Programming LanguagesThird Edition

Chapter 6 Part IISyntax / Grammars and Parsing

Objectives

• Understand context-free grammars and BNFs• Become familiar with parse trees • Understand ambiguity, associativity, and

precedence• Read Sections 6.2 – 6.4, pp. 204-220

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ParsingContext-Free Grammars and BNFs

• Context-free grammar: consists of – a series of grammar rules (Productions)

• Each rule has a single phrase structure name on the left, then a ::= metasymbol, followed by a sequence of symbols or other phrase structure names on the right

– Nonterminals: names for phrase structures, since they are broken down into further phrase structures

– Start symbol: one of the Nonterminals– Terminals: words or token symbols that cannot be

broken down further

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Example 1: Unsigned Integers

<num> ::= <digit> | <num> <digit><digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Terminals: 0, 1, … , 9Nonterminals: <num> , <digit>Start Symbol: <num>Productions: there are 12Metasymbols: “::=“ , “|”

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Example 1 (cont’d)

• Derivation: the process of building in a language by beginning with the start symbol and replacing left-hand sides by choices of right-hand sides in the rules

• Let’s derive the number 123 (on board)

• Parse tree: graphical depiction of the replacement process in a derivation

• Let’s draw parse tree for 123 (on board)

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Example 1 (cont’d)

<num> ::= <digit> | <num> <digit><digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

• Notice recursion in one of rules• Notice recursive symbol is on left• This is a left-recursive grammar• This is a left-associative grammar• Notice how parse tree cascades to left

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Example 2: Unsigned Integers

<num> ::= <digit> | <digit> <num> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Only made one change, so now grammar is• Right-recursive• Right-associative• Let’s draw parse tree for 123

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Ex 3: Simple Expression Grammar

<expr> ::= <expr> + <expr> | <expr> * <expr> |( <expr> ) | <num>

<num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Let’s derive parse tree for: 3 + 4 + 5

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Ex 3 (cont’d)

<expr> ::= <expr> + <expr> | <expr> * <expr> |( <expr> ) | <num>

<num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Is there another parse tree for: 3 + 4 + 5

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Ex 3 (cont’d)

<expr> ::= <expr> + <expr> | <expr> * <expr> |( <expr> ) | <num>

<num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

A grammar is ambiguous if there are two parse trees for the same string

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Ex 3 (cont’d)

<expr> ::= <expr> + <expr> | <expr> * <expr> |( <expr> ) | <num>

<num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Ambiguity is undesirable

Let’s see why it’s undesirable: Derive parse trees for 3 + 4 * 5

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Ex 3 (cont’d)

<expr> ::= <expr> + <expr> | <expr> * <expr> |( <expr> ) | <num>

<num> ::= <digit> | <num> <digit> <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

So what was the problem?

Which tree provides correct arithmetic interpretation?

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Ex 3 (cont’d)

Can we modify the grammar to “fix” the problem? YES!Add more levels of productions:

<expr> ::= <expr> + <term> | <term> <term> ::= <term> * <factor> | <factor><factor> ::= ( <expr> ) | <num><num> ::= <digit> | <num> <digit><digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

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Ex 3 (cont’d)

<expr> ::= <expr> + <term> | <term> <term> ::= <term> * <factor> | <factor><factor> ::= ( <expr> ) | <num><num> ::= <digit> | <num> <digit><digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

Redraw parse trees for 3 + 4 + 5 and 3 + 4 * 5

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Chapter 6Final Thoughts

• A grammar is context-free when nonterminals appear singly on the left sides of productions– There is no context under which only certain

replacements can occur• Anything not expressible using context-free

grammars is a semantic, not a syntactic, issue• BNF form of language syntax makes it easier to

write translators• Parsing stage can be automated (e.g. yacc tool in

Unix, Python)

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Chapter 6Final Thoughts

• Syntax establishes structure, not meaning– But meaning is related to syntax

• Syntax-directed semantics: process of associating the semantics of a construct to its syntactic structure– Must construct the syntax so that it reflects the

semantics to be attached later

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