Describing Syntaxand Semantics

Chapter 3

Describing Syntaxand Semantics

SYNTAX - the form of the expressions, statements and program units in a programming language

SEMANTICS - the meaning of those expressions, statements and program units

Describing Syntax

The strings of a language are called sentences or statements

The lowest level syntactic units of a programming language are called lexemes.(identifiers, constants, operators, etc.)

A token is a category of lexemes.

Describing Syntax

index = 2 * count + 17;LEXEME: TOKEN:

index identifier= equal_sign2 int_constant* mult_opcount identifier+ plus_op17 int_constant; semicolon

Describing Syntax

Languages may be formally defined byone of two methods: recognition or generation.

Describing Syntax

Given a language, L, that uses the alphabet , a recognizer will indicate if the given string of characters from is in the language L.

A compiler is an example of a recognizer.

Describing Syntax

A generator is a device which can be used to generate sentences or statements of a language.

Useful for humans as a guide for the generation of valid statements in the language.

A grammar is an example of a generator.

Describing Syntax

Noam Chomsky, linguist, described four language generation devices, called grammars, that can be used to generate four different classes of languages.

Regular grammars - used to describe tokens

Context-free grammars - used to describe whole programming languages

Describing Syntax

John Backus, introduced a new formal notation for describing a programming language syntax. (Algol 58)

The notation was modified by Peter Naur.

Backus-Naur form (BNF)

Describing Syntax

Metalanguage - a language that can be used to describe another language

BNF is a metalanguage for the description of programming languages.

Describing Syntax

BNF uses abstractions to denote various syntactic structures.

<assign> is an abstraction which denotes a valid assignment statement

Describing Syntax

BNF uses rules or productions to describevalid programs, statements and expressions within the language.

<assign> <var> := <expression>

is a rule which describes a valid assignment statement in Pascal

LHS RHS

Describing Syntax

GRAMMAR - a set of rules or productions which describe a language

RULE or PRODUCTION- describes valid programs, statements and expressions within the language.

NON-TERMINAL - an abstraction which can be expanded by the application of some rule

TERMINAL - corresponds to lexemes or tokens of the language

Describing Syntax

BNF rule or production:

<assign> <var> := <expression>

LHS RHS

The non-terminal on the LHS may be replaced with the string of terminals and non-terminals on the RHS

Describing Syntax

BNF rule or production:

<id> A | B | C

Multiple definitions can be written in a single rule byseparating different definitions with the OR symbol

Describing Syntax

BNF rules or productions for lists:

<id_list> <id> | <id>, <id_list>

Recursion is used to describe rules for variable length lists. A rule is recursive if its LHS also appears in its RHS

Describing Syntax

Derivations: Sentences in a language may be generated through a sequence of applications of the rules, beginning with a start symbol.

Parse Trees: The hierarchical syntactic structure of a sentence in the language can be described with a parse tree.

Describing Syntax

<program> begin <stmt_list> end

<stmt_list> <stmt> | <stmt>; <stmt_list>

<stmt> <var> := <expression>

<var> A | B | C

<expression> <var> + <var> | <var> - <var> | <var>

Example 3.1

Grammar for Simple Assignment Statements

<assign> <id> := <expr>

<id> A | B | C

<expr> <id> + <expr> | <id> * <expr> | ( <expr> ) | <id>

Example 3.2

An Ambiguous Grammar for Simple Assignment Statements

<assign> <id> := <expr>

<id> A | B | C

<expr> <expr> + <expr> | <expr> * <expr> | ( <expr> ) | <id>

Example 3.3

More on RECURSION IN GRAMMAR RULES

<expr> <id> + <expr> | <id> * <expr> | ( <expr> ) | <id>

When a BNF rule has the non-terminal symbol of its left hand side appearing as the rightmost symbol on its right hand side, the rule is said to be right recursive.

RECURSION IN GRAMMAR RULES

A rule which is right recursive can be used to specify right associativity (meaning that operators of equal precedence are evaluated from right to left)

Many programming languages specify that addition, subtraction, multiplication and division follow rules of left associativity. Those that contain that exponentiation operators, specify that right associativity be used for exponentiation.

An Unambiguous Grammar with Operator Precedence

<assign> <id> := <expr>

<id> A | B | C

<expr> <expr> + <term> | <term>

<term> <term> * <factor> | <factor>

<factor> ( <expr> ) | <id>

Example 3.4

Syntax Graphs

expr term

-expr

+