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COMP313A Programming Languages

COMP313A Programming Languages. Syntax Analysis (2). More on ambiguous grammars Predictive parsing Nonrecursive Predictive Parsing. Parsing token sequence: id + id * id. E  E + E | E * E | ( E ) | - E | id. Ambiguous Grammars.

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COMP313A Programming Languages

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  1. COMP313A Programming Languages Syntax Analysis (2)

  2. More on ambiguous grammars • Predictive parsing • Nonrecursive Predictive Parsing

  3. Parsing token sequence: id + id * id E  E + E | E * E | ( E ) | - E | id

  4. Ambiguous Grammars • A grammar that generates a string with 2 distinct parse trees is called an ambiguous grammar • 2+3*4 = 2 + (3*4) = 14 • 2+3*4 = (2+3) * 4 = 20 • Our experience of maths says interpretation 1 is correct but the grammar does not express this: • E  E + E | E * E | ( E ) | - E | id

  5. Removing Ambiguity • Two methods • 1. Disambiguating Rules • +ve leaves grammar unchanged • -ve grammar is not sole source of syntactic knowledge • 2. Rewrite the Grammar • Using knowledge of the meaning that we want to use later in the translation into object code to guide grammar alteration

  6. Precedence E  E addop E | Term Addop  + | - Term  Term * Term | Factor Factor  ( exp ) | number | id • Operators of equal precedence are grouped together at the same ‘level’ of the grammar  ’precedence cascade’

  7. Associativity • 45-10-5 ?30 or 40 Subtraction is left associative, left to right (=30) • E  E addop E | TermDoes not tell us how to split up 45-10-5 • E  E addop Term | TermForces left associativity via left recursion • Precedence & associativity remove ambiguity of arithmetic expressions • Which is what our maths teachers took years telling us!

  8. Ambiguous grammars Statement -> If-statement | other If-statement -> if(Exp) Statement | if (Exp) Statement else Statement Exp -> 0 | 1 Parse if (0) if (1) other else other

  9. Removing ambiguity Statement -> Matched-stmt | Unmatched-stmt Matched-stmt -> if (Exp) Matched-stmt else Matched-stmt | other Unmatched-stmt ->if (Exp) Statement | if (Exp) Matched-stmt else Unmatched-stmt

  10. Predictive Parsing • Top down parsing • LL(1) parsing • Table driven predictive parsing versus recursive descent parsing • No backtracking E -> E + T | T T -> T * F | F F -> (E) | id

  11. Two grammar problems • Eliminating left recursion A -> Aa | bA -> bA’ A’ -> aA’ | eExample E -> E + T | T T -> T * F | F F -> (E) | id The general case A -> Aa1 | Aa2 | …| Aam | b1 | b2 | …| bn

  12. Two grammar problems • Eliminating left recursion involving derivations of two or more steps S -> Aa | b A -> Ac | Sd | e A -> Ac | Aad | bd | e

  13. Two grammar problems… • Left factoring Stmt -> if Exp then Stmt else Stmt | if Expr then Stmt A -> ab1 | ab2 A -> aA’ A’ -> b1 | b2

  14. exercises Eliminate left recursion from the following grammars. • S->(L) | aL->L,S | S • Bexpr ->Bexpr or Bterm | BtermBterm -> Bterm and Bfactor | BfactorBfactor -> not Bfactor | (Bexpr) | true | false

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