1. Chapter 3 – Describing Syntax CSCE 343

2. Syntax vs. Semantics Syntax: The form or structure of the expressions, statements, and program units. Semantics: the meaning of the expressions, statements, and program units. Syntax + semantics = language definition –Used by: Other language designers Implementers Programmers

3. Terminology Sentence: string of characters over some alphabet Language: set of sentences Lexeme: lowest level syntactic unit (e.g. +, (, {, while, etc.) Token: a category of lexemes (e.g. identifier, open brace, int literal, etc.)

4. Chomsky’s Classes of Grammars Type-0: Unrestricted Type-1: Context Sensitive Grammars Type-2: Context Free Grammars Type-3: Regular Grammars Type 2,3 most useful for programming languages

5. Formal Methods For Describing Syntax Backus-Naur Form (BNF) and Context- Free Grammars –Most widely known method for describing programming language syntax Extended BNF –Improves readability and writability of BNF Grammars and Recognizers

6. Backus-Naur Form (BNF) Invented by John Backus to describe Algol 58 BNF is equivalent to context-free grammars BNF: a metalanguage (used to describe other languages) Abstractions (called nonterminals) represent classes of syntactic structures (like variables)

7. BNF Fundamentals Non-terminals: BNF abstractions Terminals: lexemes and tokens Grammar: a collection of rules –Example rule:  while ( )

8. BNF Rules Rule has left-hand side (LHS) and right- hand side (RHS) LHS is a single non-terminal RHS consists of terminals and non- terminals Grammar is a set of rules Can have more than one RHS: –Recursion for lists:  identifier | identifier,

9. Derivations For a language to be recognized, it must be derivable from the grammar. Derivation: repeated application of rules, starting with the start symbol (non- terminal) and ending with a sentence (all terminal symbols) Leftmost vs. rightmost

10. Example Grammar Grammar:   | ;  =  a | b | c | d  + | - Derivation: => => => = => a = => a = + => a = b + => a = b + c

11. Practice Write a BNF grammar for Java Boolean expressions.

12. Derivation Each step in the derivation: sentential form Sentence: sentential form that has only terminals Leftmost vs rightmost

13. Practice Use your grammar to show a leftmost and a rightmost derivation of the expression: a < b && c == d

14. Parse Trees A hierarchical representation of a derivation => => => = => a = => a = + => a = b + => a = b + c

15. Practice Use your grammar to show a parse tree of the expression: !a || c <= d

16. Parse Trees and Semantics Compilers generate code by traversing parse trees. Semantics are derived from “shape” of trees. Example: math expressions –Operations lower in tree occur first.

17. Ambiguous Grammars  |  * | +  a | b | c | d

18. Ambiguous Grammars Get rid of multiple recursion to create unambiguous grammar:  + |  / |  a | b | c | d

19. Operator Associativity Associativity indicated by recursion:  + (left associative)  + (right associative)

20. Extended BNF Optional parts in brackets []  [ ( ) ] Alternatives are placed in parenthesis  (+|-) Repetitions (0 or more) are in braces {}  letter { letter | digit }

21. BNF and EBNF BNF  + | - |  * | / | EBNF  { ( + | - ) }  { ( * | / ) }