ContextFree Grammars


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1 CFG2: Ambiguity ContextFree Grammars CMPT 379: Compilers Instructor: Anoop Sarkar anoopsarkar.github.io/compilersclass
2 Ambiguity  /  / ( )  / /
3 Ambiguity Grammar is ambiguous if more than one parse tree is possible for some sentences There is more than one leftmost (or rightmost) derivations Ambiguity is not acceptable in programming languages Leaves meaning of some programs illdefined Unfortunately, it s undecable to check whether a given CFG is ambiguous Some CFLs are inherently ambiguous (do not have an unambiguous CFG)
4 Ambiguity Handle ambiguity: Rewrite the grammar unambiguously Augment parser by enforcing precedence and associativity Conser the original ambiguous grammar:  ( ) / How can we change the grammar to get only one tree for the input  /
5 Precedence Original ambiguous grammar:  / ( ) Use different nonterminals for each Precedence level: (start from lowest level)  T T T / T T F F F ( ) Input:  /  T F T F T / T F
6 Associativity The grammar capture operator precedence  T T T / T T F F F ( ) Still ambiguous!!   is left associative (operations are grouped from left) (53) (32)
7 Recursion Grammar is recursive in nonterminal X if: X + X + means in one or more steps, X derives a sequence of symbols that includes X Grammar is left recursive in X if: X + X In one or more steps, X derives a sequence of symbols that starts with X Grammar is right recursive in X if: X + X In one or more steps, X derives a sequence of symbols that ends with X
8 Fix Associativity Left and right recursive in nonterminals and T  T T T / T T F F F ( ) xpress operator associativity: For left associativity use left recursion For right associativity use right recursion Unambiguous grammar  T T T T / F T F F F ( )
9 Dangling else ambiguity Original Grammar (amibguous) Stmt if xpr then Stmt else Stmt Stmt if xpr then Stmt Stmt Other if 1 then if 2 then 3 else 4 if else matches the closest unmatched then if 1 if 4 1 if
10 Dangling else ambiguity Original Grammar (ambiguous) Stmt if xpr then Stmt else Stmt Stmt if xpr then Stmt Stmt Other Unambiguous grammar else matches the closest unmatched then Stmt MatchedStmt /*all then are matched*/ Stmt UnmatchedStmt /*some then are unmatched*/ MatchedStmt if xpr then MatchedStmt else MatchedStmt MatchedStmt Other UnmatchedStmt if xpr then Stmt UnmatchedStmt if xpr then MatchedStmt else UnmatchedStmt
11 Dangling else ambiguity Check unambiguous danglingelse grammar with the following inputs: if xpr then if xpr then Other else Other if xpr then if xpr then Other else Other else Other if xpr then if xpr then Other else if xpr then Other else Other
12 Precedence and Associativity Declaration Impossible to automatically convert an ambiguous grammar to an unambiguous one Used with care, ambiguity can simplify the grammar Sometimes allow more natural definitions We need disambiguation mechanisms
13 Precedence and Associativity Declaration Instead of rewriting the grammar Use the more natural (ambiguous) grammar Along with disambiguation declarations Most tools allow precedence and associativity declaration to disambiguate grammars
14 Associativity Declaration Conser the grammar:  int Ambiguous: two parse trees int  int  int int int  int int int int Left associativity declaration: %left
15 Precedence Declaration Conser the grammar:  / int Ambiguous: two parse trees int  int / int /   int int / int int Precedence declaration: %left %left / 15 int int
16 Other Ambiguous Grammars Conser the grammar R R R R R R * ( R ) a b What does this grammar generate? What s the parse tree for a b*a Is this grammar ambiguous?
17 xtra Sles
18 Ambiguity Original ambiguous grammar: + * ( )  Unambiguous grammar: + T T T * F T T F F ( ) F  F Input: + * T T F T F * F Warning! Is this unambiguous? Check derivations for + Compare with F  F
19 Dangling else ambiguity Original Grammar (ambiguous) Stmt if xpr then Stmt else Stmt Stmt if xpr then Stmt Stmt Other Modified Grammar (unambiguous?) Stmt if xpr then Stmt Stmt MatchedStmt MatchedStmt if xpr then MatchedStmt else Stmt MatchedStmt Other
20
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