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 $s N$ 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{array}{r} \begin{array}{llcllll} numtype & ::= & 0 x 7 F & \Rightarrow & i 32 \\ | & 0 x 7 E & \Rightarrow & i 64 \\ | & 0 x 7 D & \Rightarrow & f 32 \\ | & 0 x 7 C & \Rightarrow & f 64 \end{array} \end{array}

Vector Types¶

Vector types are also encoded by a single byte.

\begin{array}{r} \begin{array}{llcllll} vectype & ::= & 0 x 7 B & \Rightarrow & v 128 \end{array} \end{array}

Heap Types¶

Heap types are encoded as either a single byte, or as a type index encoded as a positive signed integer.

\begin{array}{r} \begin{array}{llcllll} absheaptype & ::= & 0 x 73 & \Rightarrow & nofunc \\ | & 0 x 72 & \Rightarrow & noextern \\ | & 0 x 71 & \Rightarrow & none \\ | & 0 x 70 & \Rightarrow & func \\ | & 0 x 6 F & \Rightarrow & extern \\ | & 0 x 6 E & \Rightarrow & any \\ | & 0 x 6 D & \Rightarrow & eq \\ | & 0 x 6 C & \Rightarrow & i 31 \\ | & 0 x 6 B & \Rightarrow & struct \\ | & 0 x 6 A & \Rightarrow & array \\ heaptype & ::= & ht : absheaptype & \Rightarrow & ht \\ | & x : s 33 & \Rightarrow & x & (if x \geq 0) \end{array} \end{array}

Reference Types¶

Reference types are either encoded by a single byte followed by a heap type, or, as a short form, directly as an abstract heap type.

\begin{array}{r} \begin{array}{llcllll} reftype & ::= & 0 x 64 ht : heaptype & \Rightarrow & ref ht \\ | & 0 x 63 ht : heaptype & \Rightarrow & ref null ht \\ | & ht : absheaptype & \Rightarrow & ref null ht \end{array} \end{array}

Value Types¶

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

\begin{array}{r} \begin{array}{llcllll} valtype & ::= & t : numtype & \Rightarrow & t \\ | & t : vectype & \Rightarrow & t \\ | & t : reftype & \Rightarrow & t \end{array} \end{array}

Note

The type $bot$ cannot occur in a module.

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 $s N$ 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{array}{r} \begin{array}{llcllll} resulttype & ::= & t^{*} : vec (valtype) & \Rightarrow & [t^{*}] \end{array} \end{array}

Function Types¶

Function types are encoded by the respective vectors of parameter and result types.

\begin{array}{r} \begin{array}{llcllll} functype & ::= & {rt}_{1} : resulttype {rt}_{2} : resulttype & \Rightarrow & {rt}_{1} \to {rt}_{2} \end{array} \end{array}

Aggregate Types¶

Aggregate types are encoded with their respective field types.

\begin{array}{r} \begin{array}{llcllll} arraytype & ::= & ft : fieldtype & \Rightarrow & ft \\ structtype & ::= & {ft}^{*} : vec (fieldtype) & \Rightarrow & {ft}^{*} \\ fieldtype & ::= & st : storagetype m : mut & \Rightarrow & m st \\ storagetype & ::= & t : valtype & \Rightarrow & t \\ | & t : packedtype & \Rightarrow & t \\ packedtype & ::= & 0 x 78 & \Rightarrow & i 8 \\ | & 0 x 77 & \Rightarrow & i 16 \end{array} \end{array}

Composite Types¶

Composite types are encoded by a distinct byte followed by a type encoding of the respective form.

\begin{array}{r} \begin{array}{llcllll} comptype & ::= & 0 x 5 E at : arraytype & \Rightarrow & array at \\ | & 0 x 5 F st : structtype & \Rightarrow & struct st \\ | & 0 x 60 ft : functype & \Rightarrow & func ft \end{array} \end{array}

Recursive Types¶

Recursive types are encoded by the byte $0 x 4 E$ followed by a vector of sub types. Additional shorthands are recognized for unary recursions and sub types without super types.

\begin{array}{r} \begin{array}{llcllll} rectype & ::= & 0 x 4 E {st}^{*} : vec (subtype) & \Rightarrow & rec {st}^{*} \\ | & st : subtype & \Rightarrow & rec st \\ subtype & ::= & 0 x 50 x^{*} : vec (typeidx) ct : comptype & \Rightarrow & sub x^{*} ct \\ | & 0 x 4 F x^{*} : vec (typeidx) ct : comptype & \Rightarrow & sub final x^{*} ct \\ | & ct : comptype & \Rightarrow & sub final ϵ ct \end{array} \end{array}

Limits¶

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

\begin{array}{r} \begin{array}{llclll} limits & ::= & 0 x 00 n : u 32 & \Rightarrow & {\min n, \max ϵ} \\ | & 0 x 01 n : u 32 m : u 32 & \Rightarrow & {\min n, \max m} \end{array} \end{array}

Memory Types¶

Memory types are encoded with their limits.

\begin{array}{r} \begin{array}{llcllll} memtype & ::= & \lim : limits & \Rightarrow & \lim \end{array} \end{array}

Table Types¶

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

\begin{array}{r} \begin{array}{llclll} tabletype & ::= & et : reftype \lim : limits & \Rightarrow & \lim et \end{array} \end{array}

Global Types¶

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

\begin{array}{r} \begin{array}{llclll} globaltype & ::= & t : valtype m : mut & \Rightarrow & m t \\ mut & ::= & 0 x 00 & \Rightarrow & const \\ | & 0 x 01 & \Rightarrow & var \end{array} \end{array}