Types¶
Number Types¶
\[\begin{split}\begin{array}{llrll@{\qquad\qquad}l}
\def\mathdef4068#1{{}}\mathdef4068{number type} & \href{../text/types.html#text-numtype}{\mathtt{numtype}}_I &::=&
\def\mathdef4112#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4112{i32} &\Rightarrow& \href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}} \\ &&|&
\def\mathdef4113#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4113{i64} &\Rightarrow& \href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle64}} \\ &&|&
\def\mathdef4114#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4114{f32} &\Rightarrow& \href{../syntax/types.html#syntax-numtype}{\mathsf{f\scriptstyle32}} \\ &&|&
\def\mathdef4115#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4115{f64} &\Rightarrow& \href{../syntax/types.html#syntax-numtype}{\mathsf{f\scriptstyle64}} \\
\end{array}\end{split}\]
Vector Types¶
\[\begin{split}\begin{array}{llcll@{\qquad\qquad}l}
\def\mathdef4068#1{{}}\mathdef4068{vector type} & \href{../text/types.html#text-vectype}{\mathtt{vectype}}_I &::=&
\def\mathdef4116#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4116{v128} &\Rightarrow& \href{../syntax/types.html#syntax-vectype}{\mathsf{v\scriptstyle128}} \\
\end{array}\end{split}\]
Heap Types¶
\[\begin{split}\begin{array}{llrll@{\qquad\qquad}l}
\def\mathdef4068#1{{}}\mathdef4068{abstract heap type} & \href{../text/types.html#text-absheaptype}{\mathtt{absheaptype}} &::=&
\def\mathdef4117#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4117{any} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{any}} \\ &&|&
\def\mathdef4118#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4118{eq} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{eq}} \\ &&|&
\def\mathdef4119#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4119{i31} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{i\scriptstyle31}} \\ &&|&
\def\mathdef4120#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4120{struct} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{struct}} \\ &&|&
\def\mathdef4121#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4121{array} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{array}} \\ &&|&
\def\mathdef4122#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4122{none} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{none}} \\ &&|&
\def\mathdef4123#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4123{func} &\Rightarrow& \href{../syntax/modules.html#syntax-func}{\mathsf{func}} \\ &&|&
\def\mathdef4124#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4124{nofunc} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{nofunc}} \\ &&|&
\def\mathdef4125#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4125{extern} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{extern}} \\ &&|&
\def\mathdef4126#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4126{noexn} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{noexn}} \\ &&|&
\def\mathdef4127#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4127{exn} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{exn}} \\ &&|&
\def\mathdef4128#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4128{noextern} &\Rightarrow& \href{../syntax/types.html#syntax-heaptype}{\mathsf{noextern}} \\
\def\mathdef4068#1{{}}\mathdef4068{heap type} & \href{../text/types.html#text-heaptype}{\mathtt{heaptype}}_I &::=&
t{:}\href{../text/types.html#text-absheaptype}{\mathtt{absheaptype}} &\Rightarrow& y \\ &&|&
x{:}\href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I &\Rightarrow& x \\
\end{array}\end{split}\]
Reference Types¶
\[\begin{split}\begin{array}{llcll@{\qquad\qquad}l}
\def\mathdef4068#1{{}}\mathdef4068{reference type} & \href{../text/types.html#text-reftype}{\mathtt{reftype}}_I &::=&
\def\mathdef4129#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4129{(}~\def\mathdef4130#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4130{ref}~~\mathit{ht}{:}\href{../text/types.html#text-heaptype}{\mathtt{heaptype}}~\def\mathdef4131#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4131{)}
&\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{ref}}~\mathit{ht} \\ &&|&
\def\mathdef4132#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4132{(}~\def\mathdef4133#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4133{ref}~~\def\mathdef4134#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4134{null}~~\mathit{ht}{:}\href{../text/types.html#text-heaptype}{\mathtt{heaptype}}~\def\mathdef4135#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4135{)}
&\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{ref}}~\href{../syntax/types.html#syntax-reftype}{\mathsf{null}}~\mathit{ht} \\
\end{array}\end{split}\]
Abbreviations¶
There are shorthands for references to abstract heap types.
\[\begin{split}\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{reference type} &
\def\mathdef4136#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4136{anyref} &\equiv& \def\mathdef4137#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4137{(}~\def\mathdef4138#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4138{ref}~~\def\mathdef4139#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4139{null}~~\def\mathdef4140#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4140{any}~\def\mathdef4141#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4141{)} \\
\def\mathdef4142#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4142{eqref} &\equiv& \def\mathdef4143#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4143{(}~\def\mathdef4144#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4144{ref}~~\def\mathdef4145#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4145{null}~~\def\mathdef4146#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4146{eq}~\def\mathdef4147#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4147{)} \\
\def\mathdef4148#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4148{i31ref} &\equiv& \def\mathdef4149#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4149{(}~\def\mathdef4150#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4150{ref}~~\def\mathdef4151#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4151{null}~~\def\mathdef4152#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4152{i31}~\def\mathdef4153#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4153{)} \\
\def\mathdef4154#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4154{structref} &\equiv& \def\mathdef4155#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4155{(}~\def\mathdef4156#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4156{ref}~~\def\mathdef4157#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4157{null}~~\def\mathdef4158#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4158{struct}~\def\mathdef4159#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4159{)} \\
\def\mathdef4160#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4160{arrayref} &\equiv& \def\mathdef4161#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4161{(}~\def\mathdef4162#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4162{ref}~~\def\mathdef4163#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4163{null}~~\def\mathdef4164#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4164{array}~\def\mathdef4165#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4165{)} \\
\def\mathdef4166#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4166{nullref} &\equiv& \def\mathdef4167#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4167{(}~\def\mathdef4168#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4168{ref}~~\def\mathdef4169#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4169{null}~~\def\mathdef4170#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4170{none}~\def\mathdef4171#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4171{)} \\
\def\mathdef4172#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4172{funcref} &\equiv& \def\mathdef4173#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4173{(}~\def\mathdef4174#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4174{ref}~~\def\mathdef4175#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4175{null}~~\def\mathdef4176#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4176{func}~\def\mathdef4177#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4177{)} \\
\def\mathdef4178#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4178{nullfuncref} &\equiv& \def\mathdef4179#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4179{(}~\def\mathdef4180#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4180{ref}~~\def\mathdef4181#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4181{null}~~\def\mathdef4182#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4182{nofunc}~\def\mathdef4183#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4183{)} \\
\def\mathdef4184#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4184{exnref} &\equiv& \def\mathdef4185#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4185{(}~\def\mathdef4186#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4186{ref}~~\def\mathdef4187#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4187{null}~~\def\mathdef4188#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4188{exn}~\def\mathdef4189#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4189{)} \\
\def\mathdef4190#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4190{nullexnref} &\equiv& \def\mathdef4191#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4191{(}~\def\mathdef4192#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4192{ref}~~\def\mathdef4193#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4193{null}~~\def\mathdef4194#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4194{noexn}~\def\mathdef4195#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4195{)} \\
\def\mathdef4196#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4196{externref} &\equiv& \def\mathdef4197#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4197{(}~\def\mathdef4198#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4198{ref}~~\def\mathdef4199#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4199{null}~~\def\mathdef4200#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4200{extern}~\def\mathdef4201#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4201{)} \\
\def\mathdef4202#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4202{nullexternref} &\equiv& \def\mathdef4203#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4203{(}~\def\mathdef4204#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4204{ref}~~\def\mathdef4205#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4205{null}~~\def\mathdef4206#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4206{noextern}~\def\mathdef4207#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4207{)} \\
\end{array}\end{split}\]
Value Types¶
\[\begin{split}\begin{array}{llcll@{\qquad\qquad}l}
\def\mathdef4068#1{{}}\mathdef4068{value type} & \href{../text/types.html#text-valtype}{\mathtt{valtype}}_I &::=&
t{:}\href{../text/types.html#text-numtype}{\mathtt{numtype}}_I &\Rightarrow& t \\ &&|&
t{:}\href{../text/types.html#text-vectype}{\mathtt{vectype}}_I &\Rightarrow& t \\ &&|&
t{:}\href{../text/types.html#text-reftype}{\mathtt{reftype}}_I &\Rightarrow& t \\
\end{array}\end{split}\]
Composite Types¶
\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l}
\def\mathdef4068#1{{}}\mathdef4068{composite type} & \href{../text/types.html#text-comptype}{\mathtt{comptype}}_I &::=&
\def\mathdef4208#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4208{(}~\def\mathdef4209#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4209{struct}~~\mathit{ft}^\ast{:\,}\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/types.html#text-comptype}{\mathtt{field}}_I)~\def\mathdef4210#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4210{)}
&\Rightarrow& \href{../syntax/types.html#syntax-comptype}{\mathsf{struct}}~\mathit{ft}^\ast \\ &&|&
\def\mathdef4211#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4211{(}~\def\mathdef4212#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4212{array}~~\mathit{ft}{:}\href{../text/types.html#text-fieldtype}{\mathtt{fieldtype}}_I~\def\mathdef4213#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4213{)}
&\Rightarrow& \href{../syntax/types.html#syntax-comptype}{\mathsf{array}}~\mathit{ft} \\ &&|&
\def\mathdef4214#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4214{(}~\def\mathdef4215#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4215{func}~~t_1^\ast{:\,}\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/types.html#text-comptype}{\mathtt{param}}_I)~~t_2^\ast{:\,}\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/types.html#text-comptype}{\mathtt{result}}_I)~\def\mathdef4216#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4216{)}
&\Rightarrow& \href{../syntax/types.html#syntax-comptype}{\mathsf{func}}~[t_1^\ast] \href{../syntax/types.html#syntax-comptype}{\rightarrow} [t_2^\ast] \\
\def\mathdef4068#1{{}}\mathdef4068{parameter} & \href{../text/types.html#text-comptype}{\mathtt{param}}_I &::=&
\def\mathdef4217#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4217{(}~\def\mathdef4218#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4218{param}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}_I~\def\mathdef4219#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4219{)}
&\Rightarrow& t \\
\def\mathdef4068#1{{}}\mathdef4068{result} & \href{../text/types.html#text-comptype}{\mathtt{result}}_I &::=&
\def\mathdef4220#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4220{(}~\def\mathdef4221#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4221{result}~~t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}_I~\def\mathdef4222#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4222{)}
&\Rightarrow& t \\
\def\mathdef4068#1{{}}\mathdef4068{field} & \href{../text/types.html#text-comptype}{\mathtt{field}}_I &::=&
\def\mathdef4223#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4223{(}~\def\mathdef4224#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4224{field}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{ft}{:}\href{../text/types.html#text-fieldtype}{\mathtt{fieldtype}}_I~\def\mathdef4225#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4225{)}
&\Rightarrow& \mathit{ft} \\
\def\mathdef4068#1{{}}\mathdef4068{field type} & \href{../text/types.html#text-fieldtype}{\mathtt{fieldtype}}_I &::=&
\mathit{st}{:}\href{../binary/types.html#binary-storagetype}{\mathtt{storagetype}}
&\Rightarrow& \mathit{st} \\ &&|&
\def\mathdef4226#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4226{(}~\def\mathdef4227#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4227{mut}~~\mathit{st}{:}\href{../binary/types.html#binary-storagetype}{\mathtt{storagetype}}~\def\mathdef4228#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4228{)}
&\Rightarrow& \href{../syntax/types.html#syntax-mut}{\mathsf{mut}}~\mathit{st} \\
\def\mathdef4068#1{{}}\mathdef4068{storage type} & \href{../text/types.html#text-storagetype}{\mathtt{storagetype}}_I &::=&
t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}_I
&\Rightarrow& t \\ &&|&
t{:}\href{../text/types.html#text-packtype}{\mathtt{packtype}}
&\Rightarrow& t \\
\def\mathdef4068#1{{}}\mathdef4068{packed type} & \href{../text/types.html#text-packtype}{\mathtt{packtype}} &::=&
\def\mathdef4229#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4229{i8}
&\Rightarrow& \href{../syntax/types.html#syntax-storagetype}{\mathsf{i\scriptstyle8}} \\ &&|&
\def\mathdef4230#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4230{i16}
&\Rightarrow& \href{../syntax/types.html#syntax-storagetype}{\mathsf{i\scriptstyle16}} \\
\end{array}\end{split}\]
Note
The optional identifier names for parameters in a function type only have documentation purpose. They cannot be referenced from anywhere.
Abbreviations¶
Multiple anonymous parameters or results may be combined into a single declaration:
\[\begin{split}\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{parameter} &
\def\mathdef4231#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4231{(}~~\def\mathdef4232#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4232{param}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}^\ast~~\def\mathdef4233#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4233{)} &\equiv&
(\def\mathdef4234#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4234{(}~~\def\mathdef4235#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4235{param}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}~~\def\mathdef4236#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4236{)})^\ast \\
\def\mathdef4068#1{{}}\mathdef4068{result} &
\def\mathdef4237#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4237{(}~~\def\mathdef4238#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4238{result}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}^\ast~~\def\mathdef4239#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4239{)} &\equiv&
(\def\mathdef4240#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4240{(}~~\def\mathdef4241#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4241{result}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}~~\def\mathdef4242#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4242{)})^\ast \\
\end{array}\end{split}\]
Similarly, multiple anonymous structure fields may be combined into a single declaration:
\[\begin{split}\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{field} &
\def\mathdef4243#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4243{(}~~\def\mathdef4244#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4244{field}~~\href{../text/types.html#text-fieldtype}{\mathtt{fieldtype}}^\ast~~\def\mathdef4245#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4245{)} &\equiv&
(\def\mathdef4246#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4246{(}~~\def\mathdef4247#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4247{field}~~\href{../text/types.html#text-fieldtype}{\mathtt{fieldtype}}~~\def\mathdef4248#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4248{)})^\ast \\
\end{array}\end{split}\]
Recursive Types¶
\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l}
\def\mathdef4068#1{{}}\mathdef4068{recursive type} & \href{../text/types.html#text-rectype}{\mathtt{rectype}}_I &::=&
\def\mathdef4249#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4249{(}~\def\mathdef4250#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4250{rec}~~\mathit{st}^\ast{:\,}\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/types.html#text-typedef}{\mathtt{typedef}}_I)~\def\mathdef4251#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4251{)}
&\Rightarrow& \href{../syntax/types.html#syntax-rectype}{\mathsf{rec}}~\mathit{st}^\ast \\
\def\mathdef4068#1{{}}\mathdef4068{defined type} & \href{../text/types.html#text-typedef}{\mathtt{typedef}}_I &::=&
\def\mathdef4252#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4252{(}~\def\mathdef4253#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4253{type}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{st}{:}\href{../text/types.html#text-subtype}{\mathtt{subtype}}_I~\def\mathdef4254#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4254{)}
&\Rightarrow& \mathit{st} \\
\def\mathdef4068#1{{}}\mathdef4068{sub type} & \href{../text/types.html#text-subtype}{\mathtt{subtype}}_I &::=&
\def\mathdef4255#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4255{(}~\def\mathdef4256#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4256{sub}~~\def\mathdef4257#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4257{final}^?~~x^\ast{:\,}\href{../text/conventions.html#text-list}{\mathtt{list}}(\href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I)~~\mathit{ct}{:}\href{../text/types.html#text-comptype}{\mathtt{comptype}}_I~\def\mathdef4258#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4258{)}
&\Rightarrow& \href{../syntax/types.html#syntax-subtype}{\mathsf{sub}}~\href{../syntax/types.html#syntax-subtype}{\mathsf{final}}^?~x^\ast~\mathit{ct} \\
\end{array}\end{split}\]
Abbreviations¶
Singular recursive types can omit the \(\def\mathdef4259#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4259{rec}\) keyword:
\[\begin{split}\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{recursive type} &
\href{../text/types.html#text-typedef}{\mathtt{typedef}} &\equiv&
\def\mathdef4260#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4260{(}~~\def\mathdef4261#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4261{rec}~~\href{../text/types.html#text-typedef}{\mathtt{typedef}}~~\def\mathdef4262#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4262{)} \\
\end{array}\end{split}\]
Similarly, final sub types with no super-types can omit the \(\href{../syntax/types.html#syntax-subtype}{\mathsf{sub}}\) keyword and arguments:
\[\begin{split}\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{sub type} &
\href{../text/types.html#text-comptype}{\mathtt{comptype}} &\equiv&
\def\mathdef4263#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4263{(}~~\def\mathdef4264#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4264{sub}~~\def\mathdef4265#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4265{final}~~\epsilon~~\href{../text/types.html#text-comptype}{\mathtt{comptype}}~~\def\mathdef4266#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4266{)} \\
\end{array}\end{split}\]
Address Types¶
\[\begin{split}\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{address type} & \href{../text/types.html#text-addrtype}{\mathtt{addrtype}} &::=&
\def\mathdef4267#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4267{i32} &\Rightarrow& \href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}} \\ &&|&
\def\mathdef4268#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4268{i64} &\Rightarrow& \href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle64}} \\
\end{array}\end{split}\]
Abbreviations¶
The address type can be omitted, in which case it defaults \(\href{../syntax/types.html#syntax-numtype}{\mathsf{i\scriptstyle32}}\):
\[\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{address type} &
\def\mathdef4269#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4269{} &\equiv& \def\mathdef4270#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4270{i32}
\end{array}\]
Limits¶
\[\begin{split}\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{limits} & \href{../text/types.html#text-limits}{\mathtt{limits}}_N &::=&
n{:}\href{../text/values.html#text-int}{\def\mathdef4099#1{{\mathtt{u}#1}}\mathdef4099{\mathtt{64}}} &\Rightarrow& [ n\,{..}\,2^N ] \\ &&|&
n{:}\href{../text/values.html#text-int}{\def\mathdef4099#1{{\mathtt{u}#1}}\mathdef4099{\mathtt{64}}}~~m{:}\href{../text/values.html#text-int}{\def\mathdef4099#1{{\mathtt{u}#1}}\mathdef4099{\mathtt{64}}} &\Rightarrow& [ n\,{..}\,m ] \\
\end{array}\end{split}\]
Tag Types¶
\[\begin{split}\begin{array}{llcl}
\def\mathdef4068#1{{}}\mathdef4068{tag} & \href{../text/types.html#text-tagtype}{\mathtt{tagtype}}_I &::=&
x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I \Rightarrow\quad x \\
\end{array}\end{split}\]
Global Types¶
\[\begin{split}\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{global type} & \href{../text/types.html#text-globaltype}{\mathtt{globaltype}}_I &::=&
t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}_I &\Rightarrow& t \\ &&|&
\def\mathdef4271#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4271{(}~\def\mathdef4272#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4272{mut}~~t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}_I~\def\mathdef4273#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4273{)} &\Rightarrow& \href{../syntax/types.html#syntax-mut}{\mathsf{mut}}~t \\
\end{array}\end{split}\]
Memory Types¶
\[\begin{split}\begin{array}{llclll@{\qquad\qquad}l}
\def\mathdef4068#1{{}}\mathdef4068{memory type} & \href{../text/types.html#text-memtype}{\mathtt{memtype}}_I &::=&
\mathit{at}{:}\href{../text/types.html#text-addrtype}{\mathtt{addrtype}}~~\mathit{lim}{:}\href{../text/types.html#text-limits}{\mathtt{limits}}_{|\mathit{at}|/64\cdot\mathrm{Ki}} &\Rightarrow& \mathit{at}~\mathit{lim}~\href{../syntax/types.html#syntax-memtype}{\mathsf{page}} \\
\end{array}\end{split}\]
Table Types¶
\[\begin{split}\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{table type} & \href{../text/types.html#text-tabletype}{\mathtt{tabletype}}_I &::=&
\mathit{at}{:}\href{../text/types.html#text-addrtype}{\mathtt{addrtype}}~~\mathit{lim}{:}\href{../text/types.html#text-limits}{\mathtt{limits}}_{|\mathit{at}|}~~\mathit{et}{:}\href{../text/types.html#text-reftype}{\mathtt{reftype}}_I &\Rightarrow& \mathit{at}~\mathit{lim}~\mathit{et} \\
\end{array}\end{split}\]
External Types¶
\[\begin{split}\begin{array}{llclll}
\def\mathdef4068#1{{}}\mathdef4068{external type} & \href{../text/types.html#text-externtype}{\mathtt{externtype}}_I &::=&
\def\mathdef4274#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4274{(}~\def\mathdef4275#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4275{tag}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/types.html#text-tagtype}{\mathtt{tagtype}}~\def\mathdef4276#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4276{)}
&\Rightarrow& \href{../syntax/types.html#syntax-externtype}{\mathsf{tag}}~\mathit{tt} \\ &&|&
\def\mathdef4277#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4277{(}~\def\mathdef4278#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4278{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{gt}{:}\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}_I~\def\mathdef4279#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4279{)}
&\Rightarrow& \href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\mathit{gt} \\ &&|&
\def\mathdef4280#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4280{(}~\def\mathdef4281#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4281{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{mt}{:}\href{../text/types.html#text-memtype}{\mathtt{memtype}}_I~\def\mathdef4282#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4282{)}
&\Rightarrow& \href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~~\mathit{mt} \\ &&|&
\def\mathdef4283#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4283{(}~\def\mathdef4284#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4284{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}_I~\def\mathdef4285#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4285{)}
&\Rightarrow& \href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\mathit{tt} \\ &&|&
\def\mathdef4286#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4286{(}~\def\mathdef4287#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4287{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I~\def\mathdef4288#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4288{)}
&\Rightarrow& \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~x \\
\end{array}\end{split}\]