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\mathdef2156#1{{}}\mathdef2156{type index} & \href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef2181#1{{\mathtt{u}#1}}\mathdef2181{\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\mathdef2156#1{{}}\mathdef2156{function index} & \href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef2181#1{{\mathtt{u}#1}}\mathdef2181{\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\mathdef2156#1{{}}\mathdef2156{table index} & \href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef2181#1{{\mathtt{u}#1}}\mathdef2181{\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\mathdef2156#1{{}}\mathdef2156{memory index} & \href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef2181#1{{\mathtt{u}#1}}\mathdef2181{\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\mathdef2156#1{{}}\mathdef2156{global index} & \href{../text/modules.html#text-globalidx}{\mathtt{globalidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef2181#1{{\mathtt{u}#1}}\mathdef2181{\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\mathdef2156#1{{}}\mathdef2156{element index} & \href{../text/modules.html#text-elemidx}{\mathtt{elemidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef2181#1{{\mathtt{u}#1}}\mathdef2181{\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\mathdef2156#1{{}}\mathdef2156{data index} & \href{../text/modules.html#text-dataidx}{\mathtt{dataidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef2181#1{{\mathtt{u}#1}}\mathdef2181{\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\mathdef2156#1{{}}\mathdef2156{local index} & \href{../text/modules.html#text-localidx}{\mathtt{localidx}}_I &::=&
x{:}\href{../text/values.html#text-int}{\def\mathdef2181#1{{\mathtt{u}#1}}\mathdef2181{\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\mathdef2156#1{{}}\mathdef2156{label index} & \href{../text/modules.html#text-labelidx}{\mathtt{labelidx}}_I &::=&
l{:}\href{../text/values.html#text-int}{\def\mathdef2181#1{{\mathtt{u}#1}}\mathdef2181{\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) \\
\end{array}\end{split}\]
Types¶
Type definitions can bind a symbolic type identifier.
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{type definition} & \href{../text/modules.html#text-typedef}{\mathtt{type}} &::=&
\def\mathdef2193#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2193{(}~\def\mathdef2194#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2194{type}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{ft}{:}\href{../text/types.html#text-functype}{\mathtt{functype}}~\def\mathdef2195#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2195{)}
&\Rightarrow& \mathit{ft} \\
\end{array}\end{split}\]
Type Uses¶
A type use is a reference to a 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.
\[\begin{split}\begin{array}{llcllll}
\def\mathdef2156#1{{}}\mathdef2156{type use} & \href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I &::=&
\def\mathdef2196#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2196{(}~\def\mathdef2197#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2197{type}~~x{:}\href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I~\def\mathdef2198#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2198{)}
\quad\Rightarrow\quad x, I' \\ &&& \qquad
(\mathrel{\mbox{if}} \begin{array}[t]{@{}l@{}}
I.\href{../text/conventions.html#text-context}{\mathsf{typedefs}}[x] = [t_1^n] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] \wedge
I' = \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~(\epsilon)^n\}) \\
\end{array} \\[1ex] &&|&
\def\mathdef2199#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2199{(}~\def\mathdef2200#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2200{type}~~x{:}\href{../text/modules.html#text-typeidx}{\mathtt{typeidx}}_I~\def\mathdef2201#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2201{)}
~~(t_1{:}\href{../text/types.html#text-functype}{\mathtt{param}})^\ast~~(t_2{:}\href{../text/types.html#text-functype}{\mathtt{result}})^\ast
\quad\Rightarrow\quad x, I' \\ &&& \qquad
(\mathrel{\mbox{if}} \begin{array}[t]{@{}l@{}}
I.\href{../text/conventions.html#text-context}{\mathsf{typedefs}}[x] = [t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast] \wedge
I' = \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~\mathrm{id}(\href{../text/types.html#text-functype}{\mathtt{param}})^\ast\} ~\href{../text/conventions.html#text-context-wf}{\mbox{well-formed}}) \\
\end{array} \\
\end{array}\end{split}\]
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 updated identifier context including possible parameter identifiers. The following auxiliary function extracts optional identifiers from parameters:
\[\begin{split}\begin{array}{lcl@{\qquad\qquad}l}
\mathrm{id}(\def\mathdef2202#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2202{(}~\def\mathdef2203#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2203{param}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2204#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2204{)}) &=& \href{../text/values.html#text-id}{\mathtt{id}}^? \\
\end{array}\end{split}\]
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 identifier.
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:
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{type use} &
(t_1{:}\href{../text/types.html#text-functype}{\mathtt{param}})^\ast~~(t_2{:}\href{../text/types.html#text-functype}{\mathtt{result}})^\ast &\equiv&
\def\mathdef2205#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2205{(}~\def\mathdef2206#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2206{type}~~x~\def\mathdef2207#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2207{)}~~\href{../text/types.html#text-functype}{\mathtt{param}}^\ast~~\href{../text/types.html#text-functype}{\mathtt{result}}^\ast \\
\end{array}\end{split}\]
where \(x\) is the smallest existing type index whose definition in the current module is the function type \([t_1^\ast] \href{../syntax/types.html#syntax-functype}{\rightarrow} [t_2^\ast]\). If no such index exists, then a new type definition of the form
\[\def\mathdef2208#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2208{(}~\def\mathdef2209#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2209{type}~~\def\mathdef2210#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2210{(}~\def\mathdef2211#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2211{func}~~\href{../text/types.html#text-functype}{\mathtt{param}}^\ast~~\href{../text/types.html#text-functype}{\mathtt{result}}^\ast~\def\mathdef2212#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2212{)}~\def\mathdef2213#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2213{)}\]
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\mathdef2156#1{{}}\mathdef2156{import} & \href{../text/modules.html#text-import}{\mathtt{import}}_I &::=&
\def\mathdef2214#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2214{(}~\def\mathdef2215#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2215{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\mathdef2216#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2216{)} \\ &&& \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\mathdef2156#1{{}}\mathdef2156{import description} & \href{../text/modules.html#text-importdesc}{\mathtt{importdesc}}_I &::=&
\def\mathdef2217#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2217{(}~\def\mathdef2218#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2218{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I~\def\mathdef2219#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2219{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{func}}~x \\ &&|&
\def\mathdef2220#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2220{(}~\def\mathdef2221#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2221{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef2222#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2222{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{table}}~\mathit{tt} \\ &&|&
\def\mathdef2223#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2223{(}~\def\mathdef2224#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2224{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{mt}{:}\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef2225#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2225{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{mem}}~~\mathit{mt} \\ &&|&
\def\mathdef2226#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2226{(}~\def\mathdef2227#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2227{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{gt}{:}\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~\def\mathdef2228#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2228{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-importdesc}{\mathsf{global}}~\mathit{gt} \\
\end{array}\end{split}\]
Functions¶
Function definitions can bind a symbolic function identifier, and local identifiers for its parameters and locals.
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{function} & \href{../text/modules.html#text-func}{\mathtt{func}}_I &::=&
\def\mathdef2229#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2229{(}~\def\mathdef2230#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2230{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x,I'{:}\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}_I~~
(t{:}\href{../text/modules.html#text-local}{\mathtt{local}})^\ast~~(\mathit{in}{:}\href{../text/instructions.html#text-instr}{\mathtt{instr}}_{I''})^\ast~\def\mathdef2231#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2231{)} \\ &&& \qquad
\Rightarrow\quad \{ \href{../syntax/modules.html#syntax-func}{\mathsf{type}}~x, \href{../syntax/modules.html#syntax-func}{\mathsf{locals}}~t^\ast, \href{../syntax/modules.html#syntax-func}{\mathsf{body}}~\mathit{in}^\ast~\href{../syntax/instructions.html#syntax-instr-control}{\mathsf{end}} \} \\ &&& \qquad\qquad\qquad
(\mathrel{\mbox{if}} I'' = I' \href{../syntax/conventions.html#notation-compose}{\oplus} \{\href{../text/conventions.html#text-context}{\mathsf{locals}}~\mathrm{id}(\href{../text/modules.html#text-local}{\mathtt{local}})^\ast\} ~\href{../text/conventions.html#text-context-wf}{\mbox{well-formed}}) \\[1ex]
\def\mathdef2156#1{{}}\mathdef2156{local} & \href{../text/modules.html#text-local}{\mathtt{local}} &::=&
\def\mathdef2232#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2232{(}~\def\mathdef2233#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2233{local}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~t{:}\href{../text/types.html#text-valtype}{\mathtt{valtype}}~\def\mathdef2234#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2234{)}
\quad\Rightarrow\quad t \\
\end{array}\end{split}\]
The definition of the local identifier context \(I''\) uses the following auxiliary function to extract optional identifiers from locals:
\[\begin{split}\begin{array}{lcl@{\qquad\qquad}l}
\mathrm{id}(\def\mathdef2235#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2235{(}~\def\mathdef2236#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2236{local}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2237#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2237{)}) &=& \href{../text/values.html#text-id}{\mathtt{id}}^? \\
\end{array}\end{split}\]
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:
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{local} &
\def\mathdef2238#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2238{(}~~\def\mathdef2239#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2239{local}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}^\ast~~\def\mathdef2240#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2240{)} &\equiv&
(\def\mathdef2241#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2241{(}~~\def\mathdef2242#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2242{local}~~\href{../text/types.html#text-valtype}{\mathtt{valtype}}~~\def\mathdef2243#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2243{)})^\ast \\
\end{array}\end{split}\]
Functions can be defined as imports or exports inline:
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{module field} &
\def\mathdef2244#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2244{(}~\def\mathdef2245#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2245{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2246#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2246{(}~\def\mathdef2247#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2247{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef2248#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2248{)}~~\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}~\def\mathdef2249#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2249{)} \quad\equiv \\ & \qquad
\def\mathdef2250#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2250{(}~\def\mathdef2251#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2251{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef2252#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2252{(}~\def\mathdef2253#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2253{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/modules.html#text-typeuse}{\mathtt{typeuse}}~\def\mathdef2254#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2254{)}~\def\mathdef2255#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2255{)} \\[1ex] &
\def\mathdef2256#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2256{(}~\def\mathdef2257#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2257{func}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2258#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2258{(}~\def\mathdef2259#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2259{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef2260#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2260{)}~~\dots~\def\mathdef2261#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2261{)} \quad\equiv \\ & \qquad
\def\mathdef2262#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2262{(}~\def\mathdef2263#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2263{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef2264#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2264{(}~\def\mathdef2265#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2265{func}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef2266#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2266{)}~\def\mathdef2267#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2267{)}~~
\def\mathdef2268#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2268{(}~\def\mathdef2269#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2269{func}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef2270#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2270{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
The latter abbreviation can be applied repeatedly, with “\(\dots\)” containing another import or export.
Tables¶
Table definitions can bind a symbolic table identifier.
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{table} & \href{../text/modules.html#text-table}{\mathtt{table}}_I &::=&
\def\mathdef2271#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2271{(}~\def\mathdef2272#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2272{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{tt}{:}\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef2273#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2273{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-table}{\mathsf{type}}~\mathit{tt} \} \\
\end{array}\end{split}\]
Abbreviations¶
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:
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{module field} &
\def\mathdef2274#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2274{(}~\def\mathdef2275#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2275{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-elemtype}{\mathtt{elemtype}}~~\def\mathdef2276#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2276{(}~\def\mathdef2277#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2277{elem}~~\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}~\def\mathdef2278#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2278{)} \quad\equiv \\ & \qquad
\def\mathdef2279#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2279{(}~\def\mathdef2280#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2280{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~n~~n~~\href{../text/types.html#text-elemtype}{\mathtt{elemtype}}~\def\mathdef2281#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2281{)}~~
\def\mathdef2282#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2282{(}~\def\mathdef2283#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2283{elem}~~\def\mathdef2284#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2284{(}~\def\mathdef2285#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2285{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef2286#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2286{)}~~\def\mathdef2287#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2287{(}~\def\mathdef2288#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2288{i32.const}~~\def\mathdef2289#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2289{0}~\def\mathdef2290#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2290{)}~~\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}~\def\mathdef2291#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2291{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{module field} &
\def\mathdef2292#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2292{(}~\def\mathdef2293#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2293{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-elemtype}{\mathtt{elemtype}}~~\def\mathdef2294#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2294{(}~\def\mathdef2295#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2295{elem}~~x^n{:}\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/instructions.html#text-expr}{\mathtt{expr}})~\def\mathdef2296#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2296{)}~~\def\mathdef2297#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2297{)} \quad\equiv \\ & \qquad
\def\mathdef2298#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2298{(}~\def\mathdef2299#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2299{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~n~~n~~\href{../text/types.html#text-elemtype}{\mathtt{elemtype}}~\def\mathdef2300#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2300{)}~~
\def\mathdef2301#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2301{(}~\def\mathdef2302#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2302{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\def\mathdef2303#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2303{(}~\def\mathdef2304#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2304{i32.const}~~\def\mathdef2305#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2305{0}~\def\mathdef2306#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2306{)}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/instructions.html#text-expr}{\mathtt{expr}})~\def\mathdef2307#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2307{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
Tables can be defined as imports or exports inline:
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{module field} &
\def\mathdef2308#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2308{(}~\def\mathdef2309#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2309{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2310#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2310{(}~\def\mathdef2311#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2311{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef2312#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2312{)}~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef2313#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2313{)} \quad\equiv \\ & \qquad
\def\mathdef2314#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2314{(}~\def\mathdef2315#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2315{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef2316#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2316{(}~\def\mathdef2317#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2317{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-tabletype}{\mathtt{tabletype}}~\def\mathdef2318#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2318{)}~\def\mathdef2319#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2319{)} \\[1ex] &
\def\mathdef2320#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2320{(}~\def\mathdef2321#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2321{table}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2322#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2322{(}~\def\mathdef2323#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2323{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef2324#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2324{)}~~\dots~\def\mathdef2325#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2325{)} \quad\equiv \\ & \qquad
\def\mathdef2326#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2326{(}~\def\mathdef2327#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2327{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef2328#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2328{(}~\def\mathdef2329#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2329{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef2330#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2330{)}~\def\mathdef2331#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2331{)}~~
\def\mathdef2332#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2332{(}~\def\mathdef2333#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2333{table}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef2334#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2334{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
The latter abbreviation can be applied repeatedly, with “\(\dots\)” containing another import or export or an inline elements segment.
Memories¶
Memory definitions can bind a symbolic memory identifier.
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{memory} & \href{../text/modules.html#text-mem}{\mathtt{mem}}_I &::=&
\def\mathdef2335#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2335{(}~\def\mathdef2336#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2336{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{mt}{:}\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef2337#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2337{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-mem}{\mathsf{type}}~\mathit{mt} \} \\
\end{array}\end{split}\]
Abbreviations¶
A data segment can be given inline with a memory definition, in which case its offset is \(0\) the limits of the memory type are inferred from the length of the data, rounded up to page size:
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{module field} &
\def\mathdef2338#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2338{(}~\def\mathdef2339#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2339{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2340#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2340{(}~\def\mathdef2341#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2341{data}~~b^n{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef2342#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2342{)}~~\def\mathdef2343#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2343{)} \quad\equiv \\ & \qquad
\def\mathdef2344#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2344{(}~\def\mathdef2345#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2345{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~m~~m~\def\mathdef2346#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2346{)}~~
\def\mathdef2347#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2347{(}~\def\mathdef2348#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2348{data}~~\def\mathdef2349#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2349{(}~\def\mathdef2350#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2350{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef2351#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2351{)}~~\def\mathdef2352#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2352{(}~\def\mathdef2353#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2353{i32.const}~~\def\mathdef2354#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2354{0}~\def\mathdef2355#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2355{)}~~\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef2356#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2356{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}, m = \mathrm{ceil}(n / 64\mathrm{Ki})) \\
\end{array}\end{split}\]
Memories can be defined as imports or exports inline:
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{module field} &
\def\mathdef2357#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2357{(}~\def\mathdef2358#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2358{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2359#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2359{(}~\def\mathdef2360#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2360{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef2361#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2361{)}~~\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef2362#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2362{)} \quad\equiv \\ & \qquad
\def\mathdef2363#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2363{(}~\def\mathdef2364#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2364{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef2365#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2365{(}~\def\mathdef2366#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2366{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-memtype}{\mathtt{memtype}}~\def\mathdef2367#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2367{)}~\def\mathdef2368#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2368{)}
\\[1ex] &
\def\mathdef2369#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2369{(}~\def\mathdef2370#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2370{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2371#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2371{(}~\def\mathdef2372#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2372{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef2373#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2373{)}~~\dots~\def\mathdef2374#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2374{)} \quad\equiv \\ & \qquad
\def\mathdef2375#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2375{(}~\def\mathdef2376#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2376{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef2377#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2377{(}~\def\mathdef2378#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2378{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef2379#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2379{)}~\def\mathdef2380#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2380{)}~~
\def\mathdef2381#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2381{(}~\def\mathdef2382#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2382{memory}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef2383#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2383{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
The latter abbreviation can be applied repeatedly, with “\(\dots\)” containing another import or export or an inline data segment.
Globals¶
Global definitions can bind a symbolic global identifier.
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{global} & \href{../text/modules.html#text-global}{\mathtt{global}}_I &::=&
\def\mathdef2384#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2384{(}~\def\mathdef2385#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2385{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\mathit{gt}{:}\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef2386#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2386{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-global}{\mathsf{type}}~\mathit{gt}, \href{../syntax/modules.html#syntax-global}{\mathsf{init}}~e \} \\
\end{array}\end{split}\]
Abbreviations¶
Globals can be defined as imports or exports inline:
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{module field} &
\def\mathdef2387#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2387{(}~\def\mathdef2388#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2388{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2389#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2389{(}~\def\mathdef2390#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2390{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~\def\mathdef2391#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2391{)}~~\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~\def\mathdef2392#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2392{)} \quad\equiv \\ & \qquad
\def\mathdef2393#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2393{(}~\def\mathdef2394#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2394{import}~~\href{../text/values.html#text-name}{\mathtt{name}}_1~~\href{../text/values.html#text-name}{\mathtt{name}}_2~~\def\mathdef2395#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2395{(}~\def\mathdef2396#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2396{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\href{../text/types.html#text-globaltype}{\mathtt{globaltype}}~\def\mathdef2397#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2397{)}~\def\mathdef2398#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2398{)}
\\[1ex] &
\def\mathdef2399#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2399{(}~\def\mathdef2400#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2400{global}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2401#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2401{(}~\def\mathdef2402#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2402{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~\def\mathdef2403#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2403{)}~~\dots~\def\mathdef2404#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2404{)} \quad\equiv \\ & \qquad
\def\mathdef2405#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2405{(}~\def\mathdef2406#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2406{export}~~\href{../text/values.html#text-name}{\mathtt{name}}~~\def\mathdef2407#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2407{(}~\def\mathdef2408#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2408{global}~~\href{../text/values.html#text-id}{\mathtt{id}}'~\def\mathdef2409#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2409{)}~\def\mathdef2410#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2410{)}~~
\def\mathdef2411#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2411{(}~\def\mathdef2412#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2412{global}~~\href{../text/values.html#text-id}{\mathtt{id}}'~~\dots~\def\mathdef2413#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2413{)}
\\ & \qquad\qquad
(\mathrel{\mbox{if}} \href{../text/values.html#text-id}{\mathtt{id}}' = \href{../text/values.html#text-id}{\mathtt{id}}^? \neq \epsilon \vee \href{../text/values.html#text-id}{\mathtt{id}}' ~\href{../text/values.html#text-id-fresh}{\mbox{fresh}}) \\
\end{array}\end{split}\]
The latter abbreviation can be applied repeatedly, with “\(\dots\)” containing another import or export.
Exports¶
The syntax for exports mirrors their abstract syntax directly.
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{export} & \href{../text/modules.html#text-export}{\mathtt{export}}_I &::=&
\def\mathdef2414#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2414{(}~\def\mathdef2415#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2415{export}~~\mathit{nm}{:}\href{../text/values.html#text-name}{\mathtt{name}}~~d{:}\href{../text/modules.html#text-exportdesc}{\mathtt{exportdesc}}_I~\def\mathdef2416#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2416{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-export}{\mathsf{name}}~\mathit{nm}, \href{../syntax/modules.html#syntax-export}{\mathsf{desc}}~d \} \\
\def\mathdef2156#1{{}}\mathdef2156{export description} & \href{../text/modules.html#text-exportdesc}{\mathtt{exportdesc}}_I &::=&
\def\mathdef2417#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2417{(}~\def\mathdef2418#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2418{func}~~x{:}\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef2419#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2419{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{func}}~x \\ &&|&
\def\mathdef2420#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2420{(}~\def\mathdef2421#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2421{table}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I~\def\mathdef2422#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2422{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{table}}~x \\ &&|&
\def\mathdef2423#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2423{(}~\def\mathdef2424#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2424{memory}~~x{:}\href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I~\def\mathdef2425#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2425{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{mem}}~x \\ &&|&
\def\mathdef2426#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2426{(}~\def\mathdef2427#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2427{global}~~x{:}\href{../text/modules.html#text-globalidx}{\mathtt{globalidx}}_I~\def\mathdef2428#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2428{)}
&\Rightarrow& \href{../syntax/modules.html#syntax-exportdesc}{\mathsf{global}}~x \\
\end{array}\end{split}\]
Start Function¶
A start function is defined in terms of its index.
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{start function} & \href{../text/modules.html#text-start}{\mathtt{start}}_I &::=&
\def\mathdef2429#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2429{(}~\def\mathdef2430#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2430{start}~~x{:}\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef2431#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2431{)}
&\Rightarrow& \{ \href{../syntax/modules.html#syntax-start}{\mathsf{func}}~x \} \\
\end{array}\end{split}\]
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\mathdef2156#1{{}}\mathdef2156{element segment} & \href{../text/modules.html#text-elem}{\mathtt{elem}}_I &::=&
\def\mathdef2432#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2432{(}~\def\mathdef2433#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2433{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}~\def\mathdef2434#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2434{)} \\ &&& \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-elem}{\mathsf{passive}} \} \\ &&|&
\def\mathdef2435#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2435{(}~\def\mathdef2436#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2436{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x{:}\href{../text/modules.html#text-tableuse}{\mathtt{tableuse}}_I~~\def\mathdef2437#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2437{(}~\def\mathdef2438#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2438{offset}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef2439#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2439{)}~~(et, y^\ast){:}\href{../text/modules.html#text-elemlist}{\mathtt{elemlist}}~\def\mathdef2440#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2440{)} \\ &&& \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-elem}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-elem}{\mathsf{table}}~x, \href{../syntax/modules.html#syntax-elem}{\mathsf{offset}}~e \} \} \\
\def\mathdef2156#1{{}}\mathdef2156{element list} & \href{../text/modules.html#text-elemlist}{\mathtt{elemlist}} &::=&
et{:}\href{../text/types.html#text-elemtype}{\mathtt{elemtype}}~~y^\ast{:}\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-elemexpr}{\mathit{elemexpr}}_I) \qquad\Rightarrow\quad ( \href{../syntax/modules.html#syntax-elem}{\mathsf{type}}~et, \href{../syntax/modules.html#syntax-elem}{\mathsf{init}}~y^\ast ) \\
\def\mathdef2156#1{{}}\mathdef2156{element expression} & \href{../text/modules.html#text-elemexpr}{\mathit{elemexpr}} &::=&
\def\mathdef2441#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2441{(}~\def\mathdef2442#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2442{ref.null}~~\def\mathdef2443#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2443{func}~\def\mathdef2444#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2444{)} \\ &&|&
\def\mathdef2445#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2445{(}~\def\mathdef2446#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2446{ref.func}~~\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef2447#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2447{)} \\
\def\mathdef2156#1{{}}\mathdef2156{table use} & \href{../text/modules.html#text-tableuse}{\mathtt{tableuse}}_I &::=&
\def\mathdef2448#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2448{(}~\def\mathdef2449#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2449{table}~~x{:}\href{../text/modules.html#text-tableidx}{\mathtt{tableidx}}_I ~\def\mathdef2450#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2450{)}
\quad\Rightarrow\quad x \\
\end{array}\end{split}\]
Note
In the current version of WebAssembly, the only valid table index is 0 or a symbolic table identifier resolving to the same value.
Abbreviations¶
As an abbreviation, a single instruction may occur in place of the offset of an active element segment:
\[\begin{array}{llcll}
\def\mathdef2156#1{{}}\mathdef2156{element offset} &
\href{../text/instructions.html#text-instr}{\mathtt{instr}} &\equiv&
\def\mathdef2451#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2451{(}~\def\mathdef2452#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2452{offset}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef2453#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2453{)}
\end{array}\]
Also, the element list may be written as just a sequence of function indices:
\[\begin{array}{llcll}
\def\mathdef2156#1{{}}\mathdef2156{element list} &
\def\mathdef2454#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2454{func}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I) &\equiv&
\def\mathdef2455#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2455{funcref}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\def\mathdef2456#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2456{(}~\def\mathdef2457#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2457{ref.func}~~\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I~\def\mathdef2458#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2458{)})
\end{array}\]
Also, 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 \(\def\mathdef2459#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2459{func}\) keyword can be omitted as well.
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{table use} &
\epsilon &\equiv& \def\mathdef2460#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2460{(}~\def\mathdef2461#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2461{table}~~\def\mathdef2462#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2462{0}~\def\mathdef2463#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2463{)} \\
\def\mathdef2156#1{{}}\mathdef2156{element segment} &
\def\mathdef2464#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2464{(}~\def\mathdef2465#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2465{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2466#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2466{(}~\def\mathdef2467#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2467{offset}~~\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef2468#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2468{)}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I)~\def\mathdef2469#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2469{)}
&\equiv&
\def\mathdef2470#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2470{(}~\def\mathdef2471#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2471{elem}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~\def\mathdef2472#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2472{(}~\def\mathdef2473#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2473{table}~~\def\mathdef2474#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2474{0}~\def\mathdef2475#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2475{)}~~\def\mathdef2476#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2476{(}~\def\mathdef2477#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2477{offset}~~\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef2478#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2478{)}~~\def\mathdef2479#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2479{func}~~\href{../text/conventions.html#text-vec}{\mathtt{vec}}(\href{../text/modules.html#text-funcidx}{\mathtt{funcidx}}_I)~\def\mathdef2480#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2480{)}
\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\mathdef2156#1{{}}\mathdef2156{data segment} & \href{../text/modules.html#text-data}{\mathtt{data}}_I &::=&
\def\mathdef2481#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2481{(}~\def\mathdef2482#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2482{data}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~b^\ast{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef2483#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2483{)} \\ &&& \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-data}{\mathsf{passive}} \} \\ &&|&
\def\mathdef2484#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2484{(}~\def\mathdef2485#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2485{data}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~x{:}\href{../text/modules.html#text-memuse}{\mathtt{memuse}}_I~~\def\mathdef2486#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2486{(}~\def\mathdef2487#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2487{offset}~~e{:}\href{../text/instructions.html#text-expr}{\mathtt{expr}}_I~\def\mathdef2488#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2488{)}~~b^\ast{:}\href{../text/modules.html#text-datastring}{\mathtt{datastring}}~\def\mathdef2489#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2489{)} \\ &&& \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-data}{\mathsf{active}}~\{ \href{../syntax/modules.html#syntax-data}{\mathsf{memory}}~x', \href{../syntax/modules.html#syntax-data}{\mathsf{offset}}~e \} \} \\
\def\mathdef2156#1{{}}\mathdef2156{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\mathdef2156#1{{}}\mathdef2156{memory use} & \href{../text/modules.html#text-memuse}{\mathtt{memuse}}_I &::=&
\def\mathdef2490#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2490{(}~\def\mathdef2491#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2491{memory}~~x{:}\href{../text/modules.html#text-memidx}{\mathtt{memidx}}_I ~\def\mathdef2492#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2492{)}
\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:
\[\begin{array}{llcll}
\def\mathdef2156#1{{}}\mathdef2156{data offset} &
\href{../text/instructions.html#text-instr}{\mathtt{instr}} &\equiv&
\def\mathdef2493#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2493{(}~\def\mathdef2494#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2494{offset}~~\href{../text/instructions.html#text-instr}{\mathtt{instr}}~\def\mathdef2495#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2495{)}
\end{array}\]
Also, a memory use can be omitted, defaulting to \(\mathtt{0}\).
\[\begin{split}\begin{array}{llclll}
\def\mathdef2156#1{{}}\mathdef2156{memory use} &
\epsilon &\equiv& \def\mathdef2496#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2496{(}~\def\mathdef2497#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2497{memory}~~\def\mathdef2498#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2498{0}~\def\mathdef2499#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2499{)} \\
\end{array}\end{split}\]
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\mathdef2156#1{{}}\mathdef2156{module} & \href{../text/modules.html#text-module}{\mathtt{module}} &
\begin{array}[t]{@{}cllll}
::=&
\def\mathdef2500#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2500{(}~\def\mathdef2501#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2501{module}~~\href{../text/values.html#text-id}{\mathtt{id}}^?~~(m{:}\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}_I)^\ast~\def\mathdef2502#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2502{)}
\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\mathdef2156#1{{}}\mathdef2156{module field} & \href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}_I &
\begin{array}[t]{@{}clll}
::=&
\mathit{ty}{:}\href{../text/modules.html#text-typedef}{\mathtt{type}} &\Rightarrow& \{\href{../syntax/modules.html#syntax-module}{\mathsf{types}}~\mathit{ty}\} \\ |&
\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\mathdef2503#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2503{(}~\def\mathdef2504#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2504{type}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\mathit{ft}{:}\href{../text/types.html#text-functype}{\mathtt{functype}}~\def\mathdef2505#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2505{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{types}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?), \href{../text/conventions.html#text-context}{\mathsf{typedefs}}~\mathit{ft}\} \\
\mathrm{idc}(\def\mathdef2506#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2506{(}~\def\mathdef2507#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2507{func}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2508#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2508{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{funcs}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef2509#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2509{(}~\def\mathdef2510#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2510{table}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2511#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2511{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{tables}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef2512#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2512{(}~\def\mathdef2513#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2513{memory}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2514#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2514{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{mems}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef2515#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2515{(}~\def\mathdef2516#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2516{global}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2517#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2517{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{globals}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef2518#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2518{(}~\def\mathdef2519#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2519{elem}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2520#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2520{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{elem}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef2521#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2521{(}~\def\mathdef2522#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2522{data}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2523#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2523{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{data}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef2524#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2524{(}~\def\mathdef2525#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2525{import}~\dots~\def\mathdef2526#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2526{(}~\def\mathdef2527#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2527{func}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2528#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2528{)}~\def\mathdef2529#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2529{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{funcs}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef2530#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2530{(}~\def\mathdef2531#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2531{import}~\dots~\def\mathdef2532#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2532{(}~\def\mathdef2533#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2533{table}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2534#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2534{)}~\def\mathdef2535#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2535{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{tables}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef2536#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2536{(}~\def\mathdef2537#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2537{import}~\dots~\def\mathdef2538#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2538{(}~\def\mathdef2539#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2539{memory}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2540#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2540{)}~\def\mathdef2541#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2541{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{mems}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef2542#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2542{(}~\def\mathdef2543#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2543{import}~\dots~\def\mathdef2544#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2544{(}~\def\mathdef2545#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2545{global}~\href{../text/values.html#text-id}{\mathtt{id}}^?~\dots~\def\mathdef2546#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2546{)}~\def\mathdef2547#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2547{)}) &=&
\{\href{../text/conventions.html#text-context}{\mathsf{globals}}~(\href{../text/values.html#text-id}{\mathtt{id}}^?)\} \\
\mathrm{idc}(\def\mathdef2548#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2548{(}~\dots~\def\mathdef2549#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2549{)}) &=&
\{\} \\
\end{array}\end{split}\]
Abbreviations¶
In a source file, the toplevel \(\mathtt{(module}~\dots\mathtt{)}\) surrounding the module body may be omitted.
\[\begin{array}{llcll}
\def\mathdef2156#1{{}}\mathdef2156{module} &
\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}^\ast &\equiv&
\def\mathdef2550#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2550{(}~\def\mathdef2551#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2551{module}~~\href{../text/modules.html#text-modulefield}{\mathtt{modulefield}}^\ast~\def\mathdef2552#1{\mbox{‘}\mathtt{#1}\mbox{’}}\mathdef2552{)}
\end{array}\]