COMP313A Programming Languages

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COMP313A Programming Languages

• Syntax Analysis (2)

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

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Parsing token sequence id id id
E ? E E E E ( E ) - E id
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Ambiguous Grammars

• A grammar that generates a string with 2 distinct
  parse trees is called an ambiguous grammar
• 234 2 (34) 14
• 234 (23) 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

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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

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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

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Associativity

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

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Ambiguous grammars

• Statement -gt If-statement other
• If-statement -gt if (Exp) Statement
• if (Exp) Statement
  else Statement
• Exp -gt 0 1
• Parse if (0) if (1) other else other

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Removing ambiguity

• Statement -gt Matched-stmt Unmatched-stmt
• Matched-stmt -gt if (Exp) Matched-stmt else
  Matched-stmt other
• Unmatched-stmt -gtif (Exp) Statement
• if (Exp)
  Matched-stmt else Unmatched-stmt

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Predictive Parsing

• Top down parsing
• LL(1) parsing
• Table driven predictive parsing versus recursive
  descent parsing
• No backtracking

E -gt E T T T -gt T F F F -gt (E) id
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Two grammar problems

• Eliminating left recursion
• A -gt Aa b A -gt bA
• A -gt aA eExample E -gt E T T
• T -gt T F F
• F -gt (E) id
• The general case
• A -gt Aa1 Aa2 Aam b1 b2 bn

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Two grammar problems

• Eliminating left recursion involving derivations
  of two or more steps S -gt Aa b
• A -gt Ac Sd e
• A -gt Ac Aad bd e

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Two grammar problems

• Left factoring
• Stmt -gt if Exp then Stmt else Stmt if Expr
  then Stmt
• A -gt ab1 ab2
• A -gt aA
• A -gt b1 b2

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exercises

• Eliminate left recursion from the following
  grammars.
• S-gt(L) aL-gtL,S S
• Bexpr -gtBexpr or Bterm BtermBterm -gt Bterm and
  Bfactor BfactorBfactor -gt not Bfactor
  (Bexpr) true false