ to the stack.
  2. Push the value $({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)$ to the stack.
  3. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~y)$.
  4. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x)$.
  5. Push the value $({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + 1)$ to the stack.
  6. Push the value $({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + 1)$ to the stack.
4. Else:
  1. Push the value $({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + n - 1)$ to the stack.
  2. Push the value $({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + n - 1)$ to the stack.
  3. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~y)$.
  4. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x)$.
  5. Push the value $({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)$ to the stack.
  6. Push the value $({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)$ to the stack.
5. Push the value $({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)$ to the stack.
6. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}copy}}~x~y)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{if}~ i_1 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x_1]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|} \lor i_2 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x_2]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|} } \\ & z ; ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}copy}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \quad \mbox{otherwise, if}~ n = 0 \\ & z ; ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}copy}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~y)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x) \\ ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + 1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + 1)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}copy}}~x~y) \end{array} & \quad \mbox{otherwise, if}~ i_1 \leq i_2 \\ \end{array} } \\ & z ; ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}copy}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + n - 1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + n - 1)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~y)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x) \\ ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}copy}}~x~y) \end{array} & \quad \mbox{otherwise} \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}init}}~x~y$¶

Let $z$ be the current state.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)$ from the stack.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
If $i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|}$, then:
1. Trap.
If $j + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}|}$, then:
1. Trap.
If $n = 0$, then:
1. Do nothing.
Else if $j < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}|}$, then:
1. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ to the stack.
2. Push the value $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}{}[j]$ to the stack.
3. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x)$.
4. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)$ to the stack.
5. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j + 1)$ to the stack.
6. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)$ to the stack.
7. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}init}}~x~y)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}init}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{if}~ i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tables}}{}[x]{.}\href{../exec/runtime.html#syntax-tableinst}{\mathsf{elem}}|} \lor j + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}|} } \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}init}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \quad \mbox{otherwise, if}~ n = 0 \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}init}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[y]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}}{}[j]~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x) \\ ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j + 1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}init}}~x~y) \end{array} & \quad \mbox{otherwise} \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem{.}drop}}~x$¶

Let $z$ be the current state.
Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[x]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}} = \epsilon]$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem{.}drop}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{elems}}{}[x]{.}\href{../exec/runtime.html#syntax-eleminst}{\mathsf{elem}} = \epsilon] ; \epsilon \\ \end{array}\end{split}\]

Memory Instructions¶

Note

The alignment $\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}$ in load and store instructions does not affect the semantics. It is a hint that the offset $\mathit{ea}$ at which the memory is accessed is intended to satisfy the property $\mathit{ea} \mathbin{\mathrm{mod}} 2^{\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{align}}} = 0$. A WebAssembly implementation can use this hint to optimize for the intended use. Unaligned access violating that property is still allowed and must succeed regardless of the annotation. However, it may be substantially slower on some hardware.

${{\mathit{nt}'}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{{\href{../syntax/instructions.html#syntax-loadop}{\mathit{loadop}}}^?}}~x~{\mathit{ao}}$¶

Let $z$ be the current state.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
If ${{\href{../syntax/instructions.html#syntax-loadop}{\mathit{loadop}}}^?}$ is not defined, then:
1. Let ${\mathit{nt}}$ be the number type ${\mathit{nt}'}$.
2. If $i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + {|{\mathit{nt}}|} / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|}$, then:
  1. Trap.
3. Let $c$ be the result for which ${{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\mathit{nt}}}(c)$ $=$ $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : {|{\mathit{nt}}|} / 8]$.
4. Push the value $({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ to the stack.
If ${\mathit{nt}'}$ is ${\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}$, then:
1. If ${{\href{../syntax/instructions.html#syntax-loadop}{\mathit{loadop}}}^?}$ is defined, then:
  1. Let ${\mathit{loadop\_{\scriptstyle 0}}}$ be ${{\href{../syntax/instructions.html#syntax-loadop}{\mathit{loadop}}}^?}$.
  2. Let ${n}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}$ be the destructuring of ${\mathit{loadop\_{\scriptstyle 0}}}$.
  3. If $i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + n / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|}$, then:
    1. Trap.
2. Let ${\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}$ be the number type ${\mathit{nt}'}$.
3. If ${{\href{../syntax/instructions.html#syntax-loadop}{\mathit{loadop}}}^?}$ is defined, then:
  1. Let ${\mathit{loadop\_{\scriptstyle 0}}}$ be ${{\href{../syntax/instructions.html#syntax-loadop}{\mathit{loadop}}}^?}$.
  2. Let ${n}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}$ be the destructuring of ${\mathit{loadop\_{\scriptstyle 0}}}$.
  3. Let $c$ be the result for which ${{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{n}}(c)$ $=$ $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : n / 8]$.
  4. Push the value $({\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{{{\href{../exec/numerics.html#op-extend}{\mathrm{extend}}}}_{n, {|{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}|}}^{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}}{(c)})$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + {|{\mathit{nt}}|} / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} } \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ {{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\mathit{nt}}}(c) = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : {|{\mathit{nt}}|} / 8] } \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{n}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + n / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} } \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{n}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{{{\href{../exec/numerics.html#op-extend}{\mathrm{extend}}}}_{n, {|{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}|}}^{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}}{(c)}) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ {{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{n}}(c) = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : n / 8] } \\ \end{array}\end{split}\]

$\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{M}\mathsf{x}N\_\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}$¶

Todo

(*) Rule and prose both not spliced.

Let $F$ be the current frame.
Assert: due to validation, $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]$ exists.
Let $a$ be the memory address $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]$.
Assert: due to validation, $S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]$ exists.
Let $\mathit{mem}$ be the memory instance $S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]$.
Assert: due to validation, a value of some address type $\mathit{at}$ is on the top of the stack.
Pop the value $\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i$ from the stack.
Let $\mathit{ea}$ be the integer $i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}$.
If $\mathit{ea} + M \cdot N /8$ is larger than the length of $\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}$, then:
1. Trap.
Let $b^\ast$ be the byte sequence $\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} M \cdot N /8]$.
Let $m_k$ be the integer for which $\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}\scriptstyle\kern-0.1emM}}(m_k) = b^\ast[k \cdot M/8 \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} M/8]$.
Let $W$ be the integer $M \cdot 2$.
Let $n_k$ be the result of computing $\href{../exec/numerics.html#op-extend}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{M,W}(m_k)$.
Let $c$ be the result of computing $\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\mathsf{i}W\mathsf{x}N}(n_0 \dots n_{N-1})$.
Push the value $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c$ to the stack.

\[\begin{split}~\\[-1ex] \begin{array}{l} \begin{array}{lcl@{\qquad}l} S; F; (\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{M}\mathsf{x}N\_\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) \end{array} \\ \qquad \begin{array}[t]{@{}r@{~}l@{}} (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ \wedge & \mathit{ea} + M \cdot N / 8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}| \\ \wedge & \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}\scriptstyle\kern-0.1emM}}(m_k) = S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}[\mathit{ea} + k \cdot M/8 \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} M/8]) \\ \wedge & W = M \cdot 2 \\ \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\mathsf{i}W\mathsf{x}N}(\href{../exec/numerics.html#op-extend}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{M,W}(m_0) \dots \href{../exec/numerics.html#op-extend}{\mathrm{extend}}^{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}_{M,W}(m_{N-1}))) \end{array} \\[1ex] \begin{array}{lcl@{\qquad}l} S; F; (\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{M}\mathsf{x}N\mathsf{\_}\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \end{array} \\ \qquad (\mathrel{\mbox{otherwise}}) \\ \end{array}\end{split}\]

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{M}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{K}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + M \cdot K / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{M}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{K}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ ({{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{M}}(j) = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + k \cdot M / 8 : M / 8])^{k<K} \\ {\land}~ c = {{{{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{K}}^{{-1}}}}{({{{{{\href{../exec/numerics.html#op-extend}{\mathrm{extend}}}}_{M, N}^{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}}}{(j)}^{K}})} \land N = M \cdot 2 \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_splat}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}$¶

Todo

(*) Rule and prose both not spliced.

Let $F$ be the current frame.
Assert: due to validation, $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]$ exists.
Let $a$ be the memory address $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]$.
Assert: due to validation, $S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]$ exists.
Let $\mathit{mem}$ be the memory instance $S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]$.
Assert: due to validation, a value of some address type $\mathit{at}$ is on the top of the stack.
Pop the value $\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i$ from the stack.
Let $\mathit{ea}$ be the integer $i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}$.
If $\mathit{ea} + N/8$ is larger than the length of $\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}$, then:
1. Trap.
Let $b^\ast$ be the byte sequence $\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]$.
Let $n$ be the integer for which $\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}\scriptstyle\kern-0.1emN}}(n) = b^\ast$.
Let $L$ be the integer $128 / N$.
Let $c$ be the result of computing $\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}\scriptstyle\kern-0.1emN}\mathsf{x}L}(n^L)$.
Push the value $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c$ to the stack.

\[\begin{split}~\\[-1ex] \begin{array}{l} \begin{array}{lcl@{\qquad}l} S; F; (\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_splat}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) \end{array} \\ \qquad \begin{array}[t]{@{}r@{~}l@{}} (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ \wedge & \mathit{ea} + N/8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}| \\ \wedge & \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}\scriptstyle\kern-0.1emN}}(n) = S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8] \\ \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}\scriptstyle\kern-0.1emN}\mathsf{x}L}(n^L)) \end{array} \\[1ex] \begin{array}{lcl@{\qquad}l} S; F; (\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_splat}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \end{array} \\ \qquad (\mathrel{\mbox{otherwise}}) \\ \end{array}\end{split}\]

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{N}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{splat}}}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + N / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{N}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{splat}}}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ {{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{N}}(j) = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : N / 8] \\ {\land}~ N = {|{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}|} \\ {\land}~ M = 128 / N \\ {\land}~ c = {{{{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}^{{-1}}}}{({j^{M}})} \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_zero}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}$¶

Todo

(*) Rule and prose both not spliced.

Let $F$ be the current frame.
Assert: due to validation, $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]$ exists.
Let $a$ be the memory address $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]$.
Assert: due to validation, $S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]$ exists.
Let $\mathit{mem}$ be the memory instance $S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]$.
Assert: due to validation, a value of some address type $\mathit{at}$ is on the top of the stack.
Pop the value $\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i$ from the stack.
Let $\mathit{ea}$ be the integer $i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}$.
If $\mathit{ea} + N/8$ is larger than the length of $\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}$, then:
1. Trap.
Let $b^\ast$ be the byte sequence $\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]$.
Let $n$ be the integer for which $\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}\scriptstyle\kern-0.1emN}}(n) = b^\ast$.
Let $c$ be the result of computing $\href{../exec/numerics.html#op-extend}{\mathrm{extend}^{\mathsf{u}}}_{N,128}(n)$.
Push the value $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c$ to the stack.

\[\begin{split}~\\[-1ex] \begin{array}{l} \begin{array}{lcl@{\qquad}l} S; F; (\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_zero}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) \end{array} \\ \qquad \begin{array}[t]{@{}r@{~}l@{}} (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ \wedge & \mathit{ea} + N/8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}| \\ \wedge & \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}\scriptstyle\kern-0.1emN}}(n) = S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]) \\ \wedge & c = \href{../exec/numerics.html#op-extend}{\mathrm{extend}^{\mathsf{u}}}_{N,128}(n) \end{array} \\[1ex] \begin{array}{lcl@{\qquad}l} S; F; (\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_zero}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \end{array} \\ \qquad (\mathrel{\mbox{otherwise}}) \\ \end{array}\end{split}\]

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{N}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{zero}}}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + N / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{N}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{zero}}}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ {{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{N}}(j) = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : N / 8] \\ {\land}~ c = {{{{\href{../exec/numerics.html#op-extend}{\mathrm{extend}}}}_{N, 128}^{\href{../syntax/instructions.html#syntax-sx}{\mathsf{u}}}}}{(j)} \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_lane}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~y$¶

Todo

(*) Rule and prose both not spliced.

Let $F$ be the current frame.
Assert: due to validation, $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]$ exists.
Let $a$ be the memory address $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]$.
Assert: due to validation, $S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]$ exists.
Let $\mathit{mem}$ be the memory instance $S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]$.
Assert: due to validation, a value of value type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~v$ from the stack.
Assert: due to validation, a value of some address type $\mathit{at}$ is on the top of the stack.
Pop the value $\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i$ from the stack.
Let $\mathit{ea}$ be the integer $i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}$.
If $\mathit{ea} + N/8$ is larger than the length of $\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}$, then:
1. Trap.
Let $b^\ast$ be the byte sequence $\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]$.
Let $r$ be the constant for which $\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}\scriptstyle\kern-0.1emN}}(r) = b^\ast$.
Let $L$ be $128 / N$.
Let $j^\ast$ be the result of computing $\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}\scriptstyle\kern-0.1emN}\mathsf{x}L}(v)$.
Let $c$ be the result of computing $\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}\scriptstyle\kern-0.1emN}\mathsf{x}L}(j^\ast \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} [y] = r)$.
Push the value $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c$ to the stack.

\[\begin{split}~\\[-1ex] \begin{array}{l} \begin{array}{lcl@{\qquad}l} S; F; (\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~v)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_lane}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~y) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S; F; (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) \end{array} \\ \qquad \begin{array}[t]{@{}r@{~}l@{}} (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ \wedge & \mathit{ea} + N/8 \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}| \\ \wedge & \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}\scriptstyle\kern-0.1emN}}(r) = S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]) \\ \wedge & L = 128/N \\ \wedge & c = \href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}^{-1}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}\scriptstyle\kern-0.1emN}\mathsf{x}L}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}\scriptstyle\kern-0.1emN}\mathsf{x}L}(v) \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} [y] = r)) \end{array} \\[1ex] \begin{array}{lcl@{\qquad}l} S; F; (\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~v)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}{N}\mathsf{\_lane}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~y) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \end{array} \\ \qquad (\mathrel{\mbox{otherwise}}) \\ \end{array}\end{split}\]

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{N}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{lane}}}~x~{\mathit{ao}}~j) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + N / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c_1)~({\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{N}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{lane}}}~x~{\mathit{ao}}~j) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ {{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{N}}(k) = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : N / 8] \\ {\land}~ N = {|{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}|} \\ {\land}~ M = {|\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}|} / N \\ {\land}~ c = {{{{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}^{{-1}}}}{({{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}(c_1){}[{}[j] = k])} \\ \end{array} } \\ \end{array}\end{split}\]

${{\mathit{nt}'}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{{{\href{../syntax/instructions.html#syntax-storeop}{\mathit{storeop}}}^?}}~x~{\mathit{ao}}$¶

Let $z$ be the current state.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{nt}'''}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ from the stack.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
Let ${\mathit{nt}}$ be the number type ${\mathit{nt}'''}$.
If $i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + {|{\mathit{nt}}|} / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|}$ and ${\mathit{nt}'} = {\mathit{nt}}$ and ${{\href{../syntax/instructions.html#syntax-storeop}{\mathit{storeop}}}^?}$ is not defined, then:
1. Trap.
If ${\mathit{nt}'} = {\mathit{nt}}$ and ${{\href{../syntax/instructions.html#syntax-storeop}{\mathit{storeop}}}^?}$ is not defined, then:
1. Let ${b^\ast}$ be ${{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\mathit{nt}}}(c)$.
2. Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : {|{\mathit{nt}}|} / 8] = {b^\ast}]$.
If ${\mathit{nt}'''}$ is ${\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}$, then:
1. Let ${\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}$ be the number type ${\mathit{nt}'''}$.
2. If ${\mathit{nt}'} = {\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}$ and ${{\href{../syntax/instructions.html#syntax-storeop}{\mathit{storeop}}}^?}$ is defined, then:
  1. Let $n$ be ${{\href{../syntax/instructions.html#syntax-storeop}{\mathit{storeop}}}^?}$.
  2. If $i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + n / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|}$, then:
    1. Trap.
  3. Let ${b^\ast}$ be ${{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{n}}({{\href{../exec/numerics.html#op-wrap}{\mathrm{wrap}}}}_{{|{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}|}, n}(c))$.
  4. Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : n / 8] = {b^\ast}]$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z ; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + {|{\mathit{nt}}|} / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} } \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~({\mathit{nt}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : {|{\mathit{nt}}|} / 8] = {b^\ast}] ; \epsilon & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ {b^\ast} = {{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\mathit{nt}}}(c) } \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~({{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{n}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z ; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + n / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} } \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~({\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~({{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{n}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : n / 8] = {b^\ast}] ; \epsilon & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ {b^\ast} = {{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{n}}({{\href{../exec/numerics.html#op-wrap}{\mathrm{wrap}}}}_{{|{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}|}, n}(c)) } \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z ; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + {|\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}|} / 8 > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}~x~{\mathit{ao}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : {|\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}|} / 8] = {b^\ast}] ; \epsilon & \quad \mbox{if}~ {b^\ast} = {{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}}(c) \\ \end{array}\end{split}\]

$\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}\mathsf{\_lane}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~y$¶

Todo

(*) Rule and prose both not spliced.

Let $F$ be the current frame.
Assert: due to validation, $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]$ exists.
Let $a$ be the memory address $F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]$.
Assert: due to validation, $S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]$ exists.
Let $\mathit{mem}$ be the memory instance $S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[a]$.
Assert: due to validation, a value of value type $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}$ is on the top of the stack.
Pop the value $\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c$ from the stack.
Assert: due to validation, a value of some address type $\mathit{at}$ is on the top of the stack.
Pop the value $\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i$ from the stack.
Let $\mathit{ea}$ be the integer $i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}}$.
If $\mathit{ea} + N/8$ is larger than the length of $\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}$, then:
1. Trap.
Let $L$ be $128/N$.
Let $j^\ast$ be the result of computing $\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}\scriptstyle\kern-0.1emN}\mathsf{x}L}(c)$.
Let $b^\ast$ be the result of computing $\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}\scriptstyle\kern-0.1emN}}(j^\ast[y])$.
Replace the bytes $\mathit{mem}.\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8]$ with $b^\ast$.

\[\begin{split}~\\[-1ex] \begin{array}{l} \begin{array}{lcl@{\qquad}l} S; F; (\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}\mathsf{\_lane}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~y) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S'; F; \epsilon \end{array} \\ \qquad \begin{array}[t]{@{}r@{~}l@{}} (\mathrel{\mbox{if}} & \mathit{ea} = i + \href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} \\ \wedge & \mathit{ea} + N \leq |S.\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}| \\ \wedge & L = 128/N \\ \wedge & S' = S \href{../syntax/conventions.html#notation-replace}{\mathrel{\mbox{with}}} \href{../exec/runtime.html#syntax-store}{\mathsf{mems}}[F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}.\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{mems}}[x]].\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}[\mathit{ea} \href{../syntax/conventions.html#notation-slice}{\mathrel{\mathbf{:}}} N/8] = \href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}_{\href{../syntax/values.html#syntax-int}{\mathit{i}\scriptstyle\kern-0.1emN}}(\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}_{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}\scriptstyle\kern-0.1emN}\mathsf{x}L}(c)[y])) \end{array} \\[1ex] \begin{array}{lcl@{\qquad}l} S; F; (\mathit{at}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}.\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}{N}\mathsf{\_lane}~x~\href{../syntax/instructions.html#syntax-memarg}{\mathit{memarg}}~y) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S; F; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \end{array} \\ \qquad (\mathrel{\mbox{otherwise}}) \\ \end{array}\end{split}\]

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~({\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{N}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{lane}}}~x~{\mathit{ao}}~j) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z ; \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} + N > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~({\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{N}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{lane}}}~x~{\mathit{ao}}~j) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}{}[i + {\mathit{ao}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{offset}} : N / 8] = {b^\ast}] ; \epsilon & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ N = {|{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}|} \\ {\land}~ M = 128 / N \\ {\land}~ {b^\ast} = {{\href{../exec/numerics.html#aux-bytes}{\mathrm{bytes}}}}_{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{N}}({{\href{../exec/numerics.html#aux-lanes}{\mathrm{lanes}}}}_{{{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}}(c){}[j]) \\ \end{array} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}size}}~x$¶

Let $z$ be the current state.
Let $({\mathit{at}}~{\mathit{lim}}~\href{../syntax/types.html#syntax-memtype}{\mathsf{page}})$ be the destructuring of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}}$.
Let $n \cdot 64 \, {\mathrm{Ki}}$ be the length of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}$.
Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}size}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n) & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ n \cdot 64 \, {\mathrm{Ki}} = {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} \\ {\land}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{type}} = {\mathit{at}}~{\mathit{lim}}~\href{../syntax/types.html#syntax-memtype}{\mathsf{page}} \\ \end{array} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}grow}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Either:
1. Let ${\mathit{mi}}$ be the memory instance ${\href{../exec/modules.html#grow-mem}{\mathrm{growmem}}}(z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x], n)$.
2. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} / (64 \, {\mathrm{Ki}}))$ to the stack.
3. Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x] = {\mathit{mi}}]$.
Or:
1. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{{{\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}}}_{{|{\mathit{at}}|}}^{{-1}}}}{({-1})})$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}grow}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x] = {\mathit{mi}}] ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} / 64 \, {\mathrm{Ki}}) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ {\mathit{mi}} = {\href{../exec/modules.html#grow-mem}{\mathrm{growmem}}}(z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x], n) } \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}grow}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~{{{{\href{../exec/numerics.html#aux-signed}{\mathrm{signed}}}}_{{|{\mathit{at}}|}}^{{-1}}}}{({-1})}) \\ \end{array}\end{split}\]

Note

The $\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}grow}}$ instruction is non-deterministic. It may either succeed, returning the old memory size $\mathit{sz}$, or fail, returning ${-1}$. Failure must occur if the referenced memory instance has a maximum size defined that would be exceeded. However, failure can occur in other cases as well. In practice, the choice depends on the resources available to the embedder.

$\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}fill}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Assert: Due to validation, a value of number type ${\mathit{at}}$ is on the top of the stack.
Pop the value $({\href{../syntax/types.html#syntax-numtype}{\mathit{numtype}}}_0{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
If $i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|}$, then:
1. Trap.
If $n = 0$, then:
1. Do nothing.
Else:
1. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ to the stack.
2. Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.
3. Execute the instruction $({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{8}~x)$.
4. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)$ to the stack.
5. Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.
6. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)$ to the stack.
7. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}fill}}~x)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}fill}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \quad \mbox{if}~ i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}fill}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \quad \mbox{otherwise, if}~ n = 0 \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}fill}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{8}~x) \\ ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)~{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}fill}}~x) \end{array} & \quad \mbox{otherwise} \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}copy}}~x_1~x_2$¶

Let $z$ be the current state.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)$ from the stack.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)$ from the stack.
If $i_1 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x_1]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|}$, then:
1. Trap.
If $i_2 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x_2]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|}$, then:
1. Trap.
If $n = 0$, then:
1. Do nothing.
Else:
1. If $i_1 \leq i_2$, then:
  1. Push the value $({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)$ to the stack.
  2. Push the value $({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)$ to the stack.
  3. Execute the instruction $({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{8}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-sx}{\mathsf{u}}}}~x_2)$.
  4. Execute the instruction $({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{8}~x_1)$.
  5. Push the value $({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + 1)$ to the stack.
  6. Push the value $({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + 1)$ to the stack.
2. Else:
  1. Push the value $({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + n - 1)$ to the stack.
  2. Push the value $({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + n - 1)$ to the stack.
  3. Execute the instruction $({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{8}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-sx}{\mathsf{u}}}}~x_2)$.
  4. Execute the instruction $({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{8}~x_1)$.
  5. Push the value $({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)$ to the stack.
  6. Push the value $({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)$ to the stack.
3. Push the value $({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)$ to the stack.
4. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}copy}}~x_1~x_2)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{if}~ i_1 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x_1]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} \lor i_2 + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x_2]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} } \\ & z ; ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \quad \mbox{otherwise, if}~ n = 0 \\ & z ; ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{8}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-sx}{\mathsf{u}}}}~x_2)~({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{8}~x_1) \\ ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + 1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + 1)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}copy}}~x_1~x_2) \end{array} & \quad \mbox{otherwise, if}~ i_1 \leq i_2 \\ \end{array} } \\ & z ; ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}copy}}~x_1~x_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1 + n - 1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2 + n - 1)~({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{8}{\mathsf{\_}}{\href{../syntax/instructions.html#syntax-sx}{\mathsf{u}}}}~x_2)~({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{8}~x_1) \\ ({\mathit{at}}_1{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_1)~({\mathit{at}}_2{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i_2)~({\mathit{at}'}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}copy}}~x_1~x_2) \end{array} & \quad \mbox{otherwise} \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}init}}~x~y$¶

Let $z$ be the current state.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)$ from the stack.
Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)$ from the stack.
Assert: Due to validation, a number value is on the top of the stack.
Pop the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
If $i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|}$, then:
1. Trap.
If $j + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}|}$, then:
1. Trap.
If $n = 0$, then:
1. Do nothing.
Else if $j < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}|}$, then:
1. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ to the stack.
2. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}{}[j])$ to the stack.
3. Execute the instruction $({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{8}~x)$.
4. Push the value $({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)$ to the stack.
5. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j + 1)$ to the stack.
6. Push the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)$ to the stack.
7. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}init}}~x~y)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}init}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} & \\ & \multicolumn{4}{@{}l@{}}{\quad \quad \mbox{if}~ i + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{mems}}{}[x]{.}\href{../exec/runtime.html#syntax-meminst}{\mathsf{bytes}}|} \lor j + n > {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}|} } \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}init}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \quad \mbox{otherwise, if}~ n = 0 \\ & z ; ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}init}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & & \\ & \multicolumn{4}{@{}l@{}}{\quad \begin{array}[t]{@{}l@{}l@{}} \begin{array}[t]{@{}l@{}} ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[y]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}}{}[j])~({\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{store}}}{8}~x) \\ ({\mathit{at}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i + 1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~j + 1)~(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~n - 1)~(\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{memory{.}init}}~x~y) \end{array} & \quad \mbox{otherwise} \\ \end{array} } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data{.}drop}}~x$¶

Let $z$ be the current state.
Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[x]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}} = \epsilon]$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{data{.}drop}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{datas}}{}[x]{.}\href{../exec/runtime.html#syntax-datainst}{\mathsf{bytes}} = \epsilon] ; \epsilon \\ \end{array}\end{split}\]

Control Instructions¶

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}$¶

Let $z$ be the current state.
Let ${t_1^{m}}~\href{../syntax/types.html#syntax-functype}{\rightarrow}~{t_2^{n}}$ be the destructuring of ${{\href{../exec/runtime.html#aux-blocktype}{\mathrm{instrtype}}}}_{z}({\mathit{bt}})$.
Assert: Due to validation, there are at least $m$ values on the top of the stack.
Pop the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}$ from the stack.
Let L be the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ whose arity is $n$ and whose continuation is the end of the block.
Enter the block ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}$ with the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ L.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({{\href{../exec/runtime.html#syntax-label}{\mathsf{label}}}_{n}}{\{ \epsilon \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \quad \mbox{if}~ {{\href{../exec/runtime.html#aux-blocktype}{\mathrm{instrtype}}}}_{z}({\mathit{bt}}) = {t_1^{m}} \href{../syntax/types.html#syntax-functype}{\rightarrow} {t_2^{n}} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}$¶

Let $z$ be the current state.
Let ${t_1^{m}}~\href{../syntax/types.html#syntax-functype}{\rightarrow}~{t_2^{n}}$ be the destructuring of ${{\href{../exec/runtime.html#aux-blocktype}{\mathrm{instrtype}}}}_{z}({\mathit{bt}})$.
Assert: Due to validation, there are at least $m$ values on the top of the stack.
Pop the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}$ from the stack.
Let L be the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ whose arity is $m$ and whose continuation is the start of the block.
Enter the block ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}$ with the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ L.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({{\href{../exec/runtime.html#syntax-label}{\mathsf{label}}}_{m}}{\{ \href{../syntax/instructions.html#syntax-instr-control}{\mathsf{loop}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast} \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \quad \mbox{if}~ {{\href{../exec/runtime.html#aux-blocktype}{\mathrm{instrtype}}}}_{z}({\mathit{bt}}) = {t_1^{m}} \href{../syntax/types.html#syntax-functype}{\rightarrow} {t_2^{n}} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}_1^\ast}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}_2^\ast}$¶

Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ from the stack.
If $c \neq 0$, then:
1. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}_1^\ast})$.
Else:
1. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}_2^\ast})$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}_1^\ast}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}_2^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}_1^\ast}) & \quad \mbox{if}~ c \neq 0 \\ & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{if}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}_1^\ast}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{else}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}_2^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{block}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}_2^\ast}) & \quad \mbox{if}~ c = 0 \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l$¶

If the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$, then:
1. Let L be the topmost $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$.
2. Let $n$ be the arity of L
3. If $l = 0$, then:
  1. Assert: Due to validation, there are at least $n$ values on the top of the stack.
  2. Pop the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ from the stack.
  3. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}^\ast}$ from the top of the stack.
  4. Pop the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ L from the stack.
  5. Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ to the stack.
  6. Jump to the continuation of L.
4. Else:
  1. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ from the top of the stack.
  2. If $l > 0$, then:
    1. Pop the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ L from the stack.
    2. Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ to the stack.
    3. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l - 1)$.
Else if the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$, then:
1. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ from the top of the stack.
2. Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
3. Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ to the stack.
4. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({{\href{../exec/runtime.html#syntax-label}{\mathsf{label}}}_{n}}{\{ {{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'}^\ast} \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}^\ast}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'}^\ast} & \quad \mbox{if}~ l = 0 \\ & ({{\href{../exec/runtime.html#syntax-label}{\mathsf{label}}}_{n}}{\{ {{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'}^\ast} \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l - 1) & \quad \mbox{if}~ l > 0 \\ & ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ {{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}^\ast} \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l$¶

Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)$ from the stack.
If $c \neq 0$, then:
1. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.
Else:
1. Do nothing.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) & \quad \mbox{if}~ c \neq 0 \\ & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_if}}~l) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \quad \mbox{if}~ c = 0 \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~{l^\ast}~{l'}$¶

Assert: Due to validation, a value of number type $\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}$ is on the top of the stack.
Pop the value $(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)$ from the stack.
If $i < {|{l^\ast}|}$, then:
1. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~{l^\ast}{}[i])$.
Else:
1. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~{l'})$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~{l^\ast}~{l'}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~{l^\ast}{}[i]) & \quad \mbox{if}~ i < {|{l^\ast}|} \\ & (\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~i)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_table}}~{l^\ast}~{l'}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~{l'}) & \quad \mbox{if}~ i \geq {|{l^\ast}|} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_null}}~l$¶

Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.
Else:
1. Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_null}}~l) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) & \quad \mbox{if}~ {\href{../exec/runtime.html#syntax-val}{\mathit{val}}} = \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}} \\ & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_null}}~l) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}} & \quad \mbox{otherwise} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_non\_null}}~l$¶

Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Do nothing.
Else:
1. Push the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ to the stack.
2. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_non\_null}}~l) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \epsilon & \quad \mbox{if}~ {\href{../exec/runtime.html#syntax-val}{\mathit{val}}} = \href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}} \\ & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_non\_null}}~l) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-val}{\mathit{val}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) & \quad \mbox{otherwise} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_cast}}~l~{\mathit{rt}}_1~{\mathit{rt}}_2$¶

Let F be the topmost $\mathsf{frame}$.
Assert: Due to validation, a reference value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ from the stack.
Let ${\mathit{rt}}$ be the type of ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$.
Push the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ to the stack.
If ${\mathit{rt}}$ matches ${{\href{../exec/types.html#type-inst}{\mathrm{clos}}}}_{f{.}\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}({\mathit{rt}}_2)$, then:
1. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.
Else:
1. Do nothing.

Todo

(9) Need to handle RulePr s |- ref : rt properly in prose instead of $ref_type_of below is the official specification

Let $F$ be the current frame.
Let $\mathit{rt}'_2$ be the reference type $\href{../exec/types.html#type-inst}{\mathrm{clos}}_{F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}(\mathit{rt}_2)$.
Assert: due to validation, $\mathit{rt}'_2$ is closed.
Assert: due to validation, a reference value is on the top of the stack.
Pop the value $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$ from the stack.
Assert: due to validation, the reference value is valid with some reference type.
Let $\mathit{rt}$ be the reference type of $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$.
Push the value $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$ back to the stack.
If the reference type $\mathit{rt}$ matches $\mathit{rt}'_2$, then:
1. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & s ; f ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_cast}}~l~{\mathit{rt}}_1~{\mathit{rt}}_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ s \href{../exec/values.html#valid-ref}{\vdash} {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} : {\mathit{rt}} \\ {\land}~ \{ \begin{array}[t]{@{}l@{}} \}\end{array} \href{../valid/matching.html#match-reftype}{\vdash} {\mathit{rt}} \href{../valid/matching.html#match-reftype}{\leq} {{\href{../exec/types.html#type-inst}{\mathrm{clos}}}}_{f{.}\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}({\mathit{rt}}_2) \\ \end{array} \\ & s ; f ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_cast}}~l~{\mathit{rt}}_1~{\mathit{rt}}_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} & \quad \mbox{otherwise} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_cast\_fail}}~l~{\mathit{rt}}_1~{\mathit{rt}}_2$¶

Let F be the topmost $\mathsf{frame}$.
Assert: Due to validation, a reference value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ from the stack.
Let ${\mathit{rt}}$ be the type of ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$.
Push the value ${\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}$ to the stack.
If ${\mathit{rt}}$ matches ${{\href{../exec/types.html#type-inst}{\mathrm{clos}}}}_{f{.}\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}({\mathit{rt}}_2)$, then:
1. Do nothing.
Else:
1. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.

Todo

(9) Need to handle RulePr s |- ref : rt properly in prose instead of $ref_type_of below is the official specification

Let $F$ be the current frame.
Let $\mathit{rt}'_2$ be the reference type $\href{../exec/types.html#type-inst}{\mathrm{clos}}_{F.\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}(\mathit{rt}_2)$.
Assert: due to validation, $\mathit{rt}'_2$ is closed.
Assert: due to validation, a reference value is on the top of the stack.
Pop the value $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$ from the stack.
Assert: due to validation, the reference value is valid with some reference type.
Let $\mathit{rt}$ be the reference type of $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$.
Push the value $\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}$ back to the stack.
If the reference type $\mathit{rt}$ does not match $\mathit{rt}'_2$, then:
1. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & s ; f ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_cast\_fail}}~l~{\mathit{rt}}_1~{\mathit{rt}}_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ s \href{../exec/values.html#valid-ref}{\vdash} {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}} : {\mathit{rt}} \\ {\land}~ \{ \begin{array}[t]{@{}l@{}} \}\end{array} \href{../valid/matching.html#match-reftype}{\vdash} {\mathit{rt}} \href{../valid/matching.html#match-reftype}{\leq} {{\href{../exec/types.html#type-inst}{\mathrm{clos}}}}_{f{.}\href{../exec/runtime.html#syntax-frame}{\mathsf{module}}}({\mathit{rt}}_2) \\ \end{array} \\ & s ; f ; {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br\_on\_cast\_fail}}~l~{\mathit{rt}}_1~{\mathit{rt}}_2) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {\href{../exec/runtime.html#syntax-ref}{\mathit{ref}}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) & \quad \mbox{otherwise} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}$¶

If the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}$, then:
1. Let F be the topmost $\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}$.
2. Let $n$ be the arity of F
3. Assert: Due to validation, there are at least $n$ values on the top of the stack.
4. Pop the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ from the stack.
5. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}^\ast}$ from the top of the stack.
6. Pop the $\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}$ F from the stack.
7. Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ to the stack.
Else if the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$, then:
1. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ from the top of the stack.
2. Pop the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ L from the stack.
3. Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ to the stack.
4. Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}$.
Else:
1. If the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$, then:
  1. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ from the top of the stack.
  2. Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
  3. Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ to the stack.
  4. Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({{\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}}_{n}}{\{ f \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}^\ast}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}} \\ & ({{\href{../exec/runtime.html#syntax-label}{\mathsf{label}}}_{n}}{\{ {{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'}^\ast} \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}} \\ & ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ {{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}^\ast} \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, $x < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{module}}{.}\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcs}}|}$.
Let $a$ be the address $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{module}}{.}\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcs}}{}[x]$.
Assert: Due to validation, $a < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}|}$.
Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a)$ to the stack.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_ref}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}{}[a]{.}\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}})$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_ref}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}{}[a]{.}\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}) & \quad \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{module}}{.}\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcs}}{}[x] = a \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_ref}}~x$¶

Todo

(*) Prose not spliced, for the prose merges the two cases of null and non-null references.

Assert: due to validation, a null or function reference is on the top of the stack.
Pop the reference value $r$ from the stack.
If $r$ is $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~\mathit{ht}$, then:
1. Trap.
Assert: due to validation, $r$ is a function reference.
Let $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a$ be the reference $r$.
Invoke the function instance at address $a$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_ref}}~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ \end{array}\end{split}\]

Note

The formal rule for calling a non-null function reference is described below.

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}~x~y$¶

Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~x)$.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}cast}}~(\href{../syntax/types.html#syntax-reftype}{\mathsf{ref}}~\mathsf{null}~y))$.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_ref}}~y)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_indirect}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~x)~(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}cast}}~(\href{../syntax/types.html#syntax-reftype}{\mathsf{ref}}~\mathsf{null}~y))~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_ref}}~y) \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, $x < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{module}}{.}\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcs}}|}$.
Let $a$ be the address $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{module}}{.}\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcs}}{}[x]$.
Assert: Due to validation, $a < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}|}$.
Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a)$ to the stack.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}{}[a]{.}\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}})$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}{}[a]{.}\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}) & \quad \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{module}}{.}\href{../exec/runtime.html#syntax-moduleinst}{\mathsf{funcs}}{}[x] = a \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~x$¶

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y$¶

Let $z$ be the current state.
If the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$, then:
1. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ from the top of the stack.
2. Pop the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ L from the stack.
3. Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ to the stack.
4. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y)$.
Else if the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$, then:
1. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ from the top of the stack.
2. Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
3. Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ to the stack.
4. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y)$.
Else:
1. If the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}$, then:
  1. Assert: Due to validation, a value is on the top of the stack.
  2. Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}''}$ from the stack.
  3. If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}''}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
    1. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ from the top of the stack.
    2. Pop the $\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}$ F from the stack.
    3. Trap.
  4. If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}''}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}$ ${\href{../exec/runtime.html#syntax-funcaddr}{\mathit{funcaddr}}}$, then:
    1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}''}$.
    2. If $a < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}|}$, then:
      1. Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}{}[a]{.}\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{func}}$ ${\href{../syntax/types.html#syntax-functype}{\mathit{functype}}}$.
      2. Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~{\href{../syntax/types.html#syntax-functype}{\mathit{functype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}{}[a]{.}\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}$.
      3. Let ${t_1^{n}}~\href{../syntax/types.html#syntax-functype}{\rightarrow}~{t_2^{m}}$ be the destructuring of ${\href{../syntax/types.html#syntax-functype}{\mathit{functype}}}_0$.
      4. Assert: Due to validation, there are at least $n$ values on the top of the stack.
      5. Pop the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ from the stack.
      6. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}^\ast}$ from the top of the stack.
      7. Pop the $\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}$ F from the stack.
      8. Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ to the stack.
      9. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a)$ to the stack.
      10. Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_ref}}~y)$.

Todo

(*) Prose not spliced, Sphinx cannot build the document with deeply nested ordered list. (mainly caused by spurious conditions that should be assertions)

Assert: due to validation, a function reference is on the top of the stack.
Pop the reference value $r$ from the stack.
If $r$ is $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~\mathit{ht}$, then:
1. Trap.
Assert: due to validation, $r$ is a function reference.
Let $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a$ be the reference $r$.
Tail-invoke the function instance at address $a$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; ({{\href{../exec/runtime.html#syntax-label}{\mathsf{label}}}_{k}}{\{ {{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'}^\ast} \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y)~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y) \\ & z ; ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{k}}{\{ {{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}^\ast} \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y)~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y) \\ & z ; ({{\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}}_{k}}{\{ f \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y)~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\ & z ; ({{\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}}_{k}}{\{ f \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}^\ast}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y)~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_ref}}~y) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}{}[a]{.}\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}} \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~({t_1^{n}} \href{../syntax/types.html#syntax-functype}{\rightarrow} {t_2^{m}}) } \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_indirect}}~x~y$¶

Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~x)$.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}cast}}~(\href{../syntax/types.html#syntax-reftype}{\mathsf{ref}}~\mathsf{null}~y))$.
Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y)$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_indirect}}~x~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~x)~(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}cast}}~(\href{../syntax/types.html#syntax-reftype}{\mathsf{ref}}~\mathsf{null}~y))~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return\_call\_ref}}~y) \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw}}~x$¶

Let $z$ be the current state.
Assert: Due to validation, $x < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}|}$.
Assert: Due to validation, the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}{}[x]{.}\href{../exec/runtime.html#syntax-taginst}{\mathsf{type}}$ is some $\href{../syntax/types.html#syntax-comptype}{\mathsf{func}}$ ${\href{../syntax/types.html#syntax-functype}{\mathit{functype}}}$.
Let $(\href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~{\href{../syntax/types.html#syntax-functype}{\mathit{functype}}}_0)$ be the destructuring of the expansion of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}{}[x]{.}\href{../exec/runtime.html#syntax-taginst}{\mathsf{type}}$.
Let ${t^{n}}~\href{../syntax/types.html#syntax-functype}{\rightarrow}~{\href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}}_1$ be the destructuring of ${\href{../syntax/types.html#syntax-functype}{\mathit{functype}}}_0$.
Assert: Due to validation, ${\href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}}}_1 = \epsilon$.
Let $a$ be the length of $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}}$.
Assert: Due to validation, there are at least $n$ values on the top of the stack.
Pop the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}$ from the stack.
Let ${\mathit{exn}}$ be the exception instance $\{ \begin{array}[t]{@{}l@{}}\href{../exec/runtime.html#syntax-exninst}{\mathsf{tag}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}{}[x],\; \href{../exec/runtime.html#syntax-exninst}{\mathsf{fields}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}} \}\end{array}$.
Perform $z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}} \mathrel{{=}{\oplus}} {\mathit{exn}}]$.
Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw}}~x) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & z{}[{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}} \mathrel{{=}{\oplus}} {\mathit{exn}}] ; (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}} & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}{}[x]{.}\href{../exec/runtime.html#syntax-taginst}{\mathsf{type}} \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~({t^{n}} \href{../syntax/types.html#syntax-functype}{\rightarrow} \epsilon) \\ {\land}~ a = {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}}|} \\ {\land}~ {\mathit{exn}} = \{ \begin{array}[t]{@{}l@{}} \href{../exec/runtime.html#syntax-exninst}{\mathsf{tag}}~z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}{}[x],\; \href{../exec/runtime.html#syntax-exninst}{\mathsf{fields}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}} \}\end{array} \\ \end{array} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$¶

Let $z$ be the current state.
Assert: Due to validation, a value is on the top of the stack.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ from the stack.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is some $\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}$ ${\href{../syntax/types.html#syntax-heaptype}{\mathit{heaptype}}}$, then:
1. Trap.
If ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ is some $\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}$ ${\href{../exec/runtime.html#syntax-exnaddr}{\mathit{exnaddr}}}$, then:
1. Let $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ be the destructuring of ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$.
2. Pop all values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ from the top of the stack.
3. If ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast} \neq \epsilon$, then:
  1. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
  2. Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$.
4. Else if the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$, then:
  1. Pop the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ L from the stack.
  2. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
  3. Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$.
5. Else:
  1. If the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}$, then:
    1. Pop the $\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}$ F from the stack.
    2. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
    3. Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$.
  2. Else if not the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$, then:
    1. Throw the exception ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ as a result.
  3. Else:
    1. Let H be the topmost $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$.
    2. Let $n$ be the arity of H
    3. Let ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}''}^\ast}$ be the catch handler of H
    4. If ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}''}^\ast} = \epsilon$, then:
      1. Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
      2. Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
      3. Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$.
    5. Else if $a \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}}|}$, then:
      1. Let ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$ be ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}''}^\ast}$.
      2. If ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$ is some $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_all}}$ ${\href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}}}$, then:
        
        Let $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_all}}~l)$ be the destructuring of ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$.
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.
      3. Else if ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$ is not some $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_all\_ref}}$ ${\href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}}}$, then:
        
        Let ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$ be ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}''}^\ast}$.
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Let H be the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ whose arity is $n$ and whose catch handler is ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$.
        
        Push the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H.
        
        Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
        
        Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$.
      4. Else:
        
        Let $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_all\_ref}}~l)$ be the destructuring of ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$.
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
        
        Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.
    6. Else:
      1. Let ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ be $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}}{}[a]{.}\href{../exec/runtime.html#syntax-exninst}{\mathsf{fields}}$.
      2. Let ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$ be ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}''}^\ast}$.
      3. If ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$ is some $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch}}$ ${\href{../syntax/modules.html#syntax-tagidx}{\mathit{tagidx}}}$ ${\href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}}}$, then:
        
        Let $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch}}~x~l)$ be the destructuring of ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$.
        
        If $x < {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}|}$ and $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}}{}[a]{.}\href{../exec/runtime.html#syntax-exninst}{\mathsf{tag}} = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}{}[x]$, then:
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ to the stack.
        
        Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.
        
        Else:
        
        Let ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$ be ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}''}^\ast}$.
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Let H be the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ whose arity is $n$ and whose catch handler is ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$.
        
        Push the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H.
        
        Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
        
        Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$.
      4. Else if ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$ is some $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_ref}}$ ${\href{../syntax/modules.html#syntax-tagidx}{\mathit{tagidx}}}$ ${\href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}}}$, then:
        
        Let $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_ref}}~x~l)$ be the destructuring of ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$.
        
        If $x \geq {|z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}|}$, then:
        
        Let ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$ be ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}''}^\ast}$.
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Let H be the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ whose arity is $n$ and whose catch handler is ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$.
        
        Push the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H.
        
        Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
        
        Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$.
        
        Else if $z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}}{}[a]{.}\href{../exec/runtime.html#syntax-exninst}{\mathsf{tag}} \neq z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}{}[x]$, then:
        
        Let ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$ be ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}''}^\ast}$.
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Let H be the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ whose arity is $n$ and whose catch handler is ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$.
        
        Push the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H.
        
        Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
        
        Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$.
        
        Else:
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Push the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}$ to the stack.
        
        Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
        
        Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.
      5. Else:
        
        If ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$ is some $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_all}}$ ${\href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}}}$, then:
        
        Let $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_all}}~l)$ be the destructuring of ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$.
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.
        
        Else if ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$ is not some $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_all\_ref}}$ ${\href{../syntax/modules.html#syntax-labelidx}{\mathit{labelidx}}}$, then:
        
        Let ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$ be ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}''}^\ast}$.
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Let H be the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ whose arity is $n$ and whose catch handler is ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast}$.
        
        Push the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H.
        
        Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
        
        Execute the instruction $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}$.
        
        Else:
        
        Let $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_all\_ref}}~l)$ be the destructuring of ${\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}_0$.
        
        Pop the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H from the stack.
        
        Push the value $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)$ to the stack.
        
        Execute the instruction $(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l)$.
Else if not the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ and not the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}$ and not the first non-value entry of the stack is a $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$, then:
1. Throw the exception ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}'}$ as a result.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; (\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~{\mathit{ht}})~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & \href{../exec/runtime.html#syntax-trap}{\mathsf{trap}} \\[0.8ex] & z ; {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}} & \quad \mbox{if}~ {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast} \neq \epsilon \lor {{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast} \neq \epsilon \\[0.8ex] & z ; ({{\href{../exec/runtime.html#syntax-label}{\mathsf{label}}}_{n}}{\{ {{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}'}^\ast} \}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}} \\[0.8ex] & z ; ({{\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}}_{n}}{\{ f \}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}} \\[0.8ex] & z ; ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ \epsilon \}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}} \\[0.8ex] & z ; ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch}}~x~l)~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast} \}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}}{}[a]{.}\href{../exec/runtime.html#syntax-exninst}{\mathsf{tag}} = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}{}[x] \\ {\land}~ {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast} = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}}{}[a]{.}\href{../exec/runtime.html#syntax-exninst}{\mathsf{fields}} \\ \end{array} \\[0.8ex] & z ; ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_ref}}~x~l)~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast} \}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) & \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}}{}[a]{.}\href{../exec/runtime.html#syntax-exninst}{\mathsf{tag}} = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{tags}}{}[x] \\ {\land}~ {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast} = z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{exns}}{}[a]{.}\href{../exec/runtime.html#syntax-exninst}{\mathsf{fields}} \\ \end{array} \\[0.8ex] & z ; ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_all}}~l)~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast} \}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) \\[0.8ex] & z ; ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ (\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{catch\_all\_ref}}~l)~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast} \}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & (\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{br}}~l) \\[0.8ex] & z ; ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ {\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast} \}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ {{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}'}^\ast} \}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}exn}}~a)~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{throw\_ref}}) & \quad \mbox{otherwise} \\ \end{array}\end{split}\]

$\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{try\_table}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}^\ast}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}$¶

Let $z$ be the current state.
Let ${t_1^{m}}~\href{../syntax/types.html#syntax-functype}{\rightarrow}~{t_2^{n}}$ be the destructuring of ${{\href{../exec/runtime.html#aux-blocktype}{\mathrm{instrtype}}}}_{z}({\mathit{bt}})$.
Assert: Due to validation, there are at least $m$ values on the top of the stack.
Pop the values ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}$ from the stack.
Let H be the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ whose arity is $n$ and whose catch handler is ${{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}^\ast}$.
Push the $\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}$ H.
Let L be the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ whose arity is $n$ and whose continuation is the end of the block.
Enter the block ${{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}$ with the $\href{../exec/runtime.html#syntax-label}{\mathsf{label}}$ L.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{try\_table}}~{\mathit{bt}}~{{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}^\ast}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ {{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}^\ast} \}}~({{\href{../exec/runtime.html#syntax-label}{\mathsf{label}}}_{n}}{\{ \epsilon \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{m}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast})) & \quad \mbox{if}~ {{\href{../exec/runtime.html#aux-blocktype}{\mathrm{instrtype}}}}_{z}({\mathit{bt}}) = {t_1^{m}} \href{../syntax/types.html#syntax-functype}{\rightarrow} {t_2^{n}} \\ \end{array}\end{split}\]

Blocks¶

The following auxiliary rules define the semantics of executing an instruction sequence that forms a block.

Entering $\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast$ with label $L$¶

Push $L$ to the stack.
Jump to the start of the instruction sequence $\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast$.

Note

No formal reduction rule is needed for entering an instruction sequence, because the label $L$ is embedded in the administrative instruction that structured control instructions reduce to directly.

Exiting $\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast$ with label $L$¶

When the end of a block is reached without a jump, exception, or trap aborting it, then the following steps are performed.

Pop all values $\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast$ from the top of the stack.
Assert: due to validation, the label $L$ is now on the top of the stack.
Pop the label from the stack.
Push $\href{../exec/runtime.html#syntax-val}{\mathit{val}}^\ast$ back to the stack.
Jump to the position after the $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}$ of the structured control instruction associated with the label $L$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({{\href{../exec/runtime.html#syntax-label}{\mathsf{label}}}_{n}}{\{ {{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast} \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast} \\ \end{array}\end{split}\]

Note

This semantics also applies to the instruction sequence contained in a $\mathsf{loop}$ instruction. Therefore, execution of a loop falls off the end, unless a backwards branch is performed explicitly.

Exception Handling¶

The following auxiliary rules define the semantics of entering and exiting $\mathsf{try\_table}$ blocks.

Entering $\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast$ with label $L$ and exception handler $H$¶

Push $H$ to the stack.
Push $L$ onto the stack.
Jump to the start of the instruction sequence $\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast$.

Note

No formal reduction rule is needed for entering an exception handler because it is an administrative instruction that the $\mathsf{try\_table}$ instruction reduces to directly.

Exiting an exception handler¶

When the end of a $\mathsf{try\_table}$ block is reached without a jump, exception, or trap, then the following steps are performed.

Let $m$ be the number of values on the top of the stack.
Pop the values $\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m$ from the stack.
Assert: due to validation, a handler and a label are now on the top of the stack.
Pop the label from the stack.
Pop the handler $H$ from the stack.
Push $\href{../exec/runtime.html#syntax-val}{\mathit{val}}^m$ back to the stack.
Jump to the position after the $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}$ of the administrative instruction associated with the handler $H$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({{\href{../exec/runtime.html#syntax-handler}{\mathsf{handler}}}_{n}}{\{ {{\href{../syntax/instructions.html#syntax-catch}{\mathit{catch}}}^\ast} \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast} \\ \end{array}\end{split}\]

Function Calls¶

The following auxiliary rules define the semantics of invoking a function instance through one of the call instructions and returning from it.

Invocation of function reference $(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a)$¶

Assert: due to validation, $S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a]$ exists.
Let $f$ be the function instance, $S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a]$.
Let $\href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~[t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^m]$ be the composite type $\href{../valid/conventions.html#aux-expand-deftype}{\mathrm{expand}}(\mathit{f}.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}})$.
Let $\href{../syntax/modules.html#syntax-local}{\mathit{local}}^\ast$ be the list of locals $f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}}.\href{../syntax/modules.html#syntax-func}{\mathsf{locals}}$.
Let $\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}}$ be the expression $f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}}.\href{../syntax/modules.html#syntax-func}{\mathsf{body}}$.
Assert: due to validation, $n$ values are on the top of the stack.
Pop the values $\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n$ from the stack.
Let $F$ be the frame $\{ \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~f.\href{../exec/runtime.html#syntax-funcinst}{\mathsf{module}}, \href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/runtime.html#aux-default}{\mathrm{default}}_t)^\ast \}$.
Push the activation of $F$ with arity $m$ to the stack.
Let $L$ be the label whose arity is $m$ and whose continuation is the end of the function.
Enter the instruction sequence $\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}^\ast$ with label $L$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~(\href{../exec/runtime.html#syntax-ref}{\mathsf{ref{.}func}}~a)~(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{call\_ref}}~y) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & ({{\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}}_{m}}{\{ f \}}~({{\href{../exec/runtime.html#syntax-label}{\mathsf{label}}}_{m}}{\{ \epsilon \}}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast})) & \\ &&& \multicolumn{2}{@{}l@{}}{\quad \quad \begin{array}[t]{@{}l@{}} \mbox{if}~ z{.}\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}{}[a] = {\mathit{fi}} \\ {\land}~ {\mathit{fi}}{.}\href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}} \mathrel{\href{../valid/conventions.html#aux-expand-deftype}{\approx}} \href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~({t_1^{n}} \href{../syntax/types.html#syntax-functype}{\rightarrow} {t_2^{m}}) \\ {\land}~ {\mathit{fi}}{.}\href{../exec/runtime.html#syntax-funcinst}{\mathsf{code}} = \href{../syntax/modules.html#syntax-func}{\mathsf{func}}~x~{(\href{../syntax/modules.html#syntax-local}{\mathsf{local}}~t)^\ast}~({{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}) \\ {\land}~ f = \{ \begin{array}[t]{@{}l@{}} \href{../exec/runtime.html#syntax-frame}{\mathsf{locals}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}~{({{\href{../exec/runtime.html#aux-default}{\mathrm{default}}}}_{t})^\ast},\; \href{../exec/runtime.html#syntax-frame}{\mathsf{module}}~{\mathit{fi}}{.}\href{../exec/runtime.html#syntax-funcinst}{\mathsf{module}} \}\end{array} \\ \end{array} } \\ \end{array}\end{split}\]

Note

For non-defaultable types, the respective local is left uninitialized by these rules.

Returning from a function¶

When the end of a function is reached without a jump (including through $\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{return}}$), or an exception or trap aborting it, then the following steps are performed.

Let $F$ be the current frame.
Let $n$ be the arity of the activation of $F$.
Assert: due to validation, there are $n$ values on the top of the stack.
Pop the results $\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n$ from the stack.
Assert: due to validation, the frame $F$ is now on the top of the stack.
Pop the frame from the stack.
Push $\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n$ back to the stack.
Jump to the instruction after the original call.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & ({{\href{../exec/runtime.html#syntax-frame}{\mathsf{frame}}}_{n}}{\{ f \}}~{{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}}) & \href{../exec/conventions.html#exec-notation}{\hookrightarrow} & {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^{n}} \\ \end{array}\end{split}\]

Host Functions¶

Invoking a host function has non-deterministic behavior. It may either terminate with a trap, an exception, or return regularly. However, in the latter case, it must consume and produce the right number and types of WebAssembly values on the stack, according to its function type.

A host function may also modify the store. However, all store modifications must result in an extension of the original store, i.e., they must only modify mutable contents and must not have instances removed. Furthermore, the resulting store must be valid, i.e., all data and code in it is well-typed.

\[\begin{split}~\\[-1ex] \begin{array}{l} \begin{array}{lcl@{\qquad}l} S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/instructions.html#exec-invoke}{\mathsf{invoke}}~a) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S'; \href{../exec/runtime.html#syntax-result}{\mathit{result}} \end{array} \\ \qquad \begin{array}[t]{@{}r@{~}l@{}} (\mathrel{\mbox{if}} & S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a] = \{ \href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../valid/conventions.html#syntax-deftype}{\mathit{deftype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{hostfunc}}~\mathit{hf} \} \\ \wedge & \href{../valid/conventions.html#aux-expand-deftype}{\mathrm{expand}}(\href{../valid/conventions.html#syntax-deftype}{\mathit{deftype}}) = \href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~[t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^m] \\ \wedge & (S'; \href{../exec/runtime.html#syntax-result}{\mathit{result}}) \in \mathit{hf}(S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n)) \\ \end{array} \\ \begin{array}{lcl@{\qquad}l} S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/instructions.html#exec-invoke}{\mathsf{invoke}}~a) &\href{../exec/conventions.html#exec-notation}{\hookrightarrow}& S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n~(\href{../exec/instructions.html#exec-invoke}{\mathsf{invoke}}~a) \end{array} \\ \qquad \begin{array}[t]{@{}r@{~}l@{}} (\mathrel{\mbox{if}} & S.\href{../exec/runtime.html#syntax-store}{\mathsf{funcs}}[a] = \{ \href{../exec/runtime.html#syntax-funcinst}{\mathsf{type}}~\href{../valid/conventions.html#syntax-deftype}{\mathit{deftype}}, \href{../exec/runtime.html#syntax-funcinst}{\mathsf{hostfunc}}~\mathit{hf} \} \\ \wedge & \href{../valid/conventions.html#aux-expand-deftype}{\mathrm{expand}}(\href{../valid/conventions.html#syntax-deftype}{\mathit{deftype}}) = \href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~[t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^m] \\ \wedge & \bot \in \mathit{hf}(S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n)) \\ \end{array} \\ \end{array}\end{split}\]

Here, $\mathit{hf}(S; \href{../exec/runtime.html#syntax-val}{\mathit{val}}^n)$ denotes the implementation-defined execution of host function $\mathit{hf}$ in current store $S$ with arguments $\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n$. It yields a set of possible outcomes, where each element is either a pair of a modified store $S'$ and a result or the special value $\bot$ indicating divergence. A host function is non-deterministic if there is at least one argument for which the set of outcomes is not singular.

For a WebAssembly implementation to be sound in the presence of host functions, every host function instance must be valid, which means that it adheres to suitable pre- and post-conditions: under a valid store $S$, and given arguments $\href{../exec/runtime.html#syntax-val}{\mathit{val}}^n$ matching the ascribed parameter types $t_1^n$, executing the host function must yield a non-empty set of possible outcomes each of which is either divergence or consists of a valid store $S'$ that is an extension of $S$ and a result matching the ascribed return types $t_2^m$. All these notions are made precise in the Appendix.

Note

A host function can call back into WebAssembly by invoking a function exported from a module. However, the effects of any such call are subsumed by the non-deterministic behavior allowed for the host function.

Expressions¶

An expression is evaluated relative to a current frame pointing to its containing module instance.

$\mathsf{eval\_expr}~{{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}$¶

Execute the sequence ${{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast}$.
Pop the value ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$ from the stack.
Return ${\href{../exec/runtime.html#syntax-val}{\mathit{val}}}$.

\[\begin{split}\begin{array}[t]{@{}l@{}rcl@{}l@{}} & z ; {{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast} & \href{../exec/conventions.html#exec-notation}{\hookrightarrow^\ast} & {z'} ; {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast} & \quad \mbox{if}~ z ; {{\href{../syntax/instructions.html#syntax-instr}{\mathit{instr}}}^\ast} \href{../exec/conventions.html#exec-notation}{\hookrightarrow^\ast} {z'} ; {{\href{../exec/runtime.html#syntax-val}{\mathit{val}}}^\ast} \\ \end{array}\end{split}\]

Note

Evaluation iterates this reduction rule until reaching a value. Expressions constituting function bodies are executed during function invocation.

Instructions¶

Parametric Instructions¶

\(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{nop}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{unreachable}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{drop}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-parametric}{\mathsf{select}}~{({t^\ast})^?}\)¶

Numeric Instructions¶

\(t\mathsf{.}\href{../syntax/instructions.html#syntax-instr-numeric}{\mathsf{const}}~c\)¶

\({\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-unop}{\mathit{unop}}}\)¶

\({\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-binop}{\mathit{binop}}}\)¶

\({\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-testop}{\mathit{testop}}}\)¶

\({\mathit{nt}} {.} {\href{../syntax/instructions.html#syntax-relop}{\mathit{relop}}}\)¶

\({\mathit{nt}}_2 {.} {{\href{../syntax/instructions.html#syntax-cvtop}{\mathit{cvtop}}}}{\mathsf{\_}}{{\mathit{nt}}_1}\)¶

Reference Instructions¶

\(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}func}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}is\_null}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}as\_non\_null}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}eq}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}test}}~{\mathit{rt}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}cast}}~{\mathit{rt}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-i31}{\mathsf{ref{.}i\scriptstyle31}}\)¶

\({\href{../syntax/instructions.html#syntax-instr-i31}{\mathsf{i{\scriptstyle31}{.}get}}}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}new}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}new\_default}}~x\)¶

\({\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x~i\)¶

\(\href{../syntax/instructions.html#syntax-instr-struct}{\mathsf{struct{.}set}}~x~i\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_default}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_fixed}}~x~n\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_data}}~x~y\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}new\_elem}}~x~y\)¶

\({\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}get}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}^?}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}set}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}len}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}fill}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}copy}}~x_1~x_2\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_data}}~x~y\)¶

\(\href{../syntax/instructions.html#syntax-instr-array}{\mathsf{array{.}init\_elem}}~x~y\)¶

\(\href{../syntax/instructions.html#syntax-instr-extern}{\mathsf{any{.}convert\_extern}}\)¶

\(\href{../syntax/instructions.html#syntax-instr-extern}{\mathsf{extern{.}convert\_any}}\)¶

Vector Instructions¶

\(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}}\mathsf{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{const}}~c\)¶

\(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} {\href{../syntax/instructions.html#syntax-vvunop}{\mathit{vvunop}}}\)¶

\(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} {\href{../syntax/instructions.html#syntax-vvbinop}{\mathit{vvbinop}}}\)¶

\(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} {\href{../syntax/instructions.html#syntax-vvternop}{\mathit{vvternop}}}\)¶

\(\href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} {.} \href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{any\_true}}\)¶

\({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vunop}{\mathit{vunop}}}\)¶

\({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vbinop}{\mathit{vbinop}}}\)¶

\({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vternop}{\mathit{vternop}}}\)¶

\({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vtestop}}}\)¶

\({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vrelop}{\mathit{vrelop}}}\)¶

\({\mathit{sh}} {.} {\href{../syntax/instructions.html#syntax-vshiftop}{\mathit{vshiftop}}}\)¶

\({\mathit{sh}}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{bitmask}}\)¶

\({\mathit{sh}} {.} {\mathit{swizzlop}}\)¶

\({\mathit{sh}}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{shuffle}}~{i^\ast}\)¶

\({{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{splat}}\)¶

\({{\href{../syntax/types.html#syntax-numtype}{\mathsf{i}}}{{\href{../syntax/types.html#syntax-numtype}{\scriptstyle\kern-0.1emN}}}}{\href{../syntax/instructions.html#syntax-shape}{\mathsf{x}}}{M}{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{replace\_lane}}~i\)¶

\({\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vextunop}{\mathit{vextunop}}}}{\mathsf{\_}}{{\mathit{sh}}_1}\)¶

\({\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vextbinop}{\mathit{vextbinop}}}}{\mathsf{\_}}{{\mathit{sh}}_1}\)¶

\({\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vextternop}{\mathit{vextternop}}}}{\mathsf{\_}}{{\mathit{sh}}_1}\)¶

\({{\mathit{sh}}_2{.}\href{../syntax/instructions.html#syntax-instr-vec}{\mathsf{narrow}}}{\mathsf{\_}}{{\mathit{sh}}_1}{\mathsf{\_}}{{\href{../syntax/instructions.html#syntax-sx}{\mathit{sx}}}}\)¶

\({\mathit{sh}}_2 {.} {{\href{../syntax/instructions.html#syntax-vcvtop}{\mathit{vcvtop}}}}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-zero}{\mathit{zero}}}^?}}{\mathsf{\_}}{{\mathit{sh}}_1}{\mathsf{\_}}{{{\href{../syntax/instructions.html#syntax-half}{\mathit{half}}}^?}}\)¶

Variable Instructions¶

\(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}get}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}set}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{local{.}tee}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global{.}get}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-variable}{\mathsf{global{.}set}}~x\)¶

Table Instructions¶

\(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}get}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}set}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}size}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}grow}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}fill}}~x\)¶

\(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}copy}}~x_{1'}~x_{2'}\)¶

\(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{table{.}init}}~x~y\)¶

\(\href{../syntax/instructions.html#syntax-instr-table}{\mathsf{elem{.}drop}}~x\)¶

Memory Instructions¶

\({{\mathit{nt}'}{.}\href{../syntax/instructions.html#syntax-instr-memory}{\mathsf{load}}}{{{\href{../syntax/instructions.html#syntax-loadop}{\mathit{loadop}}}^?}}~x~{\mathit{ao}}\)¶