Types¶

Various entities in WebAssembly are classified by types. Types are checked during validation, instantiation, and possibly execution.

Number Types¶

Number types classify numeric values.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{number type} & \href{../syntax/types.html#syntax-numtype}{\mathit{numtype}} &::=& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} ~|~ \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} ~|~ \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} ~|~ \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ \end{array}\end{split}\]

The types \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}\) and \(\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}\) classify 32 and 64 bit integers, respectively. Integers are not inherently signed or unsigned, their interpretation is determined by individual operations.

The types \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}\) and \(\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}\) classify 32 and 64 bit floating-point data, respectively. They correspond to the respective binary floating-point representations, also known as single and double precision, as defined by the IEEE 754 standard (Section 3.3).

Number types are transparent, meaning that their bit patterns can be observed. Values of number type can be stored in memories.

Conventions¶

The notation \(|t|\) denotes the bit width of a number type \(t\). That is, \(|\href{../syntax/types.html#syntax-valtype}{\mathsf{i32}}| = |\href{../syntax/types.html#syntax-valtype}{\mathsf{f32}}| = 32\) and \(|\href{../syntax/types.html#syntax-valtype}{\mathsf{i64}}| = |\href{../syntax/types.html#syntax-valtype}{\mathsf{f64}}| = 64\).

Vector Types¶

Vector types classify vectors of numeric values processed by vector instructions (also known as SIMD instructions, single instruction multiple data).

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{vector type} & \href{../syntax/types.html#syntax-vectype}{\mathit{vectype}} &::=& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}} \\ \end{array}\end{split}\]

The type \(\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}\) corresponds to a 128 bit vector of packed integer or floating-point data. The packed data can be interpreted as signed or unsigned integers, single or double precision floating-point values, or a single 128 bit type. The interpretation is determined by individual operations.

Vector types, like number types are transparent, meaning that their bit patterns can be observed. Values of vector type can be stored in memories.

Conventions¶

The notation \(|t|\) for bit width extends to vector types as well, that is, \(|\href{../syntax/types.html#syntax-valtype}{\mathsf{v128}}| = 128\).

Reference Types¶

Reference types classify first-class references to objects in the runtime store.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{reference type} & \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} &::=& \href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}} ~|~ \href{../syntax/types.html#syntax-reftype}{\mathsf{exnref}} ~|~ \href{../syntax/types.html#syntax-reftype}{\mathsf{externref}} \\ \end{array}\end{split}\]

The type \(\href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}}\) denotes the infinite union of all references to functions, regardless of their function types.

The type \(\href{../syntax/types.html#syntax-reftype}{\mathsf{exnref}}\) denotes the infinite union of all references to exceptions, regardless of their associated tag types.

The type \(\href{../syntax/types.html#syntax-reftype}{\mathsf{externref}}\) denotes the infinite union of all references to objects owned by the embedder and that can be passed into WebAssembly under this type.

Reference types are opaque, meaning that neither their size nor their bit pattern can be observed. Values of reference type can be stored in tables.

Value Types¶

Value types classify the individual values that WebAssembly code can compute with and the values that a variable accepts. They are either number types, vector types, or reference types.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{value type} & \href{../syntax/types.html#syntax-valtype}{\mathit{valtype}} &::=& \href{../syntax/types.html#syntax-numtype}{\mathit{numtype}} ~|~ \href{../syntax/types.html#syntax-vectype}{\mathit{vectype}} ~|~ \href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} \\ \end{array}\end{split}\]

Conventions¶

The meta variable \(t\) ranges over value types or subclasses thereof where clear from context.

Result Types¶

Result types classify the result of executing instructions or functions, which is a sequence of values, written with brackets.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{result type} & \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}} &::=& [\href{../syntax/conventions.html#syntax-vec}{\mathit{vec}}(\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}})] \\ \end{array}\end{split}\]

Function Types¶

Function types classify the signature of functions, mapping a vector of parameters to a vector of results. They are also used to classify the inputs and outputs of instructions.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{function type} & \href{../syntax/types.html#syntax-functype}{\mathit{functype}} &::=& \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}} \href{../syntax/types.html#syntax-functype}{\rightarrow} \href{../syntax/types.html#syntax-resulttype}{\mathit{resulttype}} \\ \end{array}\end{split}\]

Limits¶

Limits classify the size range of resizeable storage associated with memory types and table types.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{limits} & \href{../syntax/types.html#syntax-limits}{\mathit{limits}} &::=& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~\href{../syntax/values.html#syntax-int}{\mathit{u32}}, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~\href{../syntax/values.html#syntax-int}{\mathit{u32}}^? \} \\ \end{array}\end{split}\]

If no maximum is given, the respective storage can grow to any size.

Memory Types¶

Memory types classify linear memories and their size range.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{memory type} & \href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} &::=& \href{../syntax/types.html#syntax-limits}{\mathit{limits}} \\ \end{array}\end{split}\]

The limits constrain the minimum and optionally the maximum size of a memory. The limits are given in units of page size.

Table Types¶

Table types classify tables over elements of reference type within a size range.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{table type} & \href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} &::=& \href{../syntax/types.html#syntax-limits}{\mathit{limits}}~\href{../syntax/types.html#syntax-reftype}{\mathit{reftype}} \\ \end{array}\end{split}\]

Like memories, tables are constrained by limits for their minimum and optionally maximum size. The limits are given in numbers of entries.

Note

In future versions of WebAssembly, additional element types may be introduced.

Tag Types¶

Tag types classify the signature of tags with a function type.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{tag type} &\href{../syntax/types.html#syntax-tagtype}{\mathit{tagtype}} &::=& \href{../syntax/types.html#syntax-functype}{\mathit{functype}} \\ \end{array}\end{split}\]

Currently tags are only used for categorizing exceptions. The parameters of \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\) define the list of values associated with the exception thrown with this tag. Furthermore, it is an invariant of the semantics that every \(\href{../syntax/types.html#syntax-functype}{\mathit{functype}}\) in a valid tag type for an exception has an empty result type.

Note

Future versions of WebAssembly may have additional uses for tags, and may allow non-empty result types in the function types of tags.

Global Types¶

Global types classify global variables, which hold a value and can either be mutable or immutable.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{global type} & \href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} &::=& \href{../syntax/types.html#syntax-mut}{\mathit{mut}}~\href{../syntax/types.html#syntax-valtype}{\mathit{valtype}} \\ \def\mathdef2616#1{{}}\mathdef2616{mutability} & \href{../syntax/types.html#syntax-mut}{\mathit{mut}} &::=& \href{../syntax/types.html#syntax-mut}{\mathsf{const}} ~|~ \href{../syntax/types.html#syntax-mut}{\mathsf{var}} \\ \end{array}\end{split}\]

External Types¶

External types classify imports and external values with their respective types.

\[\begin{split}\begin{array}{llll} \def\mathdef2616#1{{}}\mathdef2616{external types} & \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}} &::=& \href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}} ~|~ \href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} ~|~ \href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} ~|~ \href{../syntax/types.html#syntax-tagtype}{\mathsf{tag}}~\href{../syntax/types.html#syntax-tagtype}{\mathit{tagtype}} ~|~ \href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} \\ \end{array}\end{split}\]

Conventions¶

The following auxiliary notation is defined for sequences of external types. It filters out entries of a specific kind in an order-preserving fashion:

\(\href{../syntax/types.html#syntax-externtype}{\mathrm{funcs}}(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast) = [\href{../syntax/types.html#syntax-functype}{\mathit{functype}} ~|~ (\href{../syntax/types.html#syntax-externtype}{\mathsf{func}}~\href{../syntax/types.html#syntax-functype}{\mathit{functype}}) \in \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast]\)
\(\href{../syntax/types.html#syntax-externtype}{\mathrm{tables}}(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast) = [\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}} ~|~ (\href{../syntax/types.html#syntax-externtype}{\mathsf{table}}~\href{../syntax/types.html#syntax-tabletype}{\mathit{tabletype}}) \in \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast]\)
\(\href{../syntax/types.html#syntax-externtype}{\mathrm{mems}}(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast) = [\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}} ~|~ (\href{../syntax/types.html#syntax-externtype}{\mathsf{mem}}~\href{../syntax/types.html#syntax-memtype}{\mathit{memtype}}) \in \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast]\)
\(\href{../syntax/types.html#syntax-externtype}{\mathrm{tags}}(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast) = [\href{../syntax/types.html#syntax-tagtype}{\mathit{tagtype}} ~|~ (\href{../syntax/types.html#syntax-tagtype}{\mathsf{tag}}~\href{../syntax/types.html#syntax-tagtype}{\mathit{tagtype}}) \in \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast]\)
\(\href{../syntax/types.html#syntax-externtype}{\mathrm{globals}}(\href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast) = [\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}} ~|~ (\href{../syntax/types.html#syntax-externtype}{\mathsf{global}}~\href{../syntax/types.html#syntax-globaltype}{\mathit{globaltype}}) \in \href{../syntax/types.html#syntax-externtype}{\mathit{externtype}}^\ast]\)