Modules¶
Indices¶
Indices can be given either in raw numeric form or as symbolic identifiers when bound by a respective construct. Such identifiers are looked up in the suitable space of the identifier context \(I\).
\[\begin{split}\begin{array}{llcllllllll}
\def\mathdef3394#1{{}}\mathdef3394{type index} & \href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& x \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{types}}[x] = v) \\
\def\mathdef3394#1{{}}\mathdef3394{function index} & \href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& x \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{funcs}}[x] = v) \\
\def\mathdef3394#1{{}}\mathdef3394{table index} & \href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& x \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{tables}}[x] = v) \\
\def\mathdef3394#1{{}}\mathdef3394{memory index} & \href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& x \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{mems}}[x] = v) \\
\def\mathdef3394#1{{}}\mathdef3394{global index} & \href{../text/modules.html#text-globalidx}{\mathtt{globalidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& x \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{globals}}[x] = v) \\
\def\mathdef3394#1{{}}\mathdef3394{tag index} & \href{../text/modules.html#text-tagidx}{\mathtt{tagidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& x \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{tags}}[x] = v) \\
\def\mathdef3394#1{{}}\mathdef3394{element index} & \href{../text/modules.html#text-elemidx}{\mathtt{elemidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& x \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{elem}}[x] = v) \\
\def\mathdef3394#1{{}}\mathdef3394{data index} & \href{../text/modules.html#text-dataidx}{\mathtt{dataidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& x \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{data}}[x] = v) \\
\def\mathdef3394#1{{}}\mathdef3394{local index} & \href{../text/modules.html#text-localidx}{\mathtt{localidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& x \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& x & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{locals}}[x] = v) \\
\def\mathdef3394#1{{}}\mathdef3394{label index} & \href{../text/modules.html#text-labelidx}{\mathtt{labelidx}}_I &::=&
l{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& l \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& l & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{labels}}[l] = v) \\
\def\mathdef3394#1{{}}\mathdef3394{field index} & \href{../text/modules.html#text-fieldidx}{\mathtt{fieldidx}}_{I,x} &::=&
i{:}\href{../text/values.html#text-int}{\def\mathdef3423#1{{\mathtt{u}#1}}\mathdef3423{\mathtt{32}}} &\Rightarrow& i \\&&|&
v{:}\href{../text/values.html#text-id}{\mathtt{id}} &\Rightarrow& i & (\mathrel{\mbox{if}} I.\href{../text/conventions.html#text-context}{\mathsf{fields}}[x][i] = v) \\
\end{array}\end{split}\]
Type Uses¶
A type use is a reference to a function type definition. It may optionally be augmented by explicit inlined parameter and result declarations. That allows binding symbolic identifiers to name the local indices of parameters. If inline declarations are given, then their types must match the referenced function type.
\[\begin{split}\begin{array}{llcllll}
\def\mathdef3394#1{{}}\mathdef3394{type use} & \href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I &::=&
\def\mathdef3437#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3437{(}~\def\mathdef3438#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3438{type}~~x{:}\href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I~\def\mathdef3439#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3439{)}
\quad\Rightarrow\quad x, I' \\ &&& \qquad
(\mathrel{\mbox{if}} \begin{array}[t]{@{}l@{}}
I.\href{../text/conventions.html#text-context}{\mathsf{typedefs}}[x] = \href{../syntax/types.html#syntax-subtype}{\mathsf{sub}}~\href{../syntax/types.html#syntax-subtype}{\mathsf{final}}~(\href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~[t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]) \wedge
I' = \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~(\epsilon)^n\}) \\
\end{array} \\[1ex] &&|&
\def\mathdef3440#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3440{(}~\def\mathdef3441#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3441{type}~~x{:}\href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I~\def\mathdef3442#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3442{)}
~~(t_1{:}\href{../text/types.html#text-functype}{\mathtt{param}})^\ast~~(t_2{:}\href{../text/types.html#text-functype}{\mathtt{result}})^\ast
\quad\Rightarrow\quad x, I' \\ &&& \qquad
(\mathrel{\mbox{if}} \begin{array}[t]{@{}l@{}}
I.\href{../text/conventions.html#text-context}{\mathsf{typedefs}}[x] = \href{../syntax/types.html#syntax-subtype}{\mathsf{sub}}~\href{../syntax/types.html#syntax-subtype}{\mathsf{final}}~(\href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~[t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]) \wedge
I' = \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~\mathrm{id}(\href{../text/types.html#text-functype}{\mathtt{param}})^\ast\} ~\href{../text/conventions.html#text-context-wf}{\mbox{well-formed}}) \\
\end{array} \\
\end{array}\end{split}\]
Note
If inline declarations are given, their types must be syntactically equal to the types from the indexed definition; possible type substitutions from other definitions that might make them equal are not taken into account. This is to simplify syntactic pre-processing.
The synthesized attribute of a \(\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}\) is a pair consisting of both the used type index and the local identifier context containing possible parameter identifiers. The following auxiliary function extracts optional identifiers from parameters:
\[\begin{split}\begin{array}{lcl@{\qquad\qquad}l}
\mathrm{id}(\def\mathdef3443#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3443{(}~\def\mathdef3444#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3444{param}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3445#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3445{)}) &=& \href{../text/values.html#text-id}{\mathtt{id}}^? \\
\end{array}\end{split}\]
Note
Both productions overlap for the case that the function type is \([] \href{../syntax/types.html#syntax-functype}{\rightarrow} []\). However, in that case, they also produce the same results, so that the choice is immaterial.
The well-formedness condition on \(I'\) ensures that the parameters do not contain duplicate identifiers.
Abbreviations¶
A \(\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}\) may also be replaced entirely by inline parameter and result declarations. In that case, a type index is automatically inserted:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{type use} &
(t_1{:}\href{../text/types.html#text-functype}{\mathtt{param}})^\ast~~(t_2{:}\href{../text/types.html#text-functype}{\mathtt{result}})^\ast &\equiv&
\def\mathdef3446#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3446{(}~\def\mathdef3447#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3447{type}~~x~\def\mathdef3448#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3448{)}~~\href{../text/types.html#text-functype}{\mathtt{param}}^\ast~~\href{../text/types.html#text-functype}{\mathtt{result}}^\ast \\
\end{array}\end{split}\]
where \(x\) is the smallest existing type index whose recursive type definition in the current module is of the form
\[\def\mathdef3449#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3449{(}~\def\mathdef3450#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3450{rec}~\def\mathdef3451#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3451{(}~\def\mathdef3452#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3452{type}~\def\mathdef3453#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3453{(}~\def\mathdef3454#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3454{sub}~\def\mathdef3455#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3455{final}~~\def\mathdef3456#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3456{(}~\def\mathdef3457#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3457{func}~~\href{../text/types.html#text-functype}{\mathtt{param}}^\ast~~\href{../text/types.html#text-functype}{\mathtt{result}}^\ast~\def\mathdef3458#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3458{)}~\def\mathdef3459#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3459{)}~\def\mathdef3460#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3460{)}~\def\mathdef3461#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3461{)}\]
If no such index exists, then a new recursive type of the same form is inserted at the end of the module.
Abbreviations are expanded in the order they appear, such that previously inserted type definitions are reused by consecutive expansions.
Imports¶
The descriptors in imports can bind a symbolic function, table, memory, tag, or global identifier.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{import} & \href{../text/modules.html#text-import}{\mathtt{import}}_I &::=&
\def\mathdef3462#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3462{(}~\def\mathdef3463#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3463{import}~~\mathit{mod}{:}\href{../text/values.html#text-name}{\mathtt{name}}~~\mathit{nm}{:}\href{../text/values.html#text-name}{\mathtt{name}}~~d{:}\href{../text/modules.html#text-importdesc}{\mathtt{importdesc}}_I~\def\mathdef3464#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3464{)} \\ &&& \qquad
\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-import}{\mathsf{module}}~\mathit{mod}, \href{../syntax/modules.html#syntax-import}{\mathsf{name}}~\mathit{nm}, \href{../syntax/modules.html#syntax-import}{\mathsf{desc}}~d \} \\[1ex]
\def\mathdef3394#1{{}}\mathdef3394{import description} & \href{../text/modules.html#text-importdesc}{\mathtt{importdesc}}_I &::=&
\def\mathdef3465#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3465{(}~\def\mathdef3466#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3466{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I~\def\mathdef3467#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3467{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{func}}~x \\ &&|&
\def\mathdef3468#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3468{(}~\def\mathdef3469#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3469{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}_I~\def\mathdef3470#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3470{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{table}}~\mathit{tt} \\ &&|&
\def\mathdef3471#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3471{(}~\def\mathdef3472#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3472{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{mt}{:}\href{../text/types.html#text-memtype}{\mathtt{memtype}}_I~\def\mathdef3473#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3473{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{mem}}~~\mathit{mt} \\ &&|&
\def\mathdef3474#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3474{(}~\def\mathdef3475#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3475{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{gt}{:}\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}_I~\def\mathdef3476#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3476{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{global}}~\mathit{gt} \\ &&|&
\def\mathdef3477#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3477{(}~\def\mathdef3478#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3478{tag}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/modules.html#text-tag}{\mathtt{tag}}~\def\mathdef3479#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3479{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{tag}}~\mathit{tt} \\
\end{array}\end{split}\]
Abbreviations¶
As an abbreviation, imports may also be specified inline with function, table, memory, global, or tag definitions; see the respective sections.
Functions¶
Function definitions can bind a symbolic function identifier, and local identifiers for its parameters and locals.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{function} & \href{../text/modules.html#text-func}{\mathtt{func}}_I &::=&
\def\mathdef3480#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3480{(}~\def\mathdef3481#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3481{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I~~
(\mathit{loc}{:}\href{../text/modules.html#text-local}{\mathtt{local}}_I)^\ast~~(\mathit{in}{:}\href{../text/instructions.html#text-instr}{\mathtt{instr}}_{I''})^\ast~\def\mathdef3482#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3482{)} \\ &&& \qquad
\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-func}{\mathsf{type}}~x, \href{../syntax/modules.html#syntax-func}{\mathsf{locals}}~\mathit{loc}^\ast, \href{../syntax/modules.html#syntax-func}{\mathsf{body}}~\mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \} \\ &&& \qquad\qquad\qquad
(\mathrel{\mbox{if}} I'' = I \href{../syntax/conventions.html#notation-compose}{\oplus} I' \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~\mathrm{id}(\href{../text/modules.html#text-local}{\mathtt{local}})^\ast\} ~\href{../text/conventions.html#text-context-wf}{\mbox{well-formed}}) \\[1ex]
\def\mathdef3394#1{{}}\mathdef3394{local} & \href{../text/modules.html#text-local}{\mathtt{local}}_I &::=&
\def\mathdef3483#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3483{(}~\def\mathdef3484#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3484{local}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}_I~\def\mathdef3485#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3485{)}
\quad\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-local}{\mathsf{type}}~t \} \\
\end{array}\end{split}\]
The definition of the local identifier context \(I''\) uses the following auxiliary function to extract optional identifiers from locals:
\[\begin{split}\begin{array}{lcl@{\qquad\qquad}l}
\mathrm{id}(\def\mathdef3486#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3486{(}~\def\mathdef3487#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3487{local}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3488#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3488{)}) &=& \href{../text/values.html#text-id}{\mathtt{id}}^? \\
\end{array}\end{split}\]
Note
The well-formedness condition on \(I''\) ensures that parameters and locals do not contain duplicate identifiers.
Abbreviations¶
Multiple anonymous locals may be combined into a single declaration:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{local} &
\def\mathdef3489#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3489{(}~~\def\mathdef3490#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3490{local}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}^\ast~~\def\mathdef3491#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3491{)} &\equiv&
(\def\mathdef3492#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3492{(}~~\def\mathdef3493#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3493{local}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}~~\def\mathdef3494#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3494{)})^\ast \\
\end{array}\end{split}\]
Functions can be defined as imports or exports inline:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{module field} &
\def\mathdef3495#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3495{(}~\def\mathdef3496#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3496{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3497#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3497{(}~\def\mathdef3498#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3498{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3499#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3499{)}~~\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}~\def\mathdef3500#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3500{)} \quad\equiv \\ & \qquad
\def\mathdef3501#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3501{(}~\def\mathdef3502#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3502{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3503#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3503{(}~\def\mathdef3504#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3504{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}~\def\mathdef3505#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3505{)}~\def\mathdef3506#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3506{)} \\[1ex] &
\def\mathdef3507#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3507{(}~\def\mathdef3508#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3508{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3509#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3509{(}~\def\mathdef3510#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3510{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3511#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3511{)}~~\dots~\def\mathdef3512#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3512{)} \quad\equiv \\ & \qquad
\def\mathdef3513#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3513{(}~\def\mathdef3514#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3514{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3515#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3515{(}~\def\mathdef3516#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3516{func}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3517#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3517{)}~\def\mathdef3518#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3518{)}~~
\def\mathdef3519#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3519{(}~\def\mathdef3520#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3520{func}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3521#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3521{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
Note
The latter abbreviation can be applied repeatedly, if “\(\dots\)” contains additional export clauses. Consequently, a function declaration can contain any number of exports, possibly followed by an import.
Tables¶
Table definitions can bind a symbolic table identifier.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{table} & \href{../text/modules.html#text-table}{\mathtt{table}}_I &::=&
\def\mathdef3522#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3522{(}~\def\mathdef3523#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3523{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}_I~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3524#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3524{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-table}{\mathsf{type}}~\mathit{tt}, \href{../syntax/modules.html#syntax-table}{\mathsf{init}}~e \} \\
\end{array}\end{split}\]
Abbreviations¶
A table’s initialization expression can be omitted, in which case it defaults to \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}\):
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{module field} &
\def\mathdef3525#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3525{(}~\def\mathdef3526#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3526{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef3527#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3527{)}
&\equiv&
\def\mathdef3528#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3528{(}~\def\mathdef3529#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3529{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~~\def\mathdef3530#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3530{(}~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref{.}null}}~\mathit{ht}~\def\mathdef3531#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3531{)}~\def\mathdef3532#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3532{)}
\\ &&& \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/types.html#text-tabletype}{\mathtt{tabletype}} = \href{../text/types.html#text-limits}{\mathtt{limits}}~\def\mathdef3533#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3533{(}~\def\mathdef3534#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3534{ref}~\def\mathdef3535#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3535{null}^?~\mathit{ht}~\def\mathdef3536#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3536{)}) \\
\end{array}\end{split}\]
An element segment can be given inline with a table definition, in which case its offset is \(0\) and the limits of the table type are inferred from the length of the given segment:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{module field} &
\def\mathdef3537#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3537{(}~\def\mathdef3538#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3538{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~\def\mathdef3539#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3539{(}~\def\mathdef3540#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3540{elem}~~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}^n{:}\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}})~\def\mathdef3541#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3541{)}~\def\mathdef3542#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3542{)} \quad\equiv \\ & \qquad
\def\mathdef3543#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3543{(}~\def\mathdef3544#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3544{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~n~~n~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~\def\mathdef3545#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3545{)} \\ & \qquad
\def\mathdef3546#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3546{(}~\def\mathdef3547#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3547{elem}~~\def\mathdef3548#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3548{(}~\def\mathdef3549#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3549{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3550#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3550{)}~~\def\mathdef3551#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3551{(}~\def\mathdef3552#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3552{i32.const}~~\def\mathdef3553#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3553{0}~\def\mathdef3554#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3554{)}~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}})~\def\mathdef3555#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3555{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{module field} &
\def\mathdef3556#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3556{(}~\def\mathdef3557#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3557{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~\def\mathdef3558#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3558{(}~\def\mathdef3559#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3559{elem}~~x^n{:}\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}})~\def\mathdef3560#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3560{)}~\def\mathdef3561#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3561{)} \quad\equiv \\ & \qquad
\def\mathdef3562#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3562{(}~\def\mathdef3563#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3563{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~n~~n~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~\def\mathdef3564#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3564{)} \\ & \qquad
\def\mathdef3565#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3565{(}~\def\mathdef3566#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3566{elem}~~\def\mathdef3567#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3567{(}~\def\mathdef3568#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3568{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3569#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3569{)}~~\def\mathdef3570#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3570{(}~\def\mathdef3571#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3571{i32.const}~~\def\mathdef3572#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3572{0}~\def\mathdef3573#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3573{)}~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~\href{../text/conventions.html#text-list}{\mathtt{list}}(\def\mathdef3574#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3574{(}~\def\mathdef3575#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3575{ref.func}~~\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}~\def\mathdef3576#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3576{)})~\def\mathdef3577#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3577{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
Tables can be defined as imports or exports inline:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{module field} &
\def\mathdef3578#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3578{(}~\def\mathdef3579#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3579{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3580#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3580{(}~\def\mathdef3581#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3581{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3582#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3582{)}~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef3583#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3583{)} \quad\equiv \\ & \qquad
\def\mathdef3584#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3584{(}~\def\mathdef3585#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3585{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3586#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3586{(}~\def\mathdef3587#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3587{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef3588#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3588{)}~\def\mathdef3589#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3589{)} \\[1ex] &
\def\mathdef3590#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3590{(}~\def\mathdef3591#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3591{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3592#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3592{(}~\def\mathdef3593#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3593{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3594#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3594{)}~~\dots~\def\mathdef3595#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3595{)} \quad\equiv \\ & \qquad
\def\mathdef3596#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3596{(}~\def\mathdef3597#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3597{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3598#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3598{(}~\def\mathdef3599#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3599{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3600#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3600{)}~\def\mathdef3601#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3601{)}~~
\def\mathdef3602#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3602{(}~\def\mathdef3603#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3603{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3604#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3604{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
Note
The latter abbreviation can be applied repeatedly, if “\(\dots\)” contains additional export clauses. Consequently, a table declaration can contain any number of exports, possibly followed by an import.
Memories¶
Memory definitions can bind a symbolic memory identifier.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{memory} & \href{../text/modules.html#text-mem}{\mathtt{mem}}_I &::=&
\def\mathdef3605#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3605{(}~\def\mathdef3606#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3606{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{mt}{:}\href{../text/types.html#text-memtype}{\mathtt{memtype}}_I~\def\mathdef3607#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3607{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-mem}{\mathsf{type}}~\mathit{mt} \} \\
\end{array}\end{split}\]
Abbreviations¶
A data segment can be given inline with a memory definition, in which case its offset is \(0\) and the limits of the memory type are inferred from the length of the data, rounded up to page size:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{module field} &
\def\mathdef3608#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3608{(}~\def\mathdef3609#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3609{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3610#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3610{(}~\def\mathdef3611#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3611{data}~~b^n{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef3612#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3612{)}~~\def\mathdef3613#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3613{)} \quad\equiv \\ & \qquad
\def\mathdef3614#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3614{(}~\def\mathdef3615#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3615{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~m~~m~\def\mathdef3616#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3616{)} \\ & \qquad
\def\mathdef3617#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3617{(}~\def\mathdef3618#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3618{data}~~\def\mathdef3619#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3619{(}~\def\mathdef3620#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3620{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3621#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3621{)}~~\def\mathdef3622#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3622{(}~\def\mathdef3623#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3623{i32.const}~~\def\mathdef3624#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3624{0}~\def\mathdef3625#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3625{)}~~\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef3626#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3626{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}, m = \mathrm{ceil}(n / 64\,\mathrm{Ki})) \\
\end{array}\end{split}\]
Memories can be defined as imports or exports inline:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{module field} &
\def\mathdef3627#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3627{(}~\def\mathdef3628#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3628{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3629#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3629{(}~\def\mathdef3630#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3630{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3631#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3631{)}~~\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef3632#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3632{)} \quad\equiv \\ & \qquad
\def\mathdef3633#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3633{(}~\def\mathdef3634#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3634{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3635#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3635{(}~\def\mathdef3636#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3636{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef3637#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3637{)}~\def\mathdef3638#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3638{)}
\\[1ex] &
\def\mathdef3639#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3639{(}~\def\mathdef3640#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3640{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3641#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3641{(}~\def\mathdef3642#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3642{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3643#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3643{)}~~\dots~\def\mathdef3644#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3644{)} \quad\equiv \\ & \qquad
\def\mathdef3645#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3645{(}~\def\mathdef3646#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3646{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3647#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3647{(}~\def\mathdef3648#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3648{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3649#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3649{)}~\def\mathdef3650#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3650{)}~~
\def\mathdef3651#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3651{(}~\def\mathdef3652#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3652{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3653#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3653{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
Note
The latter abbreviation can be applied repeatedly, if “\(\dots\)” contains additional export clauses. Consequently, a memory declaration can contain any number of exports, possibly followed by an import.
Globals¶
Global definitions can bind a symbolic global identifier.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{global} & \href{../text/modules.html#text-global}{\mathtt{global}}_I &::=&
\def\mathdef3654#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3654{(}~\def\mathdef3655#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3655{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{gt}{:}\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}_I~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3656#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3656{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-global}{\mathsf{type}}~\mathit{gt}, \href{../syntax/modules.html#syntax-global}{\mathsf{init}}~e \} \\
\end{array}\end{split}\]
Abbreviations¶
Globals can be defined as imports or exports inline:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{module field} &
\def\mathdef3657#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3657{(}~\def\mathdef3658#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3658{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3659#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3659{(}~\def\mathdef3660#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3660{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3661#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3661{)}~~\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~\def\mathdef3662#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3662{)} \quad\equiv \\ & \qquad
\def\mathdef3663#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3663{(}~\def\mathdef3664#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3664{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3665#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3665{(}~\def\mathdef3666#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3666{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~\def\mathdef3667#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3667{)}~\def\mathdef3668#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3668{)}
\\[1ex] &
\def\mathdef3669#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3669{(}~\def\mathdef3670#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3670{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3671#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3671{(}~\def\mathdef3672#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3672{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3673#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3673{)}~~\dots~\def\mathdef3674#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3674{)} \quad\equiv \\ & \qquad
\def\mathdef3675#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3675{(}~\def\mathdef3676#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3676{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3677#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3677{(}~\def\mathdef3678#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3678{global}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3679#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3679{)}~\def\mathdef3680#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3680{)}~~
\def\mathdef3681#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3681{(}~\def\mathdef3682#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3682{global}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3683#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3683{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \vee \href{../text/values.html#text-id}{\mathtt{id}}^? = \epsilon \wedge \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
Note
The latter abbreviation can be applied repeatedly, if “\(\dots\)” contains additional export clauses. Consequently, a global declaration can contain any number of exports, possibly followed by an import.
Exports¶
The syntax for exports mirrors their abstract syntax directly.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{export} & \href{../text/modules.html#text-export}{\mathtt{export}}_I &::=&
\def\mathdef3714#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3714{(}~\def\mathdef3715#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3715{export}~~\mathit{nm}{:}\href{../text/values.html#text-name}{\mathtt{name}}~~d{:}\href{../text/modules.html#text-exportdesc}{\mathtt{exportdesc}}_I~\def\mathdef3716#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3716{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-export}{\mathsf{name}}~\mathit{nm}, \href{../syntax/modules.html#syntax-export}{\mathsf{desc}}~d \} \\
\def\mathdef3394#1{{}}\mathdef3394{export description} & \href{../text/modules.html#text-exportdesc}{\mathtt{exportdesc}}_I &::=&
\def\mathdef3717#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3717{(}~\def\mathdef3718#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3718{func}~~x{:}\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef3719#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3719{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{func}}~x \\ &&|&
\def\mathdef3720#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3720{(}~\def\mathdef3721#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3721{table}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I~\def\mathdef3722#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3722{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{table}}~x \\ &&|&
\def\mathdef3723#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3723{(}~\def\mathdef3724#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3724{memory}~~x{:}\href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I~\def\mathdef3725#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3725{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{mem}}~x \\ &&|&
\def\mathdef3726#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3726{(}~\def\mathdef3727#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3727{global}~~x{:}\href{../text/modules.html#text-globalidx}{\mathtt{globalidx}}_I~\def\mathdef3728#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3728{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{global}}~x \\&&|&
\def\mathdef3729#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3729{(}~\def\mathdef3730#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3730{tag}~~x{:}\href{../text/modules.html#text-tagidx}{\mathtt{tagidx}}_I~\def\mathdef3731#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3731{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{tag}}~x \\
\end{array}\end{split}\]
Abbreviations¶
As an abbreviation, exports may also be specified inline with function, table, memory, global, or tag definitions; see the respective sections.
Start Function¶
A start function is defined in terms of its index.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{start function} & \href{../text/modules.html#text-start}{\mathtt{start}}_I &::=&
\def\mathdef3732#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3732{(}~\def\mathdef3733#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3733{start}~~x{:}\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef3734#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3734{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-start}{\mathsf{func}}~x \} \\
\end{array}\end{split}\]
Note
At most one start function may occur in a module, which is ensured by a suitable side condition on the \(\href{../text/modules.html#text-module}{\mathtt{module}}\) grammar.
Element Segments¶
Element segments allow for an optional table index to identify the table to initialize.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{element segment} & \href{../text/modules.html#text-elem}{\mathtt{elem}}_I &::=&
\def\mathdef3735#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3735{(}~\def\mathdef3736#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3736{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I~\def\mathdef3737#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3737{)} \\ &&& \qquad
\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~et, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~y^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{passive}} \} \\ &&|&
\def\mathdef3738#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3738{(}~\def\mathdef3739#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3739{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x{:}\href{../text/modules.html#text-tableuse}{\mathtt{tableuse}}_I~~\def\mathdef3740#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3740{(}~\def\mathdef3741#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3741{offset}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3742#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3742{)}~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I~\def\mathdef3743#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3743{)} \\ &&& \qquad
\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~et, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~y^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~x, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~e \} \} \\ &&&
\def\mathdef3744#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3744{(}~\def\mathdef3745#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3745{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3746#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3746{declare}~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I~\def\mathdef3747#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3747{)} \\ &&& \qquad
\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~et, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~y^\ast, \href{../syntax/modules.html#syntax-elem}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-elemmode}{\mathsf{declare}} \} \\
\def\mathdef3394#1{{}}\mathdef3394{element list} & \href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I &::=&
t{:}\href{../text/types.html#text-reftype}{\mathtt{reftype}}_I~~y^\ast{:}\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}}_I) \qquad\Rightarrow\quad ( \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~t, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~y^\ast ) \\
\def\mathdef3394#1{{}}\mathdef3394{element expression} & \href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}}_I &::=&
\def\mathdef3748#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3748{(}~\def\mathdef3749#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3749{item}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3750#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3750{)}
\quad\Rightarrow\quad e \\
\def\mathdef3394#1{{}}\mathdef3394{table use} & \href{../text/modules.html#text-tableuse}{\mathtt{tableuse}}_I &::=&
\def\mathdef3751#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3751{(}~\def\mathdef3752#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3752{table}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I ~\def\mathdef3753#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3753{)}
\quad\Rightarrow\quad x \\
\end{array}\end{split}\]
Abbreviations¶
As an abbreviation, a single instruction may occur in place of the offset of an active element segment or as an element expression:
\[\begin{split}\begin{array}{llcll}
\def\mathdef3394#1{{}}\mathdef3394{element offset} &
\def\mathdef3754#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3754{(}~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3755#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3755{)} &\equiv&
\def\mathdef3756#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3756{(}~\def\mathdef3757#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3757{offset}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3758#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3758{)} \\
\def\mathdef3394#1{{}}\mathdef3394{element item} &
\def\mathdef3759#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3759{(}~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3760#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3760{)} &\equiv&
\def\mathdef3761#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3761{(}~\def\mathdef3762#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3762{item}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3763#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3763{)} \\
\end{array}\end{split}\]
Also, the element list may be written as just a sequence of function indices:
\[\begin{array}{llcll}
\def\mathdef3394#1{{}}\mathdef3394{element list} &
\def\mathdef3764#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3764{func}~~\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I) &\equiv&
\def\mathdef3765#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3765{(ref}~\def\mathdef3766#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3766{func)}~~\href{../text/conventions.html#text-list}{\mathtt{list}}(\def\mathdef3767#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3767{(}~\def\mathdef3768#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3768{ref.func}~~\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef3769#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3769{)})
\end{array}\]
A table use can be omitted, defaulting to \(\mathtt{0}\). Furthermore, for backwards compatibility with earlier versions of WebAssembly, if the table use is omitted, the \(\def\mathdef3770#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3770{func}\) keyword can be omitted as well.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{table use} &
\epsilon &\equiv& \def\mathdef3771#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3771{(}~\def\mathdef3772#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3772{table}~~\def\mathdef3773#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3773{0}~\def\mathdef3774#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3774{)} \\
\def\mathdef3394#1{{}}\mathdef3394{element segment} &
\def\mathdef3775#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3775{(}~\def\mathdef3776#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3776{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3777#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3777{(}~\def\mathdef3778#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3778{offset}~~\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3779#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3779{)}~~\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I)~\def\mathdef3780#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3780{)}
&\equiv&
\def\mathdef3781#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3781{(}~\def\mathdef3782#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3782{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3783#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3783{(}~\def\mathdef3784#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3784{table}~~\def\mathdef3785#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3785{0}~\def\mathdef3786#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3786{)}~~\def\mathdef3787#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3787{(}~\def\mathdef3788#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3788{offset}~~\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3789#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3789{)}~~\def\mathdef3790#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3790{func}~~\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I)~\def\mathdef3791#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3791{)}
\end{array}\end{split}\]
As another abbreviation, element segments may also be specified inline with table definitions; see the respective section.
Data Segments¶
Data segments allow for an optional memory index to identify the memory to initialize. The data is written as a string, which may be split up into a possibly empty sequence of individual string literals.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{data segment} & \href{../text/modules.html#text-data}{\mathtt{data}}_I &::=&
\def\mathdef3792#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3792{(}~\def\mathdef3793#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3793{data}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~b^\ast{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef3794#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3794{)} \\ &&& \qquad
\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^\ast, \href{../syntax/modules.html#syntax-data}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-datamode}{\mathsf{passive}} \} \\ &&|&
\def\mathdef3795#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3795{(}~\def\mathdef3796#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3796{data}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x{:}\href{../text/modules.html#text-memuse}{\mathtt{memuse}}_I~~\def\mathdef3797#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3797{(}~\def\mathdef3798#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3798{offset}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3799#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3799{)}~~b^\ast{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef3800#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3800{)} \\ &&& \qquad
\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-data}{\mathsf{init}}~b^\ast, \href{../syntax/modules.html#syntax-data}{\mathsf{mode}}~\href{../syntax/modules.html#syntax-datamode}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-data}{\mathsf{memory}}~x', \href{../syntax/modules.html#syntax-data}{\mathsf{offset}}~e \} \} \\
\def\mathdef3394#1{{}}\mathdef3394{data string} & \href{../text/modules.html#text-datastring}{\mathtt{datastring}} &::=&
(b^\ast{:}\href{../text/values.html#text-string}{\mathtt{string}})^\ast \quad\Rightarrow\quad \href{../syntax/conventions.html#notation-concat}{\bigoplus}((b^\ast)^\ast) \\
\def\mathdef3394#1{{}}\mathdef3394{memory use} & \href{../text/modules.html#text-memuse}{\mathtt{memuse}}_I &::=&
\def\mathdef3801#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3801{(}~\def\mathdef3802#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3802{memory}~~x{:}\href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I ~\def\mathdef3803#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3803{)}
\quad\Rightarrow\quad x \\
\end{array}\end{split}\]
Note
In the current version of WebAssembly, the only valid memory index is 0 or a symbolic memory identifier resolving to the same value.
Abbreviations¶
As an abbreviation, a single instruction may occur in place of the offset of an active data segment:
\[\begin{array}{llcll}
\def\mathdef3394#1{{}}\mathdef3394{data offset} &
\def\mathdef3804#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3804{(}~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3805#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3805{)} &\equiv&
\def\mathdef3806#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3806{(}~\def\mathdef3807#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3807{offset}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef3808#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3808{)}
\end{array}\]
Also, a memory use can be omitted, defaulting to \(\mathtt{0}\).
\[\begin{split}\begin{array}{llclll}
\def\mathdef3394#1{{}}\mathdef3394{memory use} &
\epsilon &\equiv& \def\mathdef3809#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3809{(}~\def\mathdef3810#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3810{memory}~~\def\mathdef3811#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3811{0}~\def\mathdef3812#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3812{)} \\
\end{array}\end{split}\]
As another abbreviation, data segments may also be specified inline with memory definitions; see the respective section.
Modules¶
A module consists of a sequence of fields that can occur in any order. All definitions and their respective bound identifiers scope over the entire module, including the text preceding them.
A module may optionally bind an identifier that names the module. The name serves a documentary role only.
Note
Tools may include the module name in the name section of the binary format.
\[\begin{split}\begin{array}{lll}
\def\mathdef3394#1{{}}\mathdef3394{module} & \href{../text/modules.html#text-module}{\mathtt{module}} &
\begin{array}[t]{@{}cllll}
::=&
\def\mathdef3813#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3813{(}~\def\mathdef3814#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3814{module}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~(m{:}\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}_I)^\ast~\def\mathdef3815#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3815{)}
\quad\Rightarrow\quad \href{../syntax/conventions.html#notation-compose}{\bigoplus} m^\ast \\
&\qquad (\mathrel{\mbox{if}} I = \href{../syntax/conventions.html#notation-compose}{\bigoplus} \mathrm{idc}(\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}})^\ast ~\href{../text/conventions.html#text-context-wf}{\mbox{well-formed}}) \\
\end{array} \\[1ex]
\def\mathdef3394#1{{}}\mathdef3394{module field} & \href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}_I &
\begin{array}[t]{@{}clll}
::=&
\mathit{ty}^\ast{:}\href{../text/types.html#text-rectype}{\mathtt{rectype}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{types}}~\mathit{ty}^\ast\} \\ |&
\mathit{im}{:}\href{../text/modules.html#text-import}{\mathtt{import}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{imports}}~\mathit{im}\} \\ |&
\mathit{fn}{:}\href{../text/modules.html#text-func}{\mathtt{func}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}}~\mathit{fn}\} \\ |&
\mathit{ta}{:}\href{../text/modules.html#text-table}{\mathtt{table}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{tables}}~\mathit{ta}\} \\ |&
\mathit{me}{:}\href{../text/modules.html#text-mem}{\mathtt{mem}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{mems}}~\mathit{me}\} \\ |&
\mathit{gl}{:}\href{../text/modules.html#text-global}{\mathtt{global}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{globals}}~\mathit{gl}\} \\ |&
\mathit{tg}{:}\href{../text/modules.html#text-tag}{\mathtt{tag}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{tags}}~\mathit{tg}\} \\ |&
\mathit{el}{:}\href{../text/modules.html#text-elem}{\mathtt{elem}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{elems}}~\mathit{el}\} \\ |&
\mathit{da}{:}\href{../text/modules.html#text-data}{\mathtt{data}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{datas}}~\mathit{da}\} \\ |&
\mathit{st}{:}\href{../text/modules.html#text-start}{\mathtt{start}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{start}}~\mathit{st}\} \\ |&
\mathit{ex}{:}\href{../text/modules.html#text-export}{\mathtt{export}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{exports}}~\mathit{ex}\} \\
\end{array}
\end{array}\end{split}\]
The following restrictions are imposed on the composition of modules: \(m_1 \href{../syntax/conventions.html#notation-compose}{\oplus} m_2\) is defined if and only if
\(m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{start}} = \epsilon \vee m_2.\href{../syntax/modules.html#syntax-module}{\mathsf{start}} = \epsilon\)
\(m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}} = m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{tables}} = m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{mems}} = m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{globals}} = m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{tags}} = \epsilon \vee m_2.\href{../syntax/modules.html#syntax-module}{\mathsf{imports}} = \epsilon\)
Note
The first condition ensures that there is at most one start function. The second condition enforces that all imports must occur before any regular definition of a function, table, memory, global, or tag, thereby maintaining the ordering of the respective index spaces.
The well-formedness condition on \(I\) in the grammar for \(\href{../text/modules.html#text-module}{\mathtt{module}}\) ensures that no namespace contains duplicate identifiers.
The definition of the initial identifier context \(I\) uses the following auxiliary definition which maps each relevant definition to a singular context with one (possibly empty) identifier:
\[\begin{split}\begin{array}{@{}lcl@{\qquad\qquad}l}
\mathrm{idc}(\def\mathdef3816#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3816{(}~\def\mathdef3817#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3817{rec}~~\href{../text/types.html#text-typedef}{\mathtt{typedef}}^\ast~\def\mathdef3818#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3818{)}) &=&
\href{../syntax/conventions.html#notation-compose}{\bigoplus} \mathrm{idc}(\href{../text/types.html#text-typedef}{\mathtt{typedef}})^\ast \\
\mathrm{idc}(\def\mathdef3819#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3819{(}~\def\mathdef3820#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3820{type}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\href{../text/types.html#text-subtype}{\mathtt{subtype}}~\def\mathdef3821#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3821{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{types}}~(v^?), \href{../text/conventions.html#text-context}{\mathsf{fields}}~\mathrm{idf}(\href{../text/types.html#text-subtype}{\mathtt{subtype}}), \href{../text/conventions.html#text-context}{\mathsf{typedefs}}~\mathit{st}\} \\
\mathrm{idc}(\def\mathdef3822#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3822{(}~\def\mathdef3823#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3823{func}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3824#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3824{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{funcs}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3825#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3825{(}~\def\mathdef3826#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3826{table}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3827#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3827{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{tables}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3828#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3828{(}~\def\mathdef3829#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3829{memory}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3830#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3830{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{mems}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3831#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3831{(}~\def\mathdef3832#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3832{global}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3833#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3833{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{globals}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3834#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3834{(}~\def\mathdef3835#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3835{tag}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3836#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3836{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{tags}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3837#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3837{(}~\def\mathdef3838#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3838{elem}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3839#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3839{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{elem}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3840#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3840{(}~\def\mathdef3841#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3841{data}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3842#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3842{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{data}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3843#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3843{(}~\def\mathdef3844#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3844{import}~\dots~\def\mathdef3845#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3845{(}~\def\mathdef3846#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3846{func}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3847#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3847{)}~\def\mathdef3848#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3848{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{funcs}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3849#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3849{(}~\def\mathdef3850#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3850{import}~\dots~\def\mathdef3851#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3851{(}~\def\mathdef3852#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3852{table}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3853#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3853{)}~\def\mathdef3854#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3854{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{tables}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3855#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3855{(}~\def\mathdef3856#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3856{import}~\dots~\def\mathdef3857#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3857{(}~\def\mathdef3858#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3858{memory}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3859#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3859{)}~\def\mathdef3860#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3860{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{mems}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3861#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3861{(}~\def\mathdef3862#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3862{import}~\dots~\def\mathdef3863#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3863{(}~\def\mathdef3864#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3864{global}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3865#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3865{)}~\def\mathdef3866#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3866{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{globals}}~(v^?)\} \\
\mathrm{idc}(\def\mathdef3867#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3867{(}~\dots~\def\mathdef3868#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3868{)}) &=&
\{\}
\\[2ex]
\mathrm{idf}(\def\mathdef3869#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3869{(}~\def\mathdef3870#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3870{sub}~\dots~\href{../text/types.html#text-comptype}{\mathtt{comptype}}~\def\mathdef3871#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3871{)}) &=&
\mathrm{idf}(\href{../text/types.html#text-comptype}{\mathtt{comptype}}) \\
\mathrm{idf}(\def\mathdef3872#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3872{(}~\def\mathdef3873#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3873{struct}~\mathit{Tfield}^\ast~\def\mathdef3874#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3874{)}) &=&
\href{../syntax/conventions.html#notation-compose}{\bigoplus} \mathrm{idf}(\href{../text/types.html#text-structtype}{\mathtt{field}})^\ast \\
\mathrm{idf}(\def\mathdef3875#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3875{(}~\def\mathdef3876#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3876{array}~\dots~\def\mathdef3877#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3877{)}) &=&
\epsilon \\
\mathrm{idf}(\def\mathdef3878#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3878{(}~\def\mathdef3879#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3879{func}~\dots~\def\mathdef3880#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3880{)}) &=&
\epsilon \\
\mathrm{idf}(\def\mathdef3881#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3881{(}~\def\mathdef3882#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3882{field}~v^?{:}\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3883#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3883{)}) &=&
v^? \\
\end{array}\end{split}\]
Abbreviations¶
In a source file, the toplevel \(\mathtt{(module}~\dots\mathtt{)}\) surrounding the module body may be omitted.
\[\begin{array}{llcll}
\def\mathdef3394#1{{}}\mathdef3394{module} &
\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}^\ast &\equiv&
\def\mathdef3884#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3884{(}~\def\mathdef3885#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3885{module}~~\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}^\ast~\def\mathdef3886#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3886{)}
\end{array}\]