1. ISBN 0-321-33025-0 Chapter 3 Describing Syntax and Semantics

2. Copyright © 2006 Addison-Wesley. All rights reserved.1-2 Chapter 3 Topics 3.1 Introduction 3.2 The General Problem of Describing Syntax 3.3 Formal Methods of Describing Syntax 3.4 Attribute Grammars 3.5 Describing the Meanings of Programs: Dynamic Semantics

3. Copyright © 2006 Addison-Wesley. All rights reserved.1-3 3.1 Introduction Syntax and semantics provide a language’s definition Syntax: the form or structure of the expressions, statements, and program units Semantics: the meaning of the expressions, statements, and program units E.g., while (x>20) { sum = sum + x; x = x+1; }

4. Copyright © 2006 Addison-Wesley. All rights reserved.1-4 3.2 The General Problem of Describing Syntax: Terminology A language is a set of sentences A sentence/statement is a string of characters over some alphabet A token is a category of lexemes (e.g., identifier) A lexeme is the lowest level syntactic unit of a language (e.g., *, sum, begin )

5. Copyright © 2006 Addison-Wesley. All rights reserved.1-5 3.2 The General Problem of Describing Syntax: Terminology E.g. language: { int index, count; … index = 2 * count + 17; } statement lexeme token: identifier token: int literal

6. Copyright © 2006 Addison-Wesley. All rights reserved.1-6 Formal Definition of Languages Recognizers –A recognition device reads input strings of the language and decides whether the input strings belong to the language –Example: syntax analysis part of a compiler –Detailed discussion in Chapter 4 Generators –A device that generates sentences of a language –One can determine if the syntax of a particular sentence is correct by comparing it to the structure of the generator

7. Copyright © 2006 Addison-Wesley. All rights reserved.1-7 3.3 Formal Methods of Describing Syntax 3.3.1 Backus-Naur Form and Context- Free Grammars (BNF form) –Most widely known method for describing programming language syntax 3.3.2 Extended BNF –Improves readability and writability of BNF

8. Copyright © 2006 Addison-Wesley. All rights reserved.1-8 BNF and Context-Free Grammars Context-Free Grammars –Developed by Noam Chomsky in the mid-1950s –Natural language linguist –Described four classes of grammars that define four classes of languages –Two classes (context-free and regular) turned out to be useful for describing the syntax of programming languages

9. Copyright © 2006 Addison-Wesley. All rights reserved.1-9 Backus-Naur Form (BNF) Backus-Naur Form (1959) –Invented by John Backus to describe Algol 58, later modified by Peter Naur –BNF is equivalent to context-free grammars –BNF is a metalanguage used to describe another language –In BNF, abstractions are used to represent classes of syntactic structures--they act like syntactic variables (also called nonterminal symbols) E.g. -> = a = ; 2 * b

10. Copyright © 2006 Addison-Wesley. All rights reserved.1-10 BNF Fundamentals Non-terminals: BNF abstractions Terminals: lexemes and tokens Grammar: a collection of rules –Examples of BNF rules: → identifier | identifier, → if then

11. Copyright © 2006 Addison-Wesley. All rights reserved.1-11 BNF Rules A rule has a left-hand side (LHS) and a right-hand side (RHS), and consists of terminal and nonterminal symbols A grammar is a finite nonempty set of rules An abstraction (or nonterminal symbol) can have more than one RHS  | begin end Qs: ? ? ? ?

12. Copyright © 2006 Addison-Wesley. All rights reserved.1-12 Specific Rule for Describing Lists Syntactic lists are described using recursion  ident | ident,

13. Copyright © 2006 Addison-Wesley. All rights reserved.1-13 Grammars and Derivations A derivation is a repeated application of rules, starting with the start symbol and ending with a sentence (all terminal symbols)

14. Copyright © 2006 Addison-Wesley. All rights reserved.1-14 An Example Grammar And Derivation  begin end  | ;  =  A | B | C  + | - | => begin end  begin ; end  begin = ; end  begin A = ; end  begin A = + ; end  begin A = B + C; end  Begin A = B + C; end  begin A = B + C; = end  begin A = B + C; B = end  begin A = B + C; B = C end Grammar Derivation of Begin A = B + C; B = C; End

15. Copyright © 2006 Addison-Wesley. All rights reserved.1-15 Derivation Every string of symbols in the derivation is a sentential form A sentence is a sentential form that has only terminal symbols A leftmost derivation is one in which the leftmost nonterminal in each sentential form is the one that is expanded A derivation can be rightmost or neither leftmost nor rightmost Derivation order has no effect on the language generated by a grammar

16. Copyright © 2006 Addison-Wesley. All rights reserved.1-16 Another Example  =  A | B | C  + | * | ( ) | => = =>A = => A = * => A = B * => A = B * ( ) => A = B * ( + ) => A = B * (A + ) => A = B * ( A + C ) Grammar Derivation of “A = B * (A + C )”

17. Copyright © 2006 Addison-Wesley. All rights reserved.1-17 Parse Tree A hierarchical representation of a derivation = A * B ( ) + A C

18. Copyright © 2006 Addison-Wesley. All rights reserved.1-18 Ambiguity in Grammars A grammar is ambiguous if and only if it generates a sentential form that has two or more distinct parse trees

19. Copyright © 2006 Addison-Wesley. All rights reserved.1-19 An Ambiguous Expression Grammar -> = -> A|B|C -> + | * |( ) | a. = A + * B C A b. = A * + A B C A = B + C * A

20. Copyright © 2006 Addison-Wesley. All rights reserved.1-20 Operator Precedence An operator in an arithmetic expression is generated lower in the parse tree (and therefore must be evaluated first) can be used to indicate that it has precedence over an operator produced higher up in the tree As in previous slides –Tree a: A = B + (C * A) –Tree b: A = (B + C ) * A

21. Copyright © 2006 Addison-Wesley. All rights reserved.1-21 An Unambiguous Expression Grammar -> = - > A | B | C - > + | - > * | - >( ) | = A + * A B C

22. Copyright © 2006 Addison-Wesley. All rights reserved.1-22 Leftmost and rightmost derivations leftmost: => = =>A =  A = +  A = B +  A = B + *  A = B + C *  A = B + C * A rightmost: => = => = + => = + * => = + *A  = + * A  = + C * A  = B + C * A  A = B + C * A Every derivation with an unambiguous grammar has a unique parse tree, although that tree can be represented by different derivations.

23. Copyright © 2006 Addison-Wesley. All rights reserved.1-23 3.3.2 Extended BNF Optional parts are placed in brackets [ ] -> if ( ) [else ] Repetitions (0 or more) are placed inside braces { } -> {, } When a single element must be chosen from a group, the options are placed in parentheses and separted by the OR operator, |. -> (* | / | %)

24. Copyright © 2006 Addison-Wesley. All rights reserved.1-24 BNF and EBNF BNF  + | - |  * | / | EBNF  {(+ | -) }  {(* | /) }

25. Copyright © 2006 Addison-Wesley. All rights reserved.1-25 EBNF variations In place of the arrow, a colon is used and the RHS is placed on the next line Instead of a vertical bar to separate alternative RHSs, they are simply placed on separate lines In place of squared brackets to indicate something being optional, the subscript opt is used. E.g. –ConstructorDeclarator -> SimpleName(FormalParameterList opt ) Rather than using the | symbol in a parenthesized list of elements to indicate a choice, the words “one of” are used. E.g. –AssignmentOperator -> one of = *= /= %= += -= >= &= |=