Главная Manuals WebAssembly Specification Release 1.1 (Draft 2021-12-18)

Search copyright infringement

Content .. 2 3 4 5 ..

WebAssembly Specification Release 1.1 (Draft 2021-12-18) - page 4

2.5.8 Data Segments

The initial contents of a

are zero bytes.

Data segments

can be used to initialize a range of memory from

a static

of

The

component of a module defines a vector of data segments.

Like element segments, data segments have a mode that identifies them as either

passive

or

active

. A passive data

segment’s contents can be copied into a memory using the

instruction. An active data segment copies

its contents into a memory during

instantiation

, as specified by a

and a

constant expression

defining

an offset into that memory.

::=

::=

|

Data segments are referenced through

Note:

In the current version of WebAssembly, at most one memory is allowed in a module. Consequently, the

only valid

is

0

.

2.5.9 Start Function

The

component of a module declares the

function index

of a

start function

that is automatically invoked when

the module is

, after

and

have been initialized.

::=

Note:

The start function is intended for initializing the state of a module. The module and its exports are not

accessible before this initialization has completed.

2.5.10 Exports

The

component of a module defines a set of

exports

that become accessible to the host environment once

the module has been

::=

::=

|

|

|

Each export is labeled by a unique

. Exportable definitions are

, and

which are referenced through a respective descriptor.

Conventions

The following auxiliary notation is defined for sequences of exports, filtering out indices of a specific kind in an

order-preserving fashion:

•

) = [

|

∈

*

]

•

) = [

|

∈

*

]

•

) = [

|

∈

*

]

•

) = [

|

∈

*

]

2.5. Modules

23

2.5.11 Imports

The

component of a module defines a set of

imports

that are required for

instantiation

::=

::=

|

|

|

Each import is labeled by a two-level

space, consisting of a

name and a

for an entity within

that module. Importable definitions are

, and

. Each import is specified by a

descriptor with a respective type that a definition provided during instantiation is required to match.
Every import defines an index in the respective

. In each index space, the indices of imports go before

the first index of any definition contained in the module itself.

Note:

Unlike export names, import names are not necessarily unique. It is possible to import the same

pair multiple times; such imports may even have different type descriptions, including different

kinds of entities. A module with such imports can still be instantiated depending on the specifics of how an

allows resolving and supplying imports. However, embedders are not required to support such overloading,

and a WebAssembly module itself cannot implement an overloaded name.

24

Chapter 2. Structure

CHAPTER

3

Validation

3.1 Conventions

Validation checks that a WebAssembly module is well-formed. Only valid modules can be

Validity is defined by a

type system

over the

abstract syntax

of a

and its contents. For each piece of abstract

syntax, there is a typing rule that specifies the constraints that apply to it. All rules are given in two

equivalent

forms:

1. In

prose

, describing the meaning in intuitive form.

2. In

formal notation

, describing the rule in mathematical form.

Note:

The prose and formal rules are equivalent, so that understanding of the formal notation is

not

required to read

this specification. The formalism offers a more concise description in notation that is used widely in programming

languages semantics and is readily amenable to mathematical proof.

In both cases, the rules are formulated in a

declarative

manner. That is, they only formulate the constraints, they do

not define an algorithm. The skeleton of a sound and complete algorithm for type-checking instruction sequences

according to this specification is provided in the

3.1.1 Contexts

Validity of an individual definition is specified relative to a

context

, which collects relevant information about the

surrounding

and the definitions in scope:

•

Types

: the list of types defined in the current module.

•

Functions

: the list of functions declared in the current module, represented by their function type.

•

Tables

: the list of tables declared in the current module, represented by their table type.

•

Memories

: the list of memories declared in the current module, represented by their memory type.

•

Globals

: the list of globals declared in the current module, represented by their global type.

13

The semantics is derived from the following article: Andreas Haas, Andreas Rossberg, Derek Schuff, Ben Titzer, Dan Gohman, Luke

Wagner, Alon Zakai, JF Bastien, Michael Holman.

Bringing the Web up to Speed with WebAssembly

. Proceedings of the 38th ACM

SIGPLAN Conference on Programming Language Design and Implementation (PLDI 2017). ACM 2017.

14

https://dl.acm.org/citation.cfm?doid=3062341.3062363

25

•

Element Segments

: the list of element segments declared in the current module, represented by their element

type.

•

Data Segments

: the list of data segments declared in the current module, each represented by an ok entry.

•

Locals

: the list of locals declared in the current function (including parameters), represented by their value

type.

•

Labels

: the stack of labels accessible from the current position, represented by their result type.

•

Return

: the return type of the current function, represented as an optional result type that is absent when no

return is allowed, as in free-standing expressions.

•

References

: the list of

function indices

that occur in the module outside functions and can hence be used to

form references inside them.

In other words, a context contains a sequence of suitable

for each

, describing each defined entry

in that space. Locals, labels and return type are only used for validating

in

function bodies

, and are

left empty elsewhere. The label stack is the only part of the context that changes as validation of an instruction

sequence proceeds.
More concretely, contexts are defined as

𝐶

with abstract syntax:

𝐶

::=

{

,

,

,

,

,

,

ok

*

,

,

,

,

}

In addition to field access written

𝐶.

field

the following notation is adopted for manipulating contexts:

• When spelling out a context, empty fields are omitted.
•

𝐶,

field

𝐴

*

denotes the same context as

𝐶

but with the elements

𝐴

*

prepended to its

field

component se-

quence.

Note:

We use

indexing notation

like

𝐶.

𝑖

]

to look up indices in their respective

in the context.

Context extension notation

𝐶,

field

𝐴

is primarily used to locally extend

relative

index spaces, such as

label indices

Accordingly, the notation is defined to append at the

front

of the respective sequence, introducing a new relative

index

0

and shifting the existing ones.

3.1.2 Prose Notation

Validation is specified by stylised rules for each relevant part of the

abstract syntax

. The rules not only state

constraints defining when a phrase is valid, they also classify it with a type. The following conventions are adopted

in stating these rules.

• A phrase

𝐴

is said to be “valid with type

𝑇

” if and only if all constraints expressed by the respective rules

are met. The form of

𝑇

depends on what

𝐴

is.

Note:

For example, if

𝐴

is a

, then

𝑇

is a

function type

; for an

𝐴

that is a

𝑇

is a

and so on.

• The rules implicitly assume a given

𝐶

.

26

Chapter 3. Validation

• In some places, this context is locally extended to a context

𝐶

′

with additional entries. The formulation

“Under context

𝐶

′

, ...

statement

...” is adopted to express that the following statement must apply under

the assumptions embodied in the extended context.

3.1.3 Formal Notation

Note:

This section gives a brief explanation of the notation for specifying typing rules formally. For the interested

reader, a more thorough introduction can be found in respective text books.

The proposition that a phrase

𝐴

has a respective type

𝑇

is written

𝐴

:

𝑇

. In general, however, typing is dependent

on a context

𝐶

. To express this explicitly, the complete form is a

judgement

𝐶

⊢

𝐴

:

𝑇

, which says that

𝐴

:

𝑇

holds under the assumptions encoded in

𝐶

.

The formal typing rules use a standard approach for specifying type systems, rendering them into

deduction rules

.

Every rule has the following general form:

premise

1

premise

2

. . .

premise

𝑛

conclusion

Such a rule is read as a big implication: if all premises hold, then the conclusion holds. Some rules have no

premises; they are

axioms

whose conclusion holds unconditionally. The conclusion always is a judgment

𝐶

⊢

𝐴

:

𝑇

, and there is one respective rule for each relevant construct

𝐴

of the abstract syntax.

Note:

For example, the typing rule for the

instruction can be given as an axiom:

𝐶

: [

The instruction is always valid with type

] (saying that it consumes two

values and produces

one), independent of any side conditions.
An instruction like

can be typed as follows:

𝐶.

𝑥

] =

𝑡

𝐶

𝑥

: []

[

𝑡

]

Here, the premise enforces that the immediate

𝑥

exists in the context. The instruction produces a value

of its respective type

𝑡

(and does not consume any values). If

𝐶.

𝑥

]

does not exist then the premise does not

hold, and the instruction is ill-typed.
Finally, a

instruction requires a recursive rule, where the premise is itself a typing judgement:

𝐶

: [

𝑡

*

1

[

𝑡

*

2

]

𝐶,

[

𝑡

*

2

]

: [

𝑡

*

1

[

𝑡

*

2

]

𝐶

blocktype instr

: [

𝑡

*

1

[

𝑡

*

2

]

A

instruction is only valid when the instruction sequence in its body is. Moreover, the result type must match

the block’s annotation

. If so, then the

instruction has the same type as the body. Inside the body an

additional label of the corresponding result type is available, which is expressed by extending the context

𝐶

with

the additional label information for the premise.

15

For example: Benjamin Pierce.

Types and Programming Languages

. The MIT Press 2002

16

https://www.cis.upenn.edu/~bcpierce/tapl/

3.1. Conventions

27

3.2 Types

Most

are universally valid. However, restrictions apply to

, which must be checked during validation.

Moreover,

are converted to plain

function types

for ease of processing.

3.2.1 Limits

must have meaningful bounds that are within a given range.

𝑚

?

}

• The value of

𝑛

must not be larger than

𝑘

.

• If the maximum

𝑚

?

is not empty, then:

–

Its value must not be larger than

𝑘

.

–

Its value must not be smaller than

𝑛

.

• Then the limit is valid within range

𝑘

.

𝑛

≤

𝑘

(

𝑚

≤

𝑘

)

?

(

𝑛

≤

𝑚

)

?

𝑚

?

}

:

𝑘

3.2.2 Block Types

may be expressed in one of two forms, both of which are converted to plain

function types

by the

following rules.

• The type

𝐶.

must be defined in the context.

• Then the block type is valid as

function type

𝐶.

.

𝐶.

]

• The block type is valid as

function type

]

.

] : []

]

3.2.3 Function Types

Function types

are always valid.

28

Chapter 3. Validation

[

𝑡

𝑛

1

[

𝑡

𝑚

2

]

• The function type is valid.

[

𝑡

*

1

[

𝑡

*

2

]

ok

3.2.4 Table Types

• The limits

must be

within range

2

32

−

1

.

• Then the table type is valid.

: 2

32

−

1

ok

3.2.5 Memory Types

• The limits

must be

within range

2

16

.

• Then the memory type is valid.

: 2

16

ok

3.2.6 Global Types

• The global type is valid.

ok

3.2.7 External Types

• The

function type

must be

• Then the external type is valid.

ok

ok

3.2. Types

29

• The

must be

• Then the external type is valid.

ok

ok

• The

must be

• Then the external type is valid.

ok

ok

• The

must be

• Then the external type is valid.

ok

ok

3.2.8 Import Subtyping

When

instantiating

a module,

external values

must be provided whose

are

matched

against the respective

external types

classifying each import. In some cases, this allows for a simple form of subtyping, as defined here.

Limits

𝑛

1

𝑚

?

1

}

match limits

𝑛

2

𝑚

?

2

}

if and only if:

•

𝑛

1

is larger than or equal to

𝑛

2

.

• Either:

–

𝑚

?

2

is empty.

• Or:

–

Both

𝑚

?

1

and

𝑚

?

2

are non-empty.

–

𝑚

1

is smaller than or equal to

𝑚

2

.

𝑛

1

≥

𝑛

2

⊢ {

𝑛

1

𝑚

?

1

} ≤ {

𝑛

2

𝜖

}

𝑛

1

≥

𝑛

2

𝑚

1

≤

𝑚

2

⊢ {

𝑛

1

𝑚

1

} ≤ {

𝑛

2

𝑚

2

}

30

Chapter 3. Validation

Functions

An

external type

matches

if and only if:

• Both

and

are the same.

Tables

An

external type

)

matches

)

if and only if:

• Limits

.

• Both

and

are the same.

Memories

An

external type

matches

if and only if:

• Limits

.

Globals

An

external type

matches

if and only if:

• Both

and

are the same.

3.3 Instructions

are classified by

stack types

[

𝑡

*

1

[

𝑡

*

2

]

that describe how instructions manipulate the

operand stack

stacktype

::=

[

opdtype

*

[

opdtype

*

]

opdtype

::=

| ⊥

The types describe the required input stack with

operand types

𝑡

*

1

that an instruction pops off and the provided

output stack with result values of types

𝑡

*

2

that it pushes back. Stack types are akin to

function types

, except that

they allow individual operands to be classified as

⊥

(

bottom

), indicating that the type is unconstrained. As an

auxiliary notion, an operand type

𝑡

1

matches

another operand type

𝑡

2

, if

𝑡

1

is either

⊥

or equal to

𝑡

2

. This is

extended to stack types in a point-wise manner.

⊢

𝑡

≤

𝑡

⊢ ⊥ ≤

𝑡

3.3. Instructions

31

(

⊢

𝑡

≤

𝑡

′

)

*

⊢

[

𝑡

*

]

≤

[

𝑡

′*

]

Note:

For example, the instruction

has type

, consuming two

values and producing

one.

Typing extends to

instruction sequences

. Such a sequence has a

function type

[

𝑡

*

1

[

𝑡

*

2

]

if the accumulative

effect of executing the instructions is consuming values of types

𝑡

*

1

off the operand stack and pushing new values

of types

𝑡

*

2

.

For some instructions, the typing rules do not fully constrain the type, and therefore allow for multiple types. Such

instructions are called

polymorphic

. Two degrees of polymorphism can be distinguished:

•

value-polymorphic

: the

𝑡

of one or several individual operands is unconstrained. That is the case

for all

parametric instructions

like

and

•

stack-polymorphic

: the entire (or most of the)

function type

[

𝑡

*

1

[

𝑡

*

2

]

of the instruction is uncon-

strained. That is the case for all

control instructions

that perform an

unconditional control transfer

, such

as

, and

In both cases, the unconstrained types or type sequences can be chosen arbitrarily, as long as they meet the con-

straints imposed for the surrounding parts of the program.

Note:

For example, the

instruction is valid with type

[

𝑡 𝑡

[

𝑡

]

, for any possible

𝑡

.

Consequently, both instruction sequences

1) (

2) (

3)

and

1

.

0) (

2

.

0) (

3)

are valid, with

𝑡

in the typing of

being instantiated to

or

, respectively.

The

instruction is valid with type

[

𝑡

*

1

[

𝑡

*

2

]

for any possible sequences of value types

𝑡

*

1

and

𝑡

*

2

.

Consequently,

unreachable i32

is valid by assuming type

for the

instruction. In contrast,

0)

is invalid, because there is no possible type to pick for the

instruction that would make the sequence

well-typed.

The

describes a type checking

that efficiently implements validation of instruction sequences

as prescribed by the rules given here.

3.3.1 Numeric Instructions

𝑐

• The instruction is valid with type

[

𝑡

]

.

𝑐

: []

[

𝑡

]

32

Chapter 3. Validation

• The instruction is valid with type

[

𝑡

[

𝑡

]

.

: [

𝑡

[

𝑡

]

• The instruction is valid with type

[

𝑡 𝑡

[

𝑡

]

.

: [

𝑡 𝑡

[

𝑡

]

• The instruction is valid with type

[

𝑡

.

: [

𝑡

• The instruction is valid with type

[

𝑡 𝑡

.

: [

𝑡 𝑡

𝑡

2

𝑡

1

• The instruction is valid with type

[

𝑡

1

[

𝑡

2

]

.

𝑡

2

𝑡

1

: [

𝑡

1

[

𝑡

2

]

3.3.2 Reference Instructions

𝑡

• The instruction is valid with type

[

𝑡

]

.

𝑡

: []

[

𝑡

]

Note:

In future versions of WebAssembly, there may be reference types for which no null reference is allowed.

• The instruction is valid with type

[

𝑡

, for any

reference type

𝑡

.

𝑡

: [

𝑡

3.3. Instructions

33

𝑥

• The function

𝐶.

𝑥

]

must be defined in the context.

• The

function index

𝑥

must be contained in

𝐶.

• The instruction is valid with type

.

𝐶.

𝑥

] =

𝑥

∈

𝐶.

𝑥

: []

3.3.3 Vector Instructions

Vector instructions can have a prefix to describe the

of the operand. Packed numeric types,

i8

and

i16

, are

not

, we define an auxiliary function to map such packed types into value types:

i8x16

)

=

i16x8

)

=

𝑡

x

𝑁

)

=

𝑡

We also define an auxiliary function to get number of packed numeric types in a

dimension

:

𝑡

x

𝑁

)

=

𝑁

𝑐

• The instruction is valid with type

.

𝑐

: []

• The instruction is valid with type

.

: [

• The instruction is valid with type

.

: [

• The instruction is valid with type

.

: [

34

Chapter 3. Validation

• The instruction is valid with type

.

: [

i8x16

• The instruction is valid with type

.

i8x16

: [

i8x16

• For all

, in

,

must be smaller than

32

.

• The instruction is valid with type

.

<

32)

16

i8x16

: [

• Let

𝑡

be

.

• The instruction is valid with type

[

𝑡

.

: [

• The lane index

must be smaller than

.

• The instruction is valid with type

.

𝑡

x

𝑁.

: [

• The lane index

must be smaller than

.

• Let

𝑡

be

.

• The instruction is valid with type

𝑡

.

: [

3.3. Instructions

35

• The instruction is valid with type

.

: [

• The instruction is valid with type

.

: [

• The instruction is valid with type

.

: [

• The instruction is valid with type

.

: [

• The instruction is valid with type

.

: [

_

zero

?

• The instruction is valid with type

.

_

zero

?

: [

• The instruction is valid with type

.

𝐶

: [

• The instruction is valid with type

.

: [

36

Chapter 3. Validation

_

s

• The instruction is valid with type

.

_

s

: [

• The instruction is valid with type

.

: [

• The instruction is valid with type

.

: [

3.3.4 Parametric Instructions

• The instruction is valid with type

[

𝑡

[]

, for any

𝑡

.

: [

𝑡

[]

Note:

Both

and

without annotation are

value-polymorphic

instructions.

(

𝑡

*

)

?

• If

𝑡

*

is present, then:

–

The length of

𝑡

*

must be

1

.

–

Then the instruction is valid with type

[

𝑡

*

𝑡

*

[

𝑡

*

]

.

• Else:

–

The instruction is valid with type

[

𝑡 𝑡

[

𝑡

]

, for any

𝑡

that

some

or

𝑡

: [

𝑡 𝑡

[

𝑡

]

⊢

𝑡

: [

𝑡 𝑡

[

𝑡

]

⊢

𝑡

: [

𝑡 𝑡

[

𝑡

]

Note:

In future versions of WebAssembly,

may allow more than one value per choice.

3.3. Instructions

37

3.3.5 Variable Instructions

𝑥

• The local

𝐶.

𝑥

]

must be defined in the context.

• Let

𝑡

be the

𝐶.

𝑥

]

.

• Then the instruction is valid with type

[

𝑡

]

.

𝐶.

𝑥

] =

𝑡

𝑥

: []

[

𝑡

]

𝑥

• The local

𝐶.

𝑥

]

must be defined in the context.

• Let

𝑡

be the

𝐶.

𝑥

]

.

• Then the instruction is valid with type

[

𝑡

[]

.

𝐶.

𝑥

] =

𝑡

𝑥

: [

𝑡

[]

𝑥

• The local

𝐶.

𝑥

]

must be defined in the context.

• Let

𝑡

be the

𝐶.

𝑥

]

.

• Then the instruction is valid with type

[

𝑡

[

𝑡

]

.

𝐶.

𝑥

] =

𝑡

𝑥

: [

𝑡

[

𝑡

]

𝑥

• The global

𝐶.

𝑥

]

must be defined in the context.

• Let

𝑡

be the

𝐶.

𝑥

]

.

• Then the instruction is valid with type

[

𝑡

]

.

𝐶.

𝑥

] =

𝑡

𝑥

: []

[

𝑡

]

𝑥

• The global

𝐶.

𝑥

]

must be defined in the context.

• Let

𝑡

be the

𝐶.

𝑥

]

.

• The mutability

must be

• Then the instruction is valid with type

[

𝑡

[]

.

𝐶.

𝑥

] =

𝑡

𝑥

: [

𝑡

[]

38

Chapter 3. Validation

Content .. 2 3 4 5 ..