Syntax (1)

Syntax The syntax of a programming language is a precise description of all its grammatically correct programs. Levels of syntax Lexical syntax Concrete syntax Abstract syntax

Levels of Syntax Lexical syntax Concrete syntax Abstract syntax all the basic symbols of the language (names, values, operators, etc.) Concrete syntax rules for writing expressions, statements and programs. Abstract syntax internal representation of the program, favouring content over form.

Grammars A metalanguage is a language used to define other languages. A grammar is a metalanguage used to define the syntax of a language. Backus-Naur Form (BNF) version of a context-free grammar

BNF Grammar Set of terminal symbols: T Set of nonterminal symbols: N Set of productions: P Start symbol: S N

Example: Binary Digits Consider the grammar: binaryDigit  0 binaryDigit  1 or equivalently: binaryDigit  0 | 1 Here, | is a metacharacter that separates alternatives.

Derivations A grammar for integers: Integer  Digit | Integer Digit Digit  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 How we can derive any unsigned integer, like 352, from this grammar?

Driving the Integer “352” using Integers Grammar Integer  Integer Digit  Integer 2  Integer Digit 2  Integer 5 2  Digit 5 2  3 5 2 Integer  Integer Digit  Integer Digit Digit  Digit Digit Digit  3 Digit Digit  3 5 Digit  3 5 2 rightmost derivation leftmost derivation

Parse Trees A parse tree is a graphical representation of a derivation. Each internal node of the tree corresponds to a step in the derivation. Each child of a node represents a right-hand side of a production. Each leaf node represents a symbol of the derived string, reading from left to right.

Example: The step Integer  Integer Digit appears in the parse tree as: Integer Digit

Example: Parse Tree for “352” as an Integer Integer  Digit | Integer Digit Digit  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Arithmetic Expression Grammar The following grammar defines the language of arithmetic expressions with 1-digit integers, addition, and subtraction. Example : Parse of the String 5-4+3 Expr  Expr + Term | Expr – Term | Term Term  0 | ... | 9 | ( Expr )

Example: Parse of the String 5-4+3 Expr  Expr + Term | Expr – Term | Term Term  0 | ... | 9 | ( Expr )

Precedence A grammar can be used to define and precedence among the operators in an expression. * and / have higher precedence than + and -. Example: expr → expr + term | expr – term | term term → term * factor | term \ factor | term % factor |factor factor → digit | (expr) digit → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Associativity A grammar can be used to define associativity among the operators in an expression. + and - are left-associative operators Example: Parse of 4**2**3+5*6+7 Expr → Expr + Term | Expr – Term | Term Term → Term * Factor | Term / Factor |Term % Factor | Factor Factor → Primary ** Factor | Primary Primary → 0 | ... | 9 | ( Expr )

Example Parse of 4**2**3+5*6+7 Expr → Expr + Term | Expr – Term | Term Term → Term * Factor | Term / Factor | Term % Factor | Factor Factor → Primary ** Factor | Primary Primary → 0 | ... | 9 | ( Expr )

Ambiguous Grammars A grammar can have more than one parse tree. Consider next grammar Example: Draw all a parse tree of (9-5+2) using previous grammar string → string + string | string – string |0|1|2|3|4|5|6|7|8|9

( 9 – 5 ) + 2 9 - ( 5 + 2 ) string 9 5 2 - + string 2 5 9 + -

Another Example: The Dangling Else With which ‘if’ does the following ‘else’ associate if (x < 0) if (y < 0) y = y - 1; else y = 0;

If statement Grammar IfStatement → if ( Expression ) Statement | if ( Expression ) Statement else Statement Statement → Assignment | IfStatement | Block Block → { Statements } Statements → Statements Statement | Statement

The Dangling Else Ambiguity

C and C++ Solution to dangling else ambiguity Associate each else with closest if Use { } to override

Extended BNF (EBNF) Additional metacharacters Braces { } zero or more occurrences of the symbols that are enclosed within braces. Parentheses ( ) Enclose a series of alternatives from which one must be chosen Brackets [ ] for an optional list; pick none or one

EBNF Example BNE EBNE A → x { y } z A → x A' z A' → | y A' Expr → Expr + Term | Expr – Term| Term EBNE Expr → Term {(+ | -) Term} A → x { y } z A → x A' z A' → | y A'

Syntax Diagram A version of EBNE Example: Expr → Term {(+ | -) Term}