5 Notational Conventions
5.1 Syntactic and Lexical Grammars
5.1.1 Context-Free Grammars
A context-free grammar consists of a number of productions. Each production has an abstract symbol called a nonterminal as its left-hand side, and a sequence of zero or more nonterminal and terminal symbols as its right-hand side. For each grammar, the terminal symbols are drawn from a specified alphabet.
A chain production is a production that has exactly one nonterminal symbol on its right-hand side along with zero or more terminal symbols.
Starting from a sentence consisting of a single distinguished nonterminal, called the goal symbol, a given context-free grammar specifies a language, namely, the (perhaps infinite) set of possible sequences of terminal symbols that can result from repeatedly replacing any nonterminal in the sequence with a right-hand side of a production for which the nonterminal is the left-hand side.
5.1.2 The Lexical and RegExp Grammars
A lexical grammar for ECMAScript is given in clause
Input elements other than white space and comments form the terminal symbols for the syntactic grammar for ECMAScript and are called ECMAScript tokens. These tokens are the reserved words, identifiers, literals, and punctuators of the ECMAScript language. Moreover, line terminators, although not considered to be tokens, also become part of the stream of input elements and guide the process of automatic semicolon insertion (/*…*/ regardless of whether it spans more than one line) is likewise simply discarded if it contains no line terminator; but if a
A RegExp grammar for ECMAScript is given in
Productions of the lexical and RegExp grammars are distinguished by having two colons “::” as separating punctuation. The lexical and RegExp grammars share some productions.
5.1.3 The Numeric String Grammar
Another grammar is used for translating Strings into numeric values. This grammar is similar to the part of the lexical grammar having to do with numeric literals and has as its terminal symbols
Productions of the numeric string grammar are distinguished by having three colons “:::” as punctuation.
5.1.4 The Syntactic Grammar
The syntactic grammar for ECMAScript is given in clauses 11, 12, 13, 14, and 15. This grammar has ECMAScript tokens defined by the lexical grammar as its terminal symbols (
When a stream of code points is to be parsed as an ECMAScript
When a parse is successful, it constructs a parse tree, a rooted tree structure in which each node is a Parse Node. Each Parse Node is an instance of a symbol in the grammar; it represents a span of the source text that can be derived from that symbol. The root node of the parse tree, representing the whole of the source text, is an instance of the parse's
New Parse Nodes are instantiated for each invocation of the parser and never reused between parses even of identical source text. Parse Nodes are considered the same Parse Node if and only if they represent the same span of source text, are instances of the same grammar symbol, and resulted from the same parser invocation.
Parsing the same String multiple times will lead to different Parse Nodes. For example, consider:
let str = "1 + 1;";
eval(str);
eval(str);
Each call to eval converts the value of str into an ECMAScript source text and performs an independent parse that creates its own separate tree of Parse Nodes. The trees are distinct even though each parse operates upon a source text that was derived from the same String value.
Productions of the syntactic grammar are distinguished by having just one colon “:” as punctuation.
The syntactic grammar as presented in clauses 12, 13, 14 and 15 is not a complete account of which token sequences are accepted as a correct ECMAScript
In certain cases, in order to avoid ambiguities, the syntactic grammar uses generalized productions that permit token sequences that do not form a valid ECMAScript
5.1.5 Grammar Notation
Terminal symbols are shown in fixed width font, both in the productions of the grammars and throughout this specification whenever the text directly refers to such a terminal symbol. These are to appear in a script exactly as written. All terminal symbol code points specified in this way are to be understood as the appropriate Unicode code points from the Basic Latin range, as opposed to any similar-looking code points from other Unicode ranges. A code point in a terminal symbol cannot be expressed by a \
Nonterminal symbols are shown in italic
states that the nonterminal while, followed by a left parenthesis token, followed by an
states that an
The subscripted suffix “opt”, which may appear after a terminal or nonterminal, indicates an optional symbol. The alternative containing the optional symbol actually specifies two right-hand sides, one that omits the optional element and one that includes it. This means that:
is a convenient abbreviation for:
and that:
is a convenient abbreviation for:
which in turn is an abbreviation for:
so, in this example, the nonterminal
A production may be parameterized by a subscripted annotation of the form “[parameters]”, which may appear as a suffix to the nonterminal symbol defined by the production. “parameters” may be either a single name or a comma separated list of names. A parameterized production is shorthand for a set of productions defining all combinations of the parameter names, preceded by an underscore, appended to the parameterized nonterminal symbol. This means that:
is a convenient abbreviation for:
and that:
is an abbreviation for:
Multiple parameters produce a combinatory number of productions, not all of which are necessarily referenced in a complete grammar.
References to nonterminals on the right-hand side of a production can also be parameterized. For example:
is equivalent to saying:
and:
is equivalent to:
A nonterminal reference may have both a parameter list and an “opt” suffix. For example:
is an abbreviation for:
Prefixing a parameter name with “?” on a right-hand side nonterminal reference makes that parameter value dependent upon the occurrence of the parameter name on the reference to the current production's left-hand side symbol. For example:
is an abbreviation for:
If a right-hand side alternative is prefixed with “[+parameter]” that alternative is only available if the named parameter was used in referencing the production's nonterminal symbol. If a right-hand side alternative is prefixed with “[~parameter]” that alternative is only available if the named parameter was not used in referencing the production's nonterminal symbol. This means that:
is an abbreviation for:
and that:
is an abbreviation for:
When the words “one of” follow the colon(s) in a grammar definition, they signify that each of the terminal symbols on the following line or lines is an alternative definition. For example, the lexical grammar for ECMAScript contains the production:
which is merely a convenient abbreviation for:
If the phrase “[empty]” appears as the right-hand side of a production, it indicates that the production's right-hand side contains no terminals or nonterminals.
If the phrase “[lookahead ∉ set]” appears in the right-hand side of a production, it indicates that the production may not be used if the immediately following input token sequence is a member of the given set. The set can be written as a comma separated list of one or two element terminal sequences enclosed in curly brackets. For convenience, the set can also be written as a nonterminal, in which case it represents the set of all terminals to which that nonterminal could expand. If the set consists of a single terminal the phrase “[lookahead ≠ terminal]” may be used.
For example, given the definitions:
the definition:
matches either the letter n followed by one or more decimal digits the first of which is even, or a decimal digit not followed by another decimal digit.
Similarly, if the phrase “[lookahead ∈ set]” appears in the right-hand side of a production, it indicates that the production may only be used if the immediately following input token sequence is a member of the given set. If the set consists of a single terminal the phrase “[lookahead = terminal]” may be used.
If the phrase “[no
indicates that the production may not be used if a throw token and the
Unless the presence of a
When an alternative in a production of the lexical grammar or the numeric string grammar appears to be a multi-code point token, it represents the sequence of code points that would make up such a token.
The right-hand side of a production may specify that certain expansions are not permitted by using the phrase “but not” and then indicating the expansions to be excluded. For example, the production:
means that the nonterminal
Finally, a few nonterminal symbols are described by a descriptive phrase in sans-serif
5.2 Algorithm Conventions
The specification often uses a numbered list to specify steps in an algorithm. These algorithms are used to precisely specify the required semantics of ECMAScript language constructs. The algorithms are not intended to imply the use of any specific implementation technique. In practice, there may be more efficient algorithms available to implement a given feature.
Algorithms may be explicitly parameterized, in which case the names and usage of the parameters must be provided as part of the algorithm's definition.
Algorithm steps may be subdivided into sequential substeps. Substeps are indented and may themselves be further divided into indented substeps. Outline numbering conventions are used to identify substeps with the first level of substeps labelled with lower case alphabetic characters and the second level of substeps labelled with lower case roman numerals. If more than three levels are required these rules repeat with the fourth level using numeric labels. For example:
- Top-level step
- Substep.
- Substep.
- Subsubstep.
- Subsubsubstep
- Subsubsubsubstep
- Subsubsubsubsubstep
- Subsubsubsubstep
- Subsubsubstep
- Subsubstep.
A step or substep may be written as an “if” predicate that conditions its substeps. In this case, the substeps are only applied if the predicate is true. If a step or substep begins with the word “else”, it is a predicate that is the negation of the preceding “if” predicate step at the same level.
A step may specify the iterative application of its substeps.
A step that begins with “Assert:” asserts an invariant condition of its algorithm. Such assertions are used to make explicit algorithmic invariants that would otherwise be implicit. Such assertions add no additional semantic requirements and hence need not be checked by an implementation. They are used simply to clarify algorithms.
Algorithm steps may declare named aliases for any value using the form “Let x be someValue”. These aliases are reference-like in that both x and someValue refer to the same underlying data and modifications to either are visible to both. Algorithm steps that want to avoid this reference-like behaviour should explicitly make a copy of the right-hand side: “Let x be a copy of someValue” creates a shallow copy of someValue.
Once declared, an alias may be referenced in any subsequent steps and must not be referenced from steps prior to the alias's declaration. Aliases may be modified using the form “
5.2.1 Abstract Operations
In order to facilitate their use in multiple parts of this specification, some algorithms, called abstract operations, are named and written in parameterized functional form so that they may be referenced by name from within other algorithms. Abstract operations are typically referenced using a functional application style such as OperationName(arg1, arg2). Some abstract operations are treated as polymorphically dispatched methods of class-like specification abstractions. Such method-like abstract operations are typically referenced using a method application style such as someValue.OperationName(arg1, arg2).
5.2.2 Syntax-Directed Operations
A syntax-directed operation is a named operation whose definition consists of algorithms, each of which is associated with one or more productions from one of the ECMAScript grammars. A production that has multiple alternative definitions will typically have a distinct algorithm for each alternative. When an algorithm is associated with a grammar production, it may reference the terminal and nonterminal symbols of the production alternative as if they were parameters of the algorithm. When used in this manner, nonterminal symbols refer to the actual alternative definition that is matched when parsing the source text. The source text matched by a grammar production is the portion of the source text that starts at the beginning of the first terminal that participated in the match and ends at the end of the last terminal that participated in the match.
When an algorithm is associated with a production alternative, the alternative is typically shown without any “[ ]” grammar annotations. Such annotations should only affect the syntactic recognition of the alternative and have no effect on the associated semantics for the alternative.
Syntax-directed operations are invoked with a parse node and, optionally, other parameters by using the conventions on steps 1, 3, and 4 in the following algorithm:
- Let status be SyntaxDirectedOperation of
SomeNonTerminal .
Unless explicitly specified otherwise, all chain productions have an implicit definition for every operation that might be applied to that production's left-hand side nonterminal. The implicit definition simply reapplies the same operation with the same parameters, if any, to the
but the Evaluation operation does not associate an algorithm with that production. In that case, the Evaluation operation implicitly includes an association of the form:
Runtime Semantics: Evaluation
- Return the result of evaluating
StatementList .
5.2.3 Runtime Semantics
Algorithms which specify semantics that must be called at runtime are called runtime semantics. Runtime semantics are defined by
5.2.3.1 Implicit Completion Values
The algorithms of this specification often implicitly return
- Return
"Infinity" .
means the same thing as:
- Return
NormalCompletion ("Infinity" ).
However, if the value expression of a “return” statement is a
The abstract operation
Assert : completionRecord is aCompletion Record .- Return completionRecord as the
Completion Record of this abstract operation.
A “return” statement without a value in an algorithm step means the same thing as:
- Return
NormalCompletion (undefined ).
Any reference to a
5.2.3.2 Throw an Exception
Algorithms steps that say to throw an exception, such as
- Throw a
TypeError exception.
mean the same things as:
- Return
ThrowCompletion (a newly createdTypeError object).
5.2.3.3 ReturnIfAbrupt
Algorithms steps that say or are otherwise equivalent to:
- ReturnIfAbrupt(argument).
mean the same thing as:
- If argument is an
abrupt completion , return argument. - Else if argument is a
Completion Record , set argument to argument.[[Value]].
Algorithms steps that say or are otherwise equivalent to:
- ReturnIfAbrupt(AbstractOperation()).
mean the same thing as:
- Let hygienicTemp be AbstractOperation().
- If hygienicTemp is an
abrupt completion , return hygienicTemp. - Else if hygienicTemp is a
Completion Record , set hygienicTemp to hygienicTemp.[[Value]].
Where hygienicTemp is ephemeral and visible only in the steps pertaining to ReturnIfAbrupt.
Algorithms steps that say or are otherwise equivalent to:
- Let result be AbstractOperation(ReturnIfAbrupt(argument)).
mean the same thing as:
- If argument is an
abrupt completion , return argument. - If argument is a
Completion Record , set argument to argument.[[Value]]. - Let result be AbstractOperation(argument).
5.2.3.4 ReturnIfAbrupt Shorthands
Invocations of ? indicate that
- ? OperationName().
is equivalent to the following step:
ReturnIfAbrupt (OperationName()).
Similarly, for method application style, the step:
- ? someValue.OperationName().
is equivalent to:
ReturnIfAbrupt (someValue.OperationName()).
Similarly, prefix ! is used to indicate that the following invocation of an abstract or
- Let val be ! OperationName().
is equivalent to the following steps:
- Let val be OperationName().
Assert : val is never anabrupt completion .- If val is a
Completion Record , set val to val.[[Value]].
Syntax-directed operations for ! or ? before the invocation of the operation:
- Perform ! SyntaxDirectedOperation of
NonTerminal .
5.2.4 Static Semantics
Context-free grammars are not sufficiently powerful to express all the rules that define whether a stream of input elements form a valid ECMAScript
Static Semantic Rules have names and typically are defined using an algorithm. Named Static Semantic Rules are associated with grammar productions and a production that has multiple alternative definitions will typically have for each alternative a distinct algorithm for each applicable named static semantic rule.
Unless otherwise specified every grammar production alternative in this specification implicitly has a definition for a static semantic rule named Contains which takes an argument named symbol whose value is a terminal or nonterminal of the grammar that includes the associated production. The default definition of Contains is:
- For each child node child of this
Parse Node , do- If child is an instance of symbol, return
true . - If child is an instance of a nonterminal, then
- Let contained be the result of child Contains symbol.
- If contained is
true , returntrue .
- If child is an instance of symbol, return
- Return
false .
The above definition is explicitly over-ridden for specific productions.
A special kind of static semantic rule is an Early Error Rule.
5.2.5 Mathematical Operations
This specification makes reference to two kinds of numeric values:
- Number:
IEEE 754-2019 double-precision floating point values, used as the default numerictype . Mathematical value : Arbitrary real numbers, used for specific situations.
In the language of this specification, numerical values and operations (including addition, subtraction, negation, multiplication, division, and comparison) are distinguished among different numeric kinds using subscripts. The subscript 𝔽 refers to Numbers, and the subscript ℝ refers to mathematical values. A subscript is used following each numeric value and operation.
For brevity, the 𝔽 subscript can be omitted on Number values—a numeric value with no subscript is interpreted to be a Number. An operation with no subscript is interpreted to be a Number operation, unless one of the parameters has a particular subscript, in which case the operation adopts that subscript. For example, 1ℝ + 2ℝ = 3ℝ is a statement about mathematical values, and 1 + 2 = 3 is a statement about Numbers.
In general, when this specification refers to a numerical value, such as in the phrase, "the length of y" or "the
It is not defined to mix Numbers and mathematical values in either arithmetic or comparison operations, and any such undefined operation would be an editorial error in this specification text.
The
This specification denotes most numeric values in base 10; it also uses numeric values of the form 0x followed by digits 0-9 or A-F as base-16 values.
In certain contexts, an operation is specified which is generic between Numbers and mathematical values. In these cases, the subscript can be a variable; t is often used for this purpose, for example 5t × 10t = 50t for any t ranging over ℝ and 𝔽, since the values involved are within the range where the semantics coincide.
Conversions between mathematical values and numbers are never implicit, and always explicit in this document. A conversion from a
When the term integer is used in this specification, it refers to a
The mathematical function
The mathematical function
The notation “
The mathematical function
5.2.6 Value Notation
In this specification, ECMAScript language values are displayed in Function.prototype.apply or let n = 42;.
Values which are internal to the specification and not directly observable from ECMAScript code are indicated with a