JavaScript 2.0 Unit Semantics

April 2002 Draft

JavaScript 2.0

Formal Description

Unit Semantics

Thursday, February 7, 2002

The unit semantics describe the actions the lexer takes in order to interpret a quoted unit pattern. The input to these semantics is the unit string literal’s contents after the string literal has been processed. For convenience, the unit grammar is repeated here. See also the description of the semantic notation.

This document is also available as a Word 98 rtf file.

The start nonterminal is UnitPattern.

White Space

Syntax

σ ∈ {wsopt, wsreq}

WhiteSpaceCharacter ⇒

«TAB» | «VT» | «FF» | «SP» | «u00A0»

| «u2000» | «u2001» | «u2002» | «u2003» | «u2004» | «u2005» | «u2006» | «u2007»

| «u2008» | «u2009» | «u200A» | «u200B»

| «u3000»

LineTerminator ⇒ «LF» | «CR» | «u2028» | «u2029»

RequiredWhiteSpace ⇒

WhiteSpaceCharacter

| LineTerminator

| RequiredWhiteSpace WhiteSpaceCharacter

| RequiredWhiteSpace LineTerminator

WhiteSpace^wsopt ⇒

RequiredWhiteSpace

| «empty»

WhiteSpace^wsreq ⇒ RequiredWhiteSpace

Unit Patterns

Syntax

UnitPattern ⇒ WhiteSpace^wsopt UnitQuotient

UnitQuotient ⇒

UnitProduct^wsopt

| UnitProduct^wsopt / WhiteSpace^wsopt UnitProduct^wsopt

UnitProduct^σ ⇒

| UnitProduct^wsopt * WhiteSpace^wsopt UnitFactor^σ

| UnitProduct^wsreq UnitFactor^σ

UnitFactor^σ ⇒

1 WhiteSpace^σ

| 1 WhiteSpace^wsopt ^ WhiteSpace^wsopt SignedInteger WhiteSpace^σ

| Identifier WhiteSpace^σ

| Identifier WhiteSpace^wsopt ^ WhiteSpace^wsopt SignedInteger WhiteSpace^σ

Semantics

tuple UnitFactor

identifier: String,

exponent: Integer

end tuple;

UnitList = UnitFactor[];

proc unitReciprocal(value: UnitList): UnitList

return [UnitFactor〈identifier: f.identifier, exponent: –(f.exponent)〉 | ∀f ∈ value]

end proc;

Value[UnitPattern ⇒ WhiteSpace^wsopt UnitQuotient]: UnitList = Value[UnitQuotient];

Value[UnitQuotient]: UnitList;

Value[UnitQuotient ⇒ UnitProduct^wsopt] = Value[UnitProduct^wsopt];

Value[UnitQuotient ⇒ UnitProduct^wsopt₁ / WhiteSpace^wsopt UnitProduct^wsopt₂] = Value[UnitProduct^wsopt₁] ⊕ unitReciprocal(Value[UnitProduct^wsopt₂]);

Value[UnitProduct^σ]: UnitList;

Value[UnitProduct^σ ⇒ UnitFactor^σ] = Value[UnitFactor^σ];

Value[UnitProduct^σ₀ ⇒ UnitProduct^wsopt₁ * WhiteSpace^wsopt UnitFactor^σ] = Value[UnitProduct^wsopt₁] ⊕ Value[UnitFactor^σ];

Value[UnitProduct^σ₀ ⇒ UnitProduct^wsreq₁ UnitFactor^σ] = Value[UnitProduct^wsreq₁] ⊕ Value[UnitFactor^σ];

Value[UnitFactor^σ]: UnitList;

Value[UnitFactor^σ ⇒ 1 WhiteSpace^σ] = [];

Value[UnitFactor^σ ⇒ 1 WhiteSpace^wsopt ^ WhiteSpace^wsopt SignedInteger WhiteSpace^σ] = [];

Value[UnitFactor^σ ⇒ Identifier WhiteSpace^σ] = [UnitFactor〈identifier: Name[Identifier], exponent: 1〉];

Value[UnitFactor^σ ⇒ Identifier WhiteSpace^wsopt ^ WhiteSpace^wsopt SignedInteger WhiteSpace^σ] = [UnitFactor〈identifier: Name[Identifier], exponent: IntegerValue[SignedInteger]〉];

Signed Integers

Syntax

SignedInteger ⇒

| + DecimalDigits

| - DecimalDigits

DecimalDigits ⇒

| DecimalDigits ASCIIDigit

ASCIIDigit ⇒ 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Semantics

IntegerValue[SignedInteger]: Integer;

IntegerValue[SignedInteger ⇒ DecimalDigits] = IntegerValue[DecimalDigits];

IntegerValue[SignedInteger ⇒ + DecimalDigits] = IntegerValue[DecimalDigits];

IntegerValue[SignedInteger ⇒ - DecimalDigits] = –IntegerValue[DecimalDigits];

IntegerValue[DecimalDigits]: Integer;

IntegerValue[DecimalDigits ⇒ ASCIIDigit] = DecimalValue[ASCIIDigit];

IntegerValue[DecimalDigits₀ ⇒ DecimalDigits₁ ASCIIDigit] = 10×IntegerValue[DecimalDigits₁] + DecimalValue[ASCIIDigit];

DecimalValue[ASCIIDigit]: Integer = digitValue(ASCIIDigit);

Identifiers

Syntax

Identifier ⇒

InitialIdentifierCharacter

| Identifier ContinuingIdentifierCharacter

InitialIdentifierCharacter ⇒ UnicodeInitialAlphabetic | $ | _

ContinuingIdentifierCharacter ⇒ UnicodeAlphanumeric | $ | _

UnicodeInitialAlphabetic ⇒ Any Unicode initial alphabetic character (includes ASCII A-Z and a-z)

UnicodeAlphanumeric ⇒ Any Unicode alphabetic or decimal digit character (includes ASCII 0-9, A-Z, and a-z)

Semantics

Name[Identifier]: String;

Name[Identifier ⇒ InitialIdentifierCharacter] = [InitialIdentifierCharacter];

Name[Identifier₀ ⇒ Identifier₁ ContinuingIdentifierCharacter] = Name[Identifier₁] ⊕ [ContinuingIdentifierCharacter];

Waldemar Horwat
Last modified Thursday, February 7, 2002