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Chapter 3 Syntax Part 1

Chapter 3 Syntax Part 1. CMSC 331 Shon Vick. Syntax and Semantics. Syntax - the form or structure of the expressions – whether an expression is well formed Semantics – the meaning of an expression. Syntactic Structure.

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Chapter 3 Syntax Part 1

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  1. Chapter 3Syntax Part 1 CMSC 331 Shon Vick

  2. Syntax and Semantics • Syntax - the form or structure of the expressions – whether an expression is well formed • Semantics – the meaning of an expression

  3. Syntactic Structure • Syntax almost always expressed using some variant of a notation called a context-free grammar (CFG) or simply grammar • BNF • EBNF • Syntax Graph

  4. A CFG has 4 parts • A set of tokens (lexemes), known as terminal symbols • A set of non-terminals • A set of rules (productions) where each production consists of a left-hand side (LHS) and a right-hand side (RHS) The LHS is a non-terminal and the RHS is a sequence of terminals and/or non-terminal symbols. • A special non-terminal symbol designated as the start symbol

  5. An example of BNF syntax for real numbers <r> ::= <ds> . <ds> <ds> ::= <d> | <d> <ds> <d> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7| 8 | 9 < > encloses non-terminal symbols ::= 'is' or 'is made up of ' or 'derives' (sometimes denoted with an arrow ->) | or

  6. Example • On the example from the previous slide: • What are the tokens? • What are the lexemes? • What are the non terminals? • What are the productions?

  7. BNF Points • A non terminal can have more than RHS or an OR can be used • Lists or sequences are expressed via recursion • A derivation is just a repeated set of production (rule) applications • Examples

  8. Example Grammar <program> -> <stmts> <stmts> -> <stmt> | <stmt> ; <stmts> <stmt> -> <var> = <expr> <var> -> a | b | c | d <expr> -> <term> + <term> | <term> - <term> <term> -> <var> | const

  9. Example Derivation <program> => <stmts> => <stmt> => <var> = <expr> => a = <expr> => a = <term> + <term> => a = <var> + <term> => a = b + <term> => a = b + const

  10. Parse Trees • Alternative representation for a derivation • Example parse tree for the previous example stmts stmt expr var = term term + a var const b

  11. Parse Trees PS -> P | P PS P -> e | '(' PS ')' | '<' PS '>' | '[' PS ']' What’s the parse tree for this statement ? < [ ] [ < > ] >

  12. Ambiguity • Two parse trees for the same expression • Consider the following grammar string -> string + string | string - string digit -> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 What are the two trees for 9 - 5 + 2

  13. EBNF - Extended BNF • Like BNF except that • Non-terminals start w/ uppercase • Parens are used for grouping terminals • Braces {} represent zero or more occurrences (iteration ) • Brackets [] represent an optional construct , that is a construct that appears either once or not at all.

  14. EBNF example Exp -> Term { ('+' | '-') Term } Term -> Factor { ('*' | '/') Factor } Factor -> '(' Exp ')' | variable | constant

  15. EBNF/BNF • EBNF and BNF are equivalent • How can {} be expressed in BNF? • How can ( ) be expressed? • How can [ ] be expressed?

  16. Syntax Graphs Terminal in circles nonterminals in rectangles; Syntax Graphs - put the terminals in circles or ellipses and put the nonterminals in rectangles; connect with lines with arrowheads e.g., Pascal type declarations type_identifier ( identifier ) , constant .. constant

  17. EBNF to BNF <goal> -> [<a>]{xy} <b> <a> -> z {z} <b> -> x [y] z

  18. EBNF to BNF <exp> -> term {+ <exp>} <term> -> <factor> {* <term>} <factor> -> NUMBER | ( <exp> )

  19. BNF to EBNF <g> - > <a> <g> -> x <b> <a> <a> -> y <a> -> x <a> <b> -> <a> <b> -> <a> <b> <b> -> y <b>

  20. Exercises With EBNF/BNF • Give a BNF/EBNF for an expression • with an odd number of a’s followed by • an even number of b’s • Give the BNF/EBNF for an expression • with some number of a’s following by 1 • plus that number of b’s

  21. Associativity Consider the following productions: list -> list + digit | (1) list - digit | digit digit -> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 right -> letter = right | (2) letter letter -> a | b | .... z

  22. Associativity • What productions would be generated for the following parse trees for the input • 9 - 5 –2 • a = b = c • How can we determine this from the grammar as given

  23. Precedence • We've shown how to handle associativity in a grammar, how about precedence • Does 9 + 5 * 2 mean ( 9 + 5 ) * 2 9 + ( 5 * 2 )

  24. Precedence E -> E + T | E - T | T T -> T * F | T / F | F F -> digit | ( E ) What binds tighter? * or +

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