# Types¶

Note

In some places, possible types include both type constructors or types denoted by type indices. Thus, the binary format for type constructors corresponds to the encodings of small negative $$\href{../binary/values.html#binary-sint}{\href{../syntax/values.html#syntax-int}{\mathit{s}N}}$$ values, such that they can unambiguously occur in the same place as (positive) type indices.

## Number Types¶

Number types are encoded by a single byte.

$\begin{split}\begin{array}{llclll@{\qquad\qquad}l} \def\mathdef1914#1{{}}\mathdef1914{number type} & \href{../binary/types.html#binary-numtype}{\mathtt{numtype}} &::=& \def\mathdef1953#1{\mathtt{0x#1}}\mathdef1953{7F} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i32}} \\ &&|& \def\mathdef1954#1{\mathtt{0x#1}}\mathdef1954{7E} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{i64}} \\ &&|& \def\mathdef1955#1{\mathtt{0x#1}}\mathdef1955{7D} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f32}} \\ &&|& \def\mathdef1956#1{\mathtt{0x#1}}\mathdef1956{7C} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{f64}} \\ \end{array}\end{split}$

## Vector Types¶

Vector types are also encoded by a single byte.

$\begin{split}\begin{array}{llclll@{\qquad\qquad}l} \def\mathdef1914#1{{}}\mathdef1914{vector type} & \href{../binary/types.html#binary-vectype}{\mathtt{vectype}} &::=& \def\mathdef1957#1{\mathtt{0x#1}}\mathdef1957{7B} &\Rightarrow& \href{../syntax/types.html#syntax-valtype}{\mathsf{v128}} \\ \end{array}\end{split}$

## Reference Types¶

Reference types are also encoded by a single byte.

$\begin{split}\begin{array}{llclll@{\qquad\qquad}l} \def\mathdef1914#1{{}}\mathdef1914{reference type} & \href{../binary/types.html#binary-reftype}{\mathtt{reftype}} &::=& \def\mathdef1958#1{\mathtt{0x#1}}\mathdef1958{70} &\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{funcref}} \\ &&|& \def\mathdef1959#1{\mathtt{0x#1}}\mathdef1959{6F} &\Rightarrow& \href{../syntax/types.html#syntax-reftype}{\mathsf{externref}} \\ \end{array}\end{split}$

## Value Types¶

Value types are encoded with their respective encoding as a number type, vector type, or reference type.

$\begin{split}\begin{array}{llclll@{\qquad\qquad}l} \def\mathdef1914#1{{}}\mathdef1914{value type} & \href{../binary/types.html#binary-valtype}{\mathtt{valtype}} &::=& t{:}\href{../binary/types.html#binary-numtype}{\mathtt{numtype}} &\Rightarrow& t \\ &&|& t{:}\href{../binary/types.html#binary-vectype}{\mathtt{vectype}} &\Rightarrow& t \\ &&|& t{:}\href{../binary/types.html#binary-reftype}{\mathtt{reftype}} &\Rightarrow& t \\ \end{array}\end{split}$

Note

Value types can occur in contexts where type indices are also allowed, such as in the case of block types. Thus, the binary format for types corresponds to the signed LEB128 encoding of small negative $$\href{../syntax/values.html#syntax-int}{\mathit{s}N}$$ values, so that they can coexist with (positive) type indices in the future.

## Result Types¶

Result types are encoded by the respective vectors of value types.

$\begin{split}\begin{array}{llclll@{\qquad\qquad}l} \def\mathdef1914#1{{}}\mathdef1914{result type} & \href{../binary/types.html#binary-resulttype}{\mathtt{resulttype}} &::=& t^\ast{:\,}\href{../binary/conventions.html#binary-vec}{\mathtt{vec}}(\href{../binary/types.html#binary-valtype}{\mathtt{valtype}}) &\Rightarrow& [t^\ast] \\ \end{array}\end{split}$

## Function Types¶

Function types are encoded by the byte $$\def\mathdef1960#1{\mathtt{0x#1}}\mathdef1960{60}$$ followed by the respective vectors of parameter and result types.

$\begin{split}\begin{array}{llclll@{\qquad\qquad}l} \def\mathdef1914#1{{}}\mathdef1914{function type} & \href{../binary/types.html#binary-functype}{\mathtt{functype}} &::=& \def\mathdef1961#1{\mathtt{0x#1}}\mathdef1961{60}~~\mathit{rt}_1{:\,}\href{../binary/types.html#binary-resulttype}{\mathtt{resulttype}}~~\mathit{rt}_2{:\,}\href{../binary/types.html#binary-resulttype}{\mathtt{resulttype}} &\Rightarrow& \mathit{rt}_1 \href{../syntax/types.html#syntax-functype}{\rightarrow} \mathit{rt}_2 \\ \end{array}\end{split}$

## Limits¶

Limits are encoded with a preceding flag indicating whether a maximum is present.

$\begin{split}\begin{array}{llclll} \def\mathdef1914#1{{}}\mathdef1914{limits} & \href{../binary/types.html#binary-limits}{\mathtt{limits}} &::=& \def\mathdef1962#1{\mathtt{0x#1}}\mathdef1962{00}~~n{:}\href{../binary/values.html#binary-int}{\def\mathdef1919#1{{\mathtt{u}#1}}\mathdef1919{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~\epsilon \} \\ &&|& \def\mathdef1963#1{\mathtt{0x#1}}\mathdef1963{01}~~n{:}\href{../binary/values.html#binary-int}{\def\mathdef1919#1{{\mathtt{u}#1}}\mathdef1919{\mathtt{32}}}~~m{:}\href{../binary/values.html#binary-int}{\def\mathdef1919#1{{\mathtt{u}#1}}\mathdef1919{\mathtt{32}}} &\Rightarrow& \{ \href{../syntax/types.html#syntax-limits}{\mathsf{min}}~n, \href{../syntax/types.html#syntax-limits}{\mathsf{max}}~m \} \\ \end{array}\end{split}$

## Memory Types¶

Memory types are encoded with their limits.

$\begin{split}\begin{array}{llclll@{\qquad\qquad}l} \def\mathdef1914#1{{}}\mathdef1914{memory type} & \href{../binary/types.html#binary-memtype}{\mathtt{memtype}} &::=& \mathit{lim}{:}\href{../binary/types.html#binary-limits}{\mathtt{limits}} &\Rightarrow& \mathit{lim} \\ \end{array}\end{split}$

## Table Types¶

Table types are encoded with their limits and the encoding of their element reference type.

$\begin{split}\begin{array}{llclll} \def\mathdef1914#1{{}}\mathdef1914{table type} & \href{../binary/types.html#binary-tabletype}{\mathtt{tabletype}} &::=& \mathit{et}{:}\href{../binary/types.html#binary-reftype}{\mathtt{reftype}}~~\mathit{lim}{:}\href{../binary/types.html#binary-limits}{\mathtt{limits}} &\Rightarrow& \mathit{lim}~\mathit{et} \\ \end{array}\end{split}$

## Global Types¶

Global types are encoded by their value type and a flag for their mutability.

$\begin{split}\begin{array}{llclll} \def\mathdef1914#1{{}}\mathdef1914{global type} & \href{../binary/types.html#binary-globaltype}{\mathtt{globaltype}} &::=& t{:}\href{../binary/types.html#binary-valtype}{\mathtt{valtype}}~~m{:}\href{../binary/types.html#binary-mut}{\mathtt{mut}} &\Rightarrow& m~t \\ \def\mathdef1914#1{{}}\mathdef1914{mutability} & \href{../binary/types.html#binary-mut}{\mathtt{mut}} &::=& \def\mathdef1964#1{\mathtt{0x#1}}\mathdef1964{00} &\Rightarrow& \href{../syntax/types.html#syntax-mut}{\mathsf{const}} \\ &&|& \def\mathdef1965#1{\mathtt{0x#1}}\mathdef1965{01} &\Rightarrow& \href{../syntax/types.html#syntax-mut}{\mathsf{var}} \\ \end{array}\end{split}$