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\mathdef3710#1{{}}\mathdef3710{type index} & \href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3735#1{{\mathtt{u}#1}}\mathdef3735{\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\mathdef3710#1{{}}\mathdef3710{function index} & \href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3735#1{{\mathtt{u}#1}}\mathdef3735{\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\mathdef3710#1{{}}\mathdef3710{table index} & \href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3735#1{{\mathtt{u}#1}}\mathdef3735{\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\mathdef3710#1{{}}\mathdef3710{memory index} & \href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3735#1{{\mathtt{u}#1}}\mathdef3735{\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\mathdef3710#1{{}}\mathdef3710{global index} & \href{../text/modules.html#text-globalidx}{\mathtt{globalidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3735#1{{\mathtt{u}#1}}\mathdef3735{\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\mathdef3710#1{{}}\mathdef3710{element index} & \href{../text/modules.html#text-elemidx}{\mathtt{elemidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3735#1{{\mathtt{u}#1}}\mathdef3735{\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\mathdef3710#1{{}}\mathdef3710{data index} & \href{../text/modules.html#text-dataidx}{\mathtt{dataidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3735#1{{\mathtt{u}#1}}\mathdef3735{\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\mathdef3710#1{{}}\mathdef3710{local index} & \href{../text/modules.html#text-localidx}{\mathtt{localidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef3735#1{{\mathtt{u}#1}}\mathdef3735{\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\mathdef3710#1{{}}\mathdef3710{label index} & \href{../text/modules.html#text-labelidx}{\mathtt{labelidx}}_I &::=&
l{:}\href{../text/values.html#text-int}{\def\mathdef3735#1{{\mathtt{u}#1}}\mathdef3735{\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\mathdef3710#1{{}}\mathdef3710{field index} & \href{../text/modules.html#text-fieldidx}{\mathtt{fieldidx}}_{I,x} &::=&
i{:}\href{../text/values.html#text-int}{\def\mathdef3735#1{{\mathtt{u}#1}}\mathdef3735{\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\mathdef3710#1{{}}\mathdef3710{type use} & \href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I &::=&
\def\mathdef3749#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3749{(}~\def\mathdef3750#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3750{type}~~x{:}\href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I~\def\mathdef3751#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3751{)}
\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\mathdef3752#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3752{(}~\def\mathdef3753#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3753{type}~~x{:}\href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I~\def\mathdef3754#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3754{)}
~~(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:
\[\begin{split}\begin{array}{lcl@{\qquad\qquad}l}
\mathrm{id}(\def\mathdef3755#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3755{(}~\def\mathdef3756#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3756{param}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3757#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3757{)}) &=& \href{../text/values.html#text-id}{\mathtt{id}}^? \\
\end{array}\end{split}\]
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:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{type use} &
(t_1{:}\href{../text/types.html#text-functype}{\mathtt{param}})^\ast~~(t_2{:}\href{../text/types.html#text-functype}{\mathtt{result}})^\ast &\equiv&
\def\mathdef3758#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3758{(}~\def\mathdef3759#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3759{type}~~x~\def\mathdef3760#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3760{)}~~\href{../text/types.html#text-functype}{\mathtt{param}}^\ast~~\href{../text/types.html#text-functype}{\mathtt{result}}^\ast \\
\end{array}\end{split}\]
where \(x\) is the smallest existing type index whose recursive type definition in the current module is of the form
\[\def\mathdef3761#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3761{(}~\def\mathdef3762#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3762{rec}~\def\mathdef3763#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3763{(}~\def\mathdef3764#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3764{type}~\def\mathdef3765#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3765{(}~\def\mathdef3766#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3766{sub}~\def\mathdef3767#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3767{final}~~\def\mathdef3768#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3768{(}~\def\mathdef3769#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3769{func}~~\href{../text/types.html#text-functype}{\mathtt{param}}^\ast~~\href{../text/types.html#text-functype}{\mathtt{result}}^\ast~\def\mathdef3770#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3770{)}~\def\mathdef3771#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3771{)}~\def\mathdef3772#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3772{)}~\def\mathdef3773#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3773{)}\]
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, or global identifier.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{import} & \href{../text/modules.html#text-import}{\mathtt{import}}_I &::=&
\def\mathdef3774#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3774{(}~\def\mathdef3775#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3775{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\mathdef3776#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3776{)} \\ &&& \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\mathdef3710#1{{}}\mathdef3710{import description} & \href{../text/modules.html#text-importdesc}{\mathtt{importdesc}}_I &::=&
\def\mathdef3777#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3777{(}~\def\mathdef3778#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3778{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I~\def\mathdef3779#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3779{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{func}}~x \\ &&|&
\def\mathdef3780#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3780{(}~\def\mathdef3781#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3781{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}_I~\def\mathdef3782#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3782{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{table}}~\mathit{tt} \\ &&|&
\def\mathdef3783#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3783{(}~\def\mathdef3784#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3784{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{mt}{:}\href{../text/types.html#text-memtype}{\mathtt{memtype}}_I~\def\mathdef3785#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3785{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{mem}}~~\mathit{mt} \\ &&|&
\def\mathdef3786#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3786{(}~\def\mathdef3787#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3787{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{gt}{:}\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}_I~\def\mathdef3788#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3788{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{global}}~\mathit{gt} \\
\end{array}\end{split}\]
Abbreviations¶
As an abbreviation, imports may also be specified inline with function, table, memory, or global definitions; see the respective sections.
Functions¶
Function definitions can bind a symbolic function identifier, and local identifiers for its parameters and locals.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{function} & \href{../text/modules.html#text-func}{\mathtt{func}}_I &::=&
\def\mathdef3789#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3789{(}~\def\mathdef3790#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3790{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I~~
(\mathit{loc}{:}\href{../text/modules.html#text-local}{\mathtt{local}}_I)^\ast~~(\mathit{in}{:}\href{../text/instructions.html#text-instr}{\mathtt{instr}}_{I''})^\ast~\def\mathdef3791#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3791{)} \\ &&& \qquad
\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-func}{\mathsf{type}}~x, \href{../syntax/modules.html#syntax-func}{\mathsf{locals}}~\mathit{loc}^\ast, \href{../syntax/modules.html#syntax-func}{\mathsf{body}}~\mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \} \\ &&& \qquad\qquad\qquad
(\mathrel{\mbox{if}} I'' = I \href{../syntax/conventions.html#notation-compose}{\oplus} I' \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~\mathrm{id}(\href{../text/modules.html#text-local}{\mathtt{local}})^\ast\} ~\href{../text/conventions.html#text-context-wf}{\mbox{well-formed}}) \\[1ex]
\def\mathdef3710#1{{}}\mathdef3710{local} & \href{../text/modules.html#text-local}{\mathtt{local}}_I &::=&
\def\mathdef3792#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3792{(}~\def\mathdef3793#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3793{local}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}_I~\def\mathdef3794#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3794{)}
\quad\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-local}{\mathsf{type}}~t \} \\
\end{array}\end{split}\]
The definition of the local identifier context \(I''\) uses the following auxiliary function to extract optional identifiers from locals:
\[\begin{split}\begin{array}{lcl@{\qquad\qquad}l}
\mathrm{id}(\def\mathdef3795#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3795{(}~\def\mathdef3796#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3796{local}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef3797#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3797{)}) &=& \href{../text/values.html#text-id}{\mathtt{id}}^? \\
\end{array}\end{split}\]
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:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{local} &
\def\mathdef3798#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3798{(}~~\def\mathdef3799#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3799{local}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}^\ast~~\def\mathdef3800#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3800{)} &\equiv&
(\def\mathdef3801#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3801{(}~~\def\mathdef3802#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3802{local}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}~~\def\mathdef3803#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3803{)})^\ast \\
\end{array}\end{split}\]
Functions can be defined as imports or exports inline:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{module field} &
\def\mathdef3804#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3804{(}~\def\mathdef3805#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3805{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3806#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3806{(}~\def\mathdef3807#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3807{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3808#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3808{)}~~\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}~\def\mathdef3809#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3809{)} \quad\equiv \\ & \qquad
\def\mathdef3810#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3810{(}~\def\mathdef3811#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3811{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3812#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3812{(}~\def\mathdef3813#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3813{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}~\def\mathdef3814#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3814{)}~\def\mathdef3815#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3815{)} \\[1ex] &
\def\mathdef3816#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3816{(}~\def\mathdef3817#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3817{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3818#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3818{(}~\def\mathdef3819#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3819{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3820#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3820{)}~~\dots~\def\mathdef3821#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3821{)} \quad\equiv \\ & \qquad
\def\mathdef3822#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3822{(}~\def\mathdef3823#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3823{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3824#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3824{(}~\def\mathdef3825#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3825{func}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3826#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3826{)}~\def\mathdef3827#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3827{)}~~
\def\mathdef3828#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3828{(}~\def\mathdef3829#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3829{func}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3830#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3830{)}
\\ & \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.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{table} & \href{../text/modules.html#text-table}{\mathtt{table}}_I &::=&
\def\mathdef3831#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3831{(}~\def\mathdef3832#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3832{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}_I~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3833#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3833{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-table}{\mathsf{type}}~\mathit{tt}, \href{../syntax/modules.html#syntax-table}{\mathsf{init}}~e \} \\
\end{array}\end{split}\]
Abbreviations¶
A table’s initialization expression can be omitted, in which case it defaults to \(\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref.null}}\):
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{module field} &
\def\mathdef3834#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3834{(}~\def\mathdef3835#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3835{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef3836#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3836{)}
&\equiv&
\def\mathdef3837#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3837{(}~\def\mathdef3838#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3838{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~~\def\mathdef3839#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3839{(}~\href{../syntax/instructions.html#syntax-instr-ref}{\mathsf{ref.null}}~\mathit{ht}~\def\mathdef3840#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3840{)}~\def\mathdef3841#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3841{)}
\\ &&& \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/types.html#text-tabletype}{\mathtt{tabletype}} = \href{../text/types.html#text-limits}{\mathtt{limits}}~\def\mathdef3842#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3842{(}~\def\mathdef3843#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3843{ref}~\def\mathdef3844#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3844{null}^?~\mathit{ht}~\def\mathdef3845#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3845{)}) \\
\end{array}\end{split}\]
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\mathdef3710#1{{}}\mathdef3710{module field} &
\def\mathdef3846#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3846{(}~\def\mathdef3847#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3847{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~\def\mathdef3848#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3848{(}~\def\mathdef3849#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3849{elem}~~\href{../syntax/instructions.html#syntax-expr}{\mathit{expr}}^n{:}\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}})~\def\mathdef3850#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3850{)}~\def\mathdef3851#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3851{)} \quad\equiv \\ & \qquad
\def\mathdef3852#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3852{(}~\def\mathdef3853#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3853{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~n~~n~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~\def\mathdef3854#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3854{)} \\ & \qquad
\def\mathdef3855#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3855{(}~\def\mathdef3856#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3856{elem}~~\def\mathdef3857#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3857{(}~\def\mathdef3858#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3858{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3859#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3859{)}~~\def\mathdef3860#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3860{(}~\def\mathdef3861#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3861{i32.const}~~\def\mathdef3862#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3862{0}~\def\mathdef3863#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3863{)}~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}})~\def\mathdef3864#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3864{)}
\\ & \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\mathdef3710#1{{}}\mathdef3710{module field} &
\def\mathdef3865#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3865{(}~\def\mathdef3866#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3866{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~\def\mathdef3867#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3867{(}~\def\mathdef3868#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3868{elem}~~x^n{:}\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}})~\def\mathdef3869#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3869{)}~\def\mathdef3870#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3870{)} \quad\equiv \\ & \qquad
\def\mathdef3871#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3871{(}~\def\mathdef3872#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3872{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~n~~n~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~\def\mathdef3873#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3873{)} \\ & \qquad
\def\mathdef3874#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3874{(}~\def\mathdef3875#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3875{elem}~~\def\mathdef3876#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3876{(}~\def\mathdef3877#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3877{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3878#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3878{)}~~\def\mathdef3879#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3879{(}~\def\mathdef3880#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3880{i32.const}~~\def\mathdef3881#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3881{0}~\def\mathdef3882#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3882{)}~~\href{../text/types.html#text-reftype}{\mathtt{reftype}}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\def\mathdef3883#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3883{(}~\def\mathdef3884#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3884{ref.func}~~\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}~\def\mathdef3885#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3885{)})~\def\mathdef3886#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3886{)}
\\ & \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\mathdef3710#1{{}}\mathdef3710{module field} &
\def\mathdef3887#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3887{(}~\def\mathdef3888#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3888{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3889#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3889{(}~\def\mathdef3890#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3890{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3891#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3891{)}~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef3892#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3892{)} \quad\equiv \\ & \qquad
\def\mathdef3893#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3893{(}~\def\mathdef3894#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3894{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3895#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3895{(}~\def\mathdef3896#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3896{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef3897#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3897{)}~\def\mathdef3898#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3898{)} \\[1ex] &
\def\mathdef3899#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3899{(}~\def\mathdef3900#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3900{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3901#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3901{(}~\def\mathdef3902#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3902{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3903#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3903{)}~~\dots~\def\mathdef3904#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3904{)} \quad\equiv \\ & \qquad
\def\mathdef3905#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3905{(}~\def\mathdef3906#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3906{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3907#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3907{(}~\def\mathdef3908#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3908{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3909#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3909{)}~\def\mathdef3910#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3910{)}~~
\def\mathdef3911#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3911{(}~\def\mathdef3912#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3912{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3913#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3913{)}
\\ & \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.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{memory} & \href{../text/modules.html#text-mem}{\mathtt{mem}}_I &::=&
\def\mathdef3914#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3914{(}~\def\mathdef3915#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3915{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{mt}{:}\href{../text/types.html#text-memtype}{\mathtt{memtype}}_I~\def\mathdef3916#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3916{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-mem}{\mathsf{type}}~\mathit{mt} \} \\
\end{array}\end{split}\]
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\mathdef3710#1{{}}\mathdef3710{module field} &
\def\mathdef3917#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3917{(}~\def\mathdef3918#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3918{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3919#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3919{(}~\def\mathdef3920#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3920{data}~~b^n{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef3921#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3921{)}~~\def\mathdef3922#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3922{)} \quad\equiv \\ & \qquad
\def\mathdef3923#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3923{(}~\def\mathdef3924#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3924{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~m~~m~\def\mathdef3925#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3925{)} \\ & \qquad
\def\mathdef3926#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3926{(}~\def\mathdef3927#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3927{data}~~\def\mathdef3928#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3928{(}~\def\mathdef3929#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3929{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3930#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3930{)}~~\def\mathdef3931#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3931{(}~\def\mathdef3932#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3932{i32.const}~~\def\mathdef3933#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3933{0}~\def\mathdef3934#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3934{)}~~\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef3935#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3935{)}
\\ & \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\mathdef3710#1{{}}\mathdef3710{module field} &
\def\mathdef3936#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3936{(}~\def\mathdef3937#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3937{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3938#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3938{(}~\def\mathdef3939#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3939{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3940#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3940{)}~~\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef3941#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3941{)} \quad\equiv \\ & \qquad
\def\mathdef3942#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3942{(}~\def\mathdef3943#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3943{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3944#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3944{(}~\def\mathdef3945#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3945{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef3946#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3946{)}~\def\mathdef3947#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3947{)}
\\[1ex] &
\def\mathdef3948#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3948{(}~\def\mathdef3949#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3949{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3950#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3950{(}~\def\mathdef3951#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3951{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3952#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3952{)}~~\dots~\def\mathdef3953#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3953{)} \quad\equiv \\ & \qquad
\def\mathdef3954#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3954{(}~\def\mathdef3955#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3955{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3956#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3956{(}~\def\mathdef3957#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3957{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3958#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3958{)}~\def\mathdef3959#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3959{)}~~
\def\mathdef3960#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3960{(}~\def\mathdef3961#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3961{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3962#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3962{)}
\\ & \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.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{global} & \href{../text/modules.html#text-global}{\mathtt{global}}_I &::=&
\def\mathdef3963#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3963{(}~\def\mathdef3964#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3964{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{gt}{:}\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}_I~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef3965#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3965{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-global}{\mathsf{type}}~\mathit{gt}, \href{../syntax/modules.html#syntax-global}{\mathsf{init}}~e \} \\
\end{array}\end{split}\]
Abbreviations¶
Globals can be defined as imports or exports inline:
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{module field} &
\def\mathdef3966#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3966{(}~\def\mathdef3967#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3967{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3968#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3968{(}~\def\mathdef3969#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3969{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef3970#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3970{)}~~\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~\def\mathdef3971#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3971{)} \quad\equiv \\ & \qquad
\def\mathdef3972#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3972{(}~\def\mathdef3973#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3973{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef3974#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3974{(}~\def\mathdef3975#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3975{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~\def\mathdef3976#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3976{)}~\def\mathdef3977#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3977{)}
\\[1ex] &
\def\mathdef3978#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3978{(}~\def\mathdef3979#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3979{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef3980#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3980{(}~\def\mathdef3981#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3981{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef3982#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3982{)}~~\dots~\def\mathdef3983#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3983{)} \quad\equiv \\ & \qquad
\def\mathdef3984#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3984{(}~\def\mathdef3985#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3985{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef3986#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3986{(}~\def\mathdef3987#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3987{global}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef3988#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3988{)}~\def\mathdef3989#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3989{)}~~
\def\mathdef3990#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3990{(}~\def\mathdef3991#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3991{global}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef3992#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3992{)}
\\ & \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\mathdef3710#1{{}}\mathdef3710{export} & \href{../text/modules.html#text-export}{\mathtt{export}}_I &::=&
\def\mathdef3993#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3993{(}~\def\mathdef3994#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3994{export}~~\mathit{nm}{:}\href{../text/values.html#text-name}{\mathtt{name}}~~d{:}\href{../text/modules.html#text-exportdesc}{\mathtt{exportdesc}}_I~\def\mathdef3995#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3995{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-export}{\mathsf{name}}~\mathit{nm}, \href{../syntax/modules.html#syntax-export}{\mathsf{desc}}~d \} \\
\def\mathdef3710#1{{}}\mathdef3710{export description} & \href{../text/modules.html#text-exportdesc}{\mathtt{exportdesc}}_I &::=&
\def\mathdef3996#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3996{(}~\def\mathdef3997#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3997{func}~~x{:}\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef3998#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3998{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{func}}~x \\ &&|&
\def\mathdef3999#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef3999{(}~\def\mathdef4000#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4000{table}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I~\def\mathdef4001#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4001{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{table}}~x \\ &&|&
\def\mathdef4002#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4002{(}~\def\mathdef4003#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4003{memory}~~x{:}\href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I~\def\mathdef4004#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4004{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{mem}}~x \\ &&|&
\def\mathdef4005#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4005{(}~\def\mathdef4006#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4006{global}~~x{:}\href{../text/modules.html#text-globalidx}{\mathtt{globalidx}}_I~\def\mathdef4007#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4007{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{global}}~x \\
\end{array}\end{split}\]
Abbreviations¶
As an abbreviation, exports may also be specified inline with function, table, memory, or global definitions; see the respective sections.
Start Function¶
A start function is defined in terms of its index.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{start function} & \href{../text/modules.html#text-start}{\mathtt{start}}_I &::=&
\def\mathdef4008#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4008{(}~\def\mathdef4009#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4009{start}~~x{:}\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef4010#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4010{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-start}{\mathsf{func}}~x \} \\
\end{array}\end{split}\]
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\mathdef3710#1{{}}\mathdef3710{element segment} & \href{../text/modules.html#text-elem}{\mathtt{elem}}_I &::=&
\def\mathdef4011#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4011{(}~\def\mathdef4012#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4012{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I~\def\mathdef4013#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4013{)} \\ &&& \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\mathdef4014#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4014{(}~\def\mathdef4015#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4015{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x{:}\href{../text/modules.html#text-tableuse}{\mathtt{tableuse}}_I~~\def\mathdef4016#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4016{(}~\def\mathdef4017#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4017{offset}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef4018#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4018{)}~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I~\def\mathdef4019#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4019{)} \\ &&& \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\mathdef4020#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4020{(}~\def\mathdef4021#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4021{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef4022#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4022{declare}~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}_I~\def\mathdef4023#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4023{)} \\ &&& \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{declarative}} \} \\
\def\mathdef3710#1{{}}\mathdef3710{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-vec}{\mathtt{vec}}(\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\mathdef3710#1{{}}\mathdef3710{element expression} & \href{../text/modules.html#text-elemexpr}{\mathtt{elemexpr}}_I &::=&
\def\mathdef4024#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4024{(}~\def\mathdef4025#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4025{item}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef4026#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4026{)}
\quad\Rightarrow\quad e \\
\def\mathdef3710#1{{}}\mathdef3710{table use} & \href{../text/modules.html#text-tableuse}{\mathtt{tableuse}}_I &::=&
\def\mathdef4027#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4027{(}~\def\mathdef4028#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4028{table}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I ~\def\mathdef4029#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4029{)}
\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:
\[\begin{split}\begin{array}{llcll}
\def\mathdef3710#1{{}}\mathdef3710{element offset} &
\def\mathdef4030#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4030{(}~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef4031#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4031{)} &\equiv&
\def\mathdef4032#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4032{(}~\def\mathdef4033#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4033{offset}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef4034#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4034{)} \\
\def\mathdef3710#1{{}}\mathdef3710{element item} &
\def\mathdef4035#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4035{(}~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef4036#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4036{)} &\equiv&
\def\mathdef4037#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4037{(}~\def\mathdef4038#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4038{item}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef4039#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4039{)} \\
\end{array}\end{split}\]
Also, the element list may be written as just a sequence of function indices:
\[\begin{array}{llcll}
\def\mathdef3710#1{{}}\mathdef3710{element list} &
\def\mathdef4040#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4040{func}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I) &\equiv&
\def\mathdef4041#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4041{(ref}~\def\mathdef4042#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4042{func)}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\def\mathdef4043#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4043{(}~\def\mathdef4044#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4044{ref.func}~~\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef4045#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4045{)})
\end{array}\]
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 \(\def\mathdef4046#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4046{func}\) keyword can be omitted as well.
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{table use} &
\epsilon &\equiv& \def\mathdef4047#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4047{(}~\def\mathdef4048#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4048{table}~~\def\mathdef4049#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4049{0}~\def\mathdef4050#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4050{)} \\
\def\mathdef3710#1{{}}\mathdef3710{element segment} &
\def\mathdef4051#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4051{(}~\def\mathdef4052#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4052{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef4053#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4053{(}~\def\mathdef4054#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4054{offset}~~\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef4055#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4055{)}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I)~\def\mathdef4056#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4056{)}
&\equiv&
\def\mathdef4057#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4057{(}~\def\mathdef4058#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4058{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef4059#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4059{(}~\def\mathdef4060#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4060{table}~~\def\mathdef4061#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4061{0}~\def\mathdef4062#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4062{)}~~\def\mathdef4063#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4063{(}~\def\mathdef4064#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4064{offset}~~\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef4065#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4065{)}~~\def\mathdef4066#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4066{func}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I)~\def\mathdef4067#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4067{)}
\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\mathdef3710#1{{}}\mathdef3710{data segment} & \href{../text/modules.html#text-data}{\mathtt{data}}_I &::=&
\def\mathdef4068#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4068{(}~\def\mathdef4069#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4069{data}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~b^\ast{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef4070#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4070{)} \\ &&& \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\mathdef4071#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4071{(}~\def\mathdef4072#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4072{data}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x{:}\href{../text/modules.html#text-memuse}{\mathtt{memuse}}_I~~\def\mathdef4073#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4073{(}~\def\mathdef4074#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4074{offset}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef4075#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4075{)}~~b^\ast{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef4076#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4076{)} \\ &&& \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\mathdef3710#1{{}}\mathdef3710{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}{\mathrm{concat}}((b^\ast)^\ast) \\
\def\mathdef3710#1{{}}\mathdef3710{memory use} & \href{../text/modules.html#text-memuse}{\mathtt{memuse}}_I &::=&
\def\mathdef4077#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4077{(}~\def\mathdef4078#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4078{memory}~~x{:}\href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I ~\def\mathdef4079#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4079{)}
\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:
\[\begin{array}{llcll}
\def\mathdef3710#1{{}}\mathdef3710{data offset} &
\def\mathdef4080#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4080{(}~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef4081#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4081{)} &\equiv&
\def\mathdef4082#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4082{(}~\def\mathdef4083#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4083{offset}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef4084#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4084{)}
\end{array}\]
Also, a memory use can be omitted, defaulting to \(\mathtt{0}\).
\[\begin{split}\begin{array}{llclll}
\def\mathdef3710#1{{}}\mathdef3710{memory use} &
\epsilon &\equiv& \def\mathdef4085#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4085{(}~\def\mathdef4086#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4086{memory}~~\def\mathdef4087#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4087{0}~\def\mathdef4088#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4088{)} \\
\end{array}\end{split}\]
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\mathdef3710#1{{}}\mathdef3710{module} & \href{../text/modules.html#text-module}{\mathtt{module}} &
\begin{array}[t]{@{}cllll}
::=&
\def\mathdef4089#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4089{(}~\def\mathdef4090#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4090{module}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~(m{:}\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}_I)^\ast~\def\mathdef4091#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4091{)}
\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\mathdef3710#1{{}}\mathdef3710{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{ex}{:}\href{../text/modules.html#text-export}{\mathtt{export}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{exports}}~\mathit{ex}\} \\ |&
\mathit{st}{:}\href{../text/modules.html#text-start}{\mathtt{start}}_I &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{start}}~\mathit{st}\} \\ |&
\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}\} \\
\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
\(m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{start}} = \epsilon \vee m_2.\href{../syntax/modules.html#syntax-module}{\mathsf{start}} = \epsilon\)
\(m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{funcs}} = m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{tables}} = m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{mems}} = m_1.\href{../syntax/modules.html#syntax-module}{\mathsf{globals}} = \epsilon \vee m_2.\href{../syntax/modules.html#syntax-module}{\mathsf{imports}} = \epsilon\)
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, or global, 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\mathdef4092#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4092{(}~\def\mathdef4093#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4093{rec}~~\href{../text/types.html#text-typedef}{\mathtt{typedef}}^\ast~\def\mathdef4094#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4094{)}) &=&
\href{../syntax/conventions.html#notation-compose}{\bigoplus} \mathrm{idc}(\href{../text/types.html#text-typedef}{\mathtt{typedef}})^\ast \\
\mathrm{idc}(\def\mathdef4095#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4095{(}~\def\mathdef4096#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4096{type}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\href{../text/types.html#text-subtype}{\mathtt{subtype}}~\def\mathdef4097#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4097{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{types}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?), \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\mathdef4098#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4098{(}~\def\mathdef4099#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4099{func}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4100#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4100{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{funcs}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef4101#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4101{(}~\def\mathdef4102#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4102{table}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4103#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4103{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{tables}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef4104#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4104{(}~\def\mathdef4105#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4105{memory}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4106#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4106{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{mems}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef4107#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4107{(}~\def\mathdef4108#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4108{global}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4109#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4109{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{globals}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef4110#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4110{(}~\def\mathdef4111#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4111{elem}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4112#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4112{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{elem}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef4113#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4113{(}~\def\mathdef4114#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4114{data}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4115#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4115{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{data}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef4116#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4116{(}~\def\mathdef4117#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4117{import}~\dots~\def\mathdef4118#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4118{(}~\def\mathdef4119#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4119{func}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4120#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4120{)}~\def\mathdef4121#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4121{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{funcs}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef4122#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4122{(}~\def\mathdef4123#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4123{import}~\dots~\def\mathdef4124#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4124{(}~\def\mathdef4125#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4125{table}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4126#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4126{)}~\def\mathdef4127#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4127{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{tables}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef4128#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4128{(}~\def\mathdef4129#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4129{import}~\dots~\def\mathdef4130#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4130{(}~\def\mathdef4131#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4131{memory}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4132#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4132{)}~\def\mathdef4133#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4133{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{mems}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef4134#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4134{(}~\def\mathdef4135#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4135{import}~\dots~\def\mathdef4136#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4136{(}~\def\mathdef4137#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4137{global}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4138#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4138{)}~\def\mathdef4139#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4139{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{globals}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef4140#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4140{(}~\dots~\def\mathdef4141#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4141{)}) &=&
\{\} \\[2ex]
\mathrm{idf}(\def\mathdef4142#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4142{(}~\def\mathdef4143#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4143{sub}~\dots~\href{../text/types.html#text-comptype}{\mathtt{comptype}}~\def\mathdef4144#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4144{)}) &=&
\mathrm{idf}(\href{../text/types.html#text-comptype}{\mathtt{comptype}}) \\
\mathrm{idf}(\def\mathdef4145#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4145{(}~\def\mathdef4146#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4146{struct}~\mathit{Tfield}^\ast~\def\mathdef4147#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4147{)}) &=&
\href{../syntax/conventions.html#notation-compose}{\bigoplus} \mathrm{idf}(\href{../text/types.html#text-structtype}{\mathtt{field}})^\ast \\
\mathrm{idf}(\def\mathdef4148#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4148{(}~\def\mathdef4149#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4149{array}~\dots~\def\mathdef4150#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4150{)}) &=&
\epsilon \\
\mathrm{idf}(\def\mathdef4151#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4151{(}~\def\mathdef4152#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4152{func}~\dots~\def\mathdef4153#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4153{)}) &=&
\epsilon \\
\mathrm{idf}(\def\mathdef4154#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4154{(}~\def\mathdef4155#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4155{field}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef4156#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4156{)}) &=&
\href{../text/values.html#text-id}{\mathtt{id}}^? \\
\end{array}\end{split}\]
Abbreviations¶
In a source file, the toplevel \(\mathtt{(module}~\dots\mathtt{)}\) surrounding the module body may be omitted.
\[\begin{array}{llcll}
\def\mathdef3710#1{{}}\mathdef3710{module} &
\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}^\ast &\equiv&
\def\mathdef4157#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4157{(}~\def\mathdef4158#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4158{module}~~\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}^\ast~\def\mathdef4159#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef4159{)}
\end{array}\]