AstSemantics.md

Abstract Syntax Tree Semantics

WebAssembly code is represented as an Abstract Syntax Tree (AST) where each node represents an expression. Each function body consists of a list of expressions. All expressions and operators are typed, with no implicit conversions, subtyping, or overloading rules.

This document explains the high-level design of the AST: its types, constructs, and semantics. For full details consult the formal Specification, for file-level encoding details consult Binary Encoding, and for the human-readable text representation consult Text Format.

Verification of WebAssembly code requires only a single pass with constant-time type checking and well-formedness checking.

WebAssembly offers a set of language-independent operators that closely match operators in many programming languages and are efficiently implementable on all modern computers.

The rationale document details why WebAssembly is designed as detailed in this document.

Order of evaluation

The evaluation order of child nodes is deterministic.

All nodes other than control flow constructs need to evaluate their child nodes in the order they appear in the serialized AST.

For example, the s-expression presentation of the i32.add node (i32.add (set_local $x (i32.const 1)) (set_local $x (i32.const 2))) would first evaluate the child node (set_local $x (i32.const 1)) and afterwards the child node (set_local $x (i32.const 2)).

The value of the local variable $x will be 2 after the i32.add node is fully evaluated.

Traps

Some operators may trap under some conditions, as noted below. In the MVP, trapping means that execution in the WebAssembly instance is terminated and abnormal termination is reported to the outside environment. In a JavaScript environment such as a browser, a trap results in throwing a JavaScript exception. If developer tools are active, attaching a debugger before the termination would be sensible.

Call stack space is limited by unspecified and dynamically varying constraints and is a source of nondeterminism. If program call stack usage exceeds the available call stack space at any time, a trap occurs.

Implementations must have an internal maximum call stack size, and every call must take up some resources toward exhausting that size (of course, dynamic resources may be exhausted much earlier). This rule exists to avoid differences in observable behavior; if some implementations have this property and others don't, the same program which runs successfully on some implementations may consume unbounded resources and fail on others. Also, in the future, it is expected that WebAssembly will add some form of stack-introspection functionality, in which case such optimizations would be directly observable.

Support for explicit tail calls is planned in the future, which would add an explicit tail-call operator with well-defined effects on stack introspection.

Types

WebAssembly has the following value types:

• i32: 32-bit integer
• i64: 64-bit integer
• f32: 32-bit floating point
• f64: 64-bit floating point

Each parameter and local variable has exactly one value type. Function signatures consist of a sequence of zero or more parameter types and a sequence of zero or more return types. (Note: in the MVP, a function can have at most one return type).

Note that the value types i32 and i64 are not inherently signed or unsigned. The interpretation of these types is determined by individual operators.

Linear Memory

A linear memory is a contiguous, byte-addressable range of memory spanning from offset 0 and extending up to a varying memory size. This size is always a multiple of the WebAssembly page size, which is fixed to 64KiB (though large page support may be added in an opt-in manner in the future). The initial state of a linear memory is defined by the module's linear memory and data sections. The memory size can be dynamically increased by the grow_memory operator.

A linear memory can be considered to be an untyped array of bytes, and it is unspecified how embedders map this array into their process' own virtual memory. Linear memory is sandboxed; it does not alias other linear memories, the execution engine's internal data structures, the execution stack, local variables, or other process memory.

Every WebAssembly instance has one specially-designated default linear memory which is the linear memory accessed by all the memory operators below. In the MVP, there are only default linear memories but new memory operators may be added after the MVP which can also access non-default memories.

Linear memories (default or otherwise) can either be imported or defined inside the module, with defaultness indicated by a flag on the import or definition. After import or definition, there is no difference when accessing a linear memory whether it was imported or defined internally.

In the MVP, linear memory cannot be shared between threads of execution. The addition of threads will allow this.

Linear Memory Accesses

Linear memory access is accomplished with explicit load and store operators. Integer loads can specify a storage size which is smaller than the result type as well as a signedness which determines whether the bytes are sign- or zero- extended into the result type.

• i32.load8_s: load 1 byte and sign-extend i8 to i32
• i32.load8_u: load 1 byte and zero-extend i8 to i32
• i32.load16_s: load 2 bytes and sign-extend i16 to i32
• i32.load16_u: load 2 bytes and zero-extend i16 to i32
• i32.load: load 4 bytes as i32
• i64.load8_s: load 1 byte and sign-extend i8 to i64
• i64.load8_u: load 1 byte and zero-extend i8 to i64
• i64.load16_s: load 2 bytes and sign-extend i16 to i64
• i64.load16_u: load 2 bytes and zero-extend i16 to i64
• i64.load32_s: load 4 bytes and sign-extend i32 to i64
• i64.load32_u: load 4 bytes and zero-extend i32 to i64
• i64.load: load 8 bytes as i64
• f32.load: load 4 bytes as f32
• f64.load: load 8 bytes as f64

Stores have an additional input operand which is the value to store to memory. Like loads, integer stores may specify a smaller storage size than the operand size in which case integer wrapping is implied.

• i32.store8: wrap i32 to i8 and store 1 byte
• i32.store16: wrap i32 to i16 and store 2 bytes
• i32.store: (no conversion) store 4 bytes
• i64.store8: wrap i64 to i8 and store 1 byte
• i64.store16: wrap i64 to i16 and store 2 bytes
• i64.store32: wrap i64 to i32 and store 4 bytes
• i64.store: (no conversion) store 8 bytes
• f32.store: (no conversion) store 4 bytes
• f64.store: (no conversion) store 8 bytes

Store operators do not produce a value.

The above operators operate on the default linear memory.

Addressing

Each linear memory access operator has an address operand and an unsigned integer byte offset immediate. The infinite-precision unsigned sum of the address operand's value with the offset's value is called the effective address, which is interpreted as an unsigned byte index into the linear memory.

Linear memory operators access the bytes starting at the effective address and extend for the number of bytes implied by the storage size. If any of the accessed bytes are beyond the current memory size, the access is considered out-of-bounds.

The use of infinite-precision in the effective address computation means that the addition of the offset to the address never causes wrapping, so if the address for an access is out-of-bounds, the effective address will always also be out-of-bounds.

In wasm32, address operands and offset attributes have type i32, and linear memory sizes are limited to 4 GiB (of course, actual sizes are further limited by available resources). In wasm64, address operands and offsets have type i64. The MVP only includes wasm32; subsequent versions will add support for wasm64 and thus >4 GiB linear memory.

Alignment

Each linear memory access operator also has an immediate positive integer power of 2 alignment attribute. An alignment value which is the same as the memory attribute size is considered to be a natural alignment. The alignment applies to the effective address and not merely the address operand, i.e. the immediate offset is taken into account when considering alignment.

The alignment has same type (determined by wasm32/wasm64, as described above) as the address and offset operands.

If the effective address of a memory access is a multiple of the alignment attribute value of the memory access, the memory access is considered aligned, otherwise it is considered misaligned. Aligned and misaligned accesses have the same behavior.

Alignment affects performance as follows:

• Aligned accesses with at least natural alignment are fast.
• Aligned accesses with less than natural alignment may be somewhat slower (think: implementation makes multiple accesses, either in software or in hardware).
• Misaligned access of any kind may be massively slower (think: implementation takes a signal and fixes things up).

Thus, it is recommend that WebAssembly producers align frequently-used data to permit the use of natural alignment access, and use loads and stores with the greatest alignment values practical, while always avoiding misaligned accesses.

Out of Bounds

Out of bounds accesses trap.

Resizing

In the MVP, linear memory can be resized by a grow_memory operator. The operand to this operator is in units of the WebAssembly page size, which is defined to be 64KiB (though large page support may be added in the future).

• grow_memory : grow linear memory by a given unsigned delta of pages. Return the previous memory size in units of pages or -1 on failure.

When a linear memory has a declared maximum memory size, grow_memory must fail if it would grow past the maximum. However, grow_memory may still fail before the maximum if it was not possible to reserve the space up front or if enabling the reserved memory fails. When there is no maximum memory size declared, grow_memory is expected to perform a system allocation which may fail.

The current size of the linear memory can be queried by the following operator:

• current_memory : return the current memory size in units of pages.

As stated above, linear memory is contiguous, meaning there are no "holes" in the linear address space. After the MVP, there are future features proposed to allow setting protection and creating mappings within the contiguous linear memory.

In the MVP, memory can only be grown. After the MVP, a memory shrinking operator may be added. However, due to normal fragmentation, applications are instead expected release unused physical pages from the working set using the discard future feature.

The above operators operate on the default linear memory.

Table

A table is similar to a linear memory whose elements, instead of being bytes, are opaque values of a particular table element type. This allows the table to contain values—like GC references, raw OS handles, or native pointers—that are accessed by WebAssembly code indirectly through an integer index. This feature bridges the gap between low-level, untrusted linear memory and high-level opaque handles/references at the cost of a bounds-checked table indirection.

The table's element type constrains the type of elements stored in the table and allows engines to avoid some type checks on table use. When a WebAssembly value is stored in a table, the value's type must precisely match the element type. Just like linear memory, updates to a table are observed immediately by all instances that reference the table. Depending on the operator/API used to store the value, this check may be static or dynamic. Host environments may also allow storing non-WebAssembly values in tables in which case, as with imports, the meaning of using the value is defined by the host environment.

Every WebAssembly instance has one specially-designated default table which is indexed by call_indirect and other future table operators. Tables can either be imported or defined inside the module, with defaultness indicated by a flag on the import or definition. After import or definition, there is no difference when calling into a table whether it was imported or defined internally.

In the MVP, the primary purpose of tables is to implement indirect function calls in C/C++ using an integer index as the pointer-to-function and the table to hold the array of indirectly-callable functions. Thus, in the MVP:

• tables may only be accessed from WebAssembly code via call_indirect;
• the only allowed table element type is anyfunc (function with any signature);
• tables may not be directly mutated or resized from WebAssembly code; this can only be done through the host environment (e.g., the the WebAssembly JavaScript API).

These restrictions may be relaxed in the future.

Local variables

Each function has a fixed, pre-declared number of local variables which occupy a single index space local to the function. Parameters are addressed as local variables. Local variables do not have addresses and are not aliased by linear memory. Local variables have value types and are initialized to the appropriate zero value for their type at the beginning of the function, except parameters which are initialized to the values of the arguments passed to the function.

• get_local: read the current value of a local variable
• set_local: set the current value of a local variable
• tee_local: like set_local, but also returns the set value

The details of index space for local variables and their types will be further clarified, e.g. whether locals with type i32 and i64 must be contiguous and separate from others, etc.

Global variables

A global variable stores a single value of a fixed value type and may be declared either mutable or immutable. This provides WebAssembly with memory locations that are disjoint from any linear memory and thus cannot be arbitrarily aliased as bits.

Global variables are accessed via an integer index into the module-defined global index space. Global variables can either be imported or defined inside the module. After import or definition, there is no difference when accessing a global.

• get_global: get the current value of a global variable
• set_global: set the current value of a global variable

It is a validation error for a set_global to index an immutable global variable.

In the MVP, the primary use case of global variables is to represent instantiation-time immutable values as a useful building block for dynamic linking.

After the MVP, when reference types are added to the set of value types, global variables will be necessary to allow sharing reference types between threads since shared linear memory cannot load or store references.

Control flow structures

WebAssembly offers basic structured control flow with the following constructs. Since all AST nodes are expressions in WebAssembly, control constructs may yield a value and may appear as children of other expressions.

• nop: an empty operator that does not yield a value
• block: a fixed-length sequence of expressions with a label at the end
• loop: a block with an additional label at the beginning which may be used to form loops
• if: if expression with a list of then expressions and a list of else expressions
• br: branch to a given label in an enclosing construct
• br_if: conditionally branch to a given label in an enclosing construct
• br_table: a jump table which jumps to a label in an enclosing construct
• return: return zero or more values from this function

Branches and nesting

The br and br_if constructs express low-level branching. Branches may only reference labels defined by an outer enclosing construct. This means that, for example, references to a block's label can only occur within the block's body.

In practice, outer blocks can be used to place labels for any given branching pattern, except for one restriction: one can't branch into the middle of a loop from outside it. This restriction ensures all control flow graphs are well-structured in the exact sense as in high-level languages like Java, JavaScript, Rust and Go. To further see the parallel, note that a br to a block's label is functionally equivalent to a labeled break in high-level languages in that a br simply breaks out of a block.

Branches that exit a block, loop, or br_table may take a subexpression that yields a value for the exited construct. If present, it is the first operand before any others.

Yielding values from control constructs

The nop, br, br_if, br_table, and return constructs do not yield values. Other control constructs may yield values if their subexpressions yield values:

• block: yields either the value of the last expression in the block or the result of an inner branch that targeted the label of the block
• loop: yields either the value of the last expression in the loop or the result of an inner branch that targeted the end label of the loop
• if: yields either the value of the last then expression or the last else expression or the result of an inner branch that targeted the label of one of these.

In all constructs containing block-like sequences of expressions, all expressions but the last must not yield a value. The drop operator can be used to explicitly discard unwanted expression results.

br_table

A br_table consists of a zero-based array of labels, a default label, and an index operand. A br_table jumps to the label indexed in the array or the default label if the index is out of bounds.

Calls

Each function has a signature, which consists of:

• Return types, which are a sequence of value types
• Argument types, which are a sequence of value types

WebAssembly doesn't support variable-length argument lists (aka varargs). Compilers targeting WebAssembly can instead support them through explicit accesses to linear memory.

In the MVP, the length of the return types sequence may only be 0 or 1. This restriction may be lifted in the future.

Direct calls to a function specify the callee by an index into the function index space.

• call: call function directly

A direct call to a function with a mismatched signature is a module verification error.

Indirect calls to a function indicate the callee with an i32 index into a table. The expected signature of the target function (specified by its index in the types section) is given as a second immediate.

• call_indirect: call function indirectly

Unlike call, which checks that the caller and callee signatures match statically as part of validation, call_indirect checks for signature match dynamically, comparing the caller's expected signature with the callee function's signature and and trapping if there is a mismatch. Since the callee may be in a different module which necessarily has a separate types section, and thus index space of types, the signature match must compare the underlying func_type. As noted above, table elements may also be host-environment-defined values in which case the meaning of a call (and how the signature is checked) is defined by the host-environment, much like calling an import.

In the MVP, the single call_indirect operator accesses the default table.

Multiple return value calls will be possible, though possibly not in the MVP. The details of multiple-return-value calls needs clarification. Calling a function that returns multiple values will likely have to be a statement that specifies multiple local variables to which to assign the corresponding return values.

Constants

These operators have an immediate operand of their associated type which is produced as their result value. All possible values of all types are supported (including NaN values of all possible bit patterns).

• i32.const: produce the value of an i32 immediate
• i64.const: produce the value of an i64 immediate
• f32.const: produce the value of an f32 immediate
• f64.const: produce the value of an f64 immediate

32-bit Integer operators

Integer operators are signed, unsigned, or sign-agnostic. Signed operators use two's complement signed integer representation.

Signed and unsigned operators trap whenever the result cannot be represented in the result type. This includes division and remainder by zero, and signed division overflow (INT32_MIN / -1). Signed remainder with a non-zero denominator always returns the correct value, even when the corresponding division would trap. Sign-agnostic operators silently wrap overflowing results into the result type.

• i32.add: sign-agnostic addition
• i32.sub: sign-agnostic subtraction
• i32.mul: sign-agnostic multiplication (lower 32-bits)
• i32.div_s: signed division (result is truncated toward zero)
• i32.div_u: unsigned division (result is floored)
• i32.rem_s: signed remainder (result has the sign of the dividend)
• i32.rem_u: unsigned remainder
• i32.and: sign-agnostic bitwise and
• i32.or: sign-agnostic bitwise inclusive or
• i32.xor: sign-agnostic bitwise exclusive or
• i32.shl: sign-agnostic shift left
• i32.shr_u: zero-replicating (logical) shift right
• i32.shr_s: sign-replicating (arithmetic) shift right
• i32.rotl: sign-agnostic rotate left
• i32.rotr: sign-agnostic rotate right
• i32.eq: sign-agnostic compare equal
• i32.ne: sign-agnostic compare unequal
• i32.lt_s: signed less than
• i32.le_s: signed less than or equal
• i32.lt_u: unsigned less than
• i32.le_u: unsigned less than or equal
• i32.gt_s: signed greater than
• i32.ge_s: signed greater than or equal
• i32.gt_u: unsigned greater than
• i32.ge_u: unsigned greater than or equal
• i32.clz: sign-agnostic count leading zero bits (All zero bits are considered leading if the value is zero)
• i32.ctz: sign-agnostic count trailing zero bits (All zero bits are considered trailing if the value is zero)
• i32.popcnt: sign-agnostic count number of one bits
• i32.eqz: compare equal to zero (return 1 if operand is zero, 0 otherwise)

Shifts counts are wrapped to be less than the log-base-2 of the number of bits in the value to be shifted, as an unsigned quantity. For example, in a 32-bit shift, only the least 5 significant bits of the count affect the result. In a 64-bit shift, only the least 6 significant bits of the count affect the result.

Rotate counts are treated as unsigned. A count value greater than or equal to the number of bits in the value to be rotated yields the same result as if the count was wrapped to its least significant N bits, where N is 5 for an i32 value or 6 for an i64 value.

All comparison operators yield 32-bit integer results with 1 representing true and 0 representing false.

64-bit integer operators

The same operators are available on 64-bit integers as the those available for 32-bit integers.

Floating point operators

Floating point arithmetic follows the IEEE 754-2008 standard, except that:

• The IEEE 754-2008 section 6.2 recommendation that operations propagate NaN bits from their operands is permitted but not required.
• WebAssembly uses "non-stop" mode, and floating point exceptions are not otherwise observable. In particular, neither alternate floating point exception handling attributes nor the non-computational operators on status flags are supported. There is no observable difference between quiet and signalling NaN. However, positive infinity, negative infinity, and NaN are still always produced as result values to indicate overflow, invalid, and divide-by-zero conditions, as specified by IEEE 754-2008.
• WebAssembly uses the round-to-nearest ties-to-even rounding attribute, except where otherwise specified. Non-default directed rounding attributes are not supported.

In the future, these limitations may be lifted, enabling full IEEE 754-2008 support.

Note that not all operators required by IEEE 754-2008 are provided directly. However, WebAssembly includes enough functionality to support reasonable library implementations of the remaining required operators.

When the result of any arithmetic operation other than neg, abs, or copysign is a NaN, the sign bit and the fraction field (which does not include the implicit leading digit of the significand) of the NaN are computed as follows:

• If the fraction fields of all NaN inputs to the instruction all consist of 1 in the most significant bit and 0 in the remaining bits, or if there are no NaN inputs, the result is a NaN with a nondeterministic sign bit, 1 in the most significant bit of the fraction field, and all zeros in the remaining bits of the fraction field.

• Otherwise the result is a NaN with a nondeterministic sign bit, 1 in the most significant bit of the fraction field, and nondeterminsitic values in the remaining bits of the fraction field.

32-bit floating point operations are as follows:

• f32.add: addition
• f32.sub: subtraction
• f32.mul: multiplication
• f32.div: division
• f32.abs: absolute value
• f32.neg: negation
• f32.copysign: copysign
• f32.ceil: ceiling operator
• f32.floor: floor operator
• f32.trunc: round to nearest integer towards zero
• f32.nearest: round to nearest integer, ties to even
• f32.eq: compare ordered and equal
• f32.ne: compare unordered or unequal
• f32.lt: compare ordered and less than
• f32.le: compare ordered and less than or equal
• f32.gt: compare ordered and greater than
• f32.ge: compare ordered and greater than or equal
• f32.sqrt: square root
• f32.min: minimum (binary operator); if either operand is NaN, returns NaN
• f32.max: maximum (binary operator); if either operand is NaN, returns NaN

64-bit floating point operators:

• f64.add: addition
• f64.sub: subtraction
• f64.mul: multiplication
• f64.div: division
• f64.abs: absolute value
• f64.neg: negation
• f64.copysign: copysign
• f64.ceil: ceiling operator
• f64.floor: floor operator
• f64.trunc: round to nearest integer towards zero
• f64.nearest: round to nearest integer, ties to even
• f64.eq: compare ordered and equal
• f64.ne: compare unordered or unequal
• f64.lt: compare ordered and less than
• f64.le: compare ordered and less than or equal
• f64.gt: compare ordered and greater than
• f64.ge: compare ordered and greater than or equal
• f64.sqrt: square root
• f64.min: minimum (binary operator); if either operand is NaN, returns NaN
• f64.max: maximum (binary operator); if either operand is NaN, returns NaN

min and max operators treat -0.0 as being effectively less than 0.0.

In floating point comparisons, the operands are unordered if either operand is NaN, and ordered otherwise.

Datatype conversions, truncations, reinterpretations, promotions, and demotions

• i32.wrap/i64: wrap a 64-bit integer to a 32-bit integer
• i32.trunc_s/f32: truncate a 32-bit float to a signed 32-bit integer
• i32.trunc_s/f64: truncate a 64-bit float to a signed 32-bit integer
• i32.trunc_u/f32: truncate a 32-bit float to an unsigned 32-bit integer
• i32.trunc_u/f64: truncate a 64-bit float to an unsigned 32-bit integer
• i32.reinterpret/f32: reinterpret the bits of a 32-bit float as a 32-bit integer
• i64.extend_s/i32: extend a signed 32-bit integer to a 64-bit integer
• i64.extend_u/i32: extend an unsigned 32-bit integer to a 64-bit integer
• i64.trunc_s/f32: truncate a 32-bit float to a signed 64-bit integer
• i64.trunc_s/f64: truncate a 64-bit float to a signed 64-bit integer
• i64.trunc_u/f32: truncate a 32-bit float to an unsigned 64-bit integer
• i64.trunc_u/f64: truncate a 64-bit float to an unsigned 64-bit integer
• i64.reinterpret/f64: reinterpret the bits of a 64-bit float as a 64-bit integer
• f32.demote/f64: demote a 64-bit float to a 32-bit float
• f32.convert_s/i32: convert a signed 32-bit integer to a 32-bit float
• f32.convert_s/i64: convert a signed 64-bit integer to a 32-bit float
• f32.convert_u/i32: convert an unsigned 32-bit integer to a 32-bit float
• f32.convert_u/i64: convert an unsigned 64-bit integer to a 32-bit float
• f32.reinterpret/i32: reinterpret the bits of a 32-bit integer as a 32-bit float
• f64.promote/f32: promote a 32-bit float to a 64-bit float
• f64.convert_s/i32: convert a signed 32-bit integer to a 64-bit float
• f64.convert_s/i64: convert a signed 64-bit integer to a 64-bit float
• f64.convert_u/i32: convert an unsigned 32-bit integer to a 64-bit float
• f64.convert_u/i64: convert an unsigned 64-bit integer to a 64-bit float
• f64.reinterpret/i64: reinterpret the bits of a 64-bit integer as a 64-bit float

Wrapping and extension of integer values always succeed. Promotion and demotion of floating point values always succeed. Demotion of floating point values uses round-to-nearest ties-to-even rounding, and may overflow to infinity or negative infinity as specified by IEEE 754-2008.

If the operand of promotion or demotion is a NaN, the result is a NaN with the following sign bit and fraction field (which does not include the implicit leading digit of the significand):

• If the fraction fields of the operand consists of 1 in the most significant bit and 0 in the remaining bits, the result is a NaN with a nondeterministic sign bit, 1 in the most significant bit of the fraction field, and all zeros in the remaining bits of the fraction field.
• Otherwise the result is a NaN with a nondeterministic sign bit, 1 in the most significant bit of the fraction field, and nondeterminsitic values in the remaining bits of the fraction field.

Reinterpretations always succeed.

Conversions from integer to floating point always succeed, and use round-to-nearest ties-to-even rounding.

Truncation from floating point to integer where IEEE 754-2008 would specify an invalid operator exception (e.g. when the floating point value is NaN or outside the range which rounds to an integer in range) traps.

Type-parametric operators.

• drop: a unary operator that discards the value of its operand.
• select: a ternary operator with two operands, which have the same type as each other, plus a boolean (i32) condition. select returns the first operand if the condition operand is non-zero, or the second otherwise.

Unreachable

• unreachable: An expression which can take on any type, and which, if executed, always traps. It is intended to be used for example after calls to functions which are known by the producer not to return (otherwise the producer would have to create another expression with an unused value to satisfy the type check). This trap is intended to be impossible for user code to catch or handle, even in the future when it may be possible to handle some other kinds of traps or exceptions.