E E+E E E (E) id. id + id E E+E. id E + E id id + E id id + id. Overview. derivations and parse trees. Grammars and ambiguity. ambiguous grammars


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1 Overview Grammars and ambiguity CS164 3:305:00 TT 10 vans derivations and parse trees dferent derivations produce may produce same parse tree ambiguous grammars what they are and how to fix them 1 2 Recall: derivations and parse trees A derivation is a sequence of productions S d d Derivation xample Grammar () A derivation can be drawn as a parse tree Start symbol is the tree s root For a production X d Y 1 Y n add children Y 1,, Y n to node X String You need parse trees to build ASTs 3 4 Derivation xample (Cont.) Derivation in Detail (1) 5 6 1
2 Derivation in Detail (2) Derivation in Detail (3) 7 8 Derivation in Detail (4) Derivation in Detail (5) 9 10 Derivation in Detail (6) Notes on Derivations A parse tree has Terminals at the leaves Nonterminals at the erior nodes An inorder traversal of the leaves is the original input The parse tree shows the association of operations, the input string does not
3 Leftmost and Rightmost Derivations Rightmost Derivation in Detail (1) The example is a leftmost derivation At each step, replace the leftmost nonterminal There is an equivalent notion of a rightmost derivation Rightmost Derivation in Detail (2) Rightmost Derivation in Detail (3) Rightmost Derivation in Detail (4) Rightmost Derivation in Detail (5)
4 Rightmost Derivation in Detail (6) Derivations and Parse Trees Note that rightmost and leftmost derivations have the same parse tree The dference is only in the order in which branches are added Ambiguity Grammar d ( ) ambiguity Strings 22 Ambiguity. xample Ambiguity. xample This string has two parse trees This string has two parse trees is leftassociative has higher precedence than
5 Ambiguity (Cont.) A grammar is ambiguous it has more than one parse tree for some string quivalently, there is more than one rightmost or leftmost derivation for some string Ambiguity is bad Leaves meaning of some programs illdefined Ambiguity is common in programming languages Arithmetic expressions IFTHNLS Dealing with Ambiguity There are several ways to handle ambiguity Most direct method is to rewrite the grammar unambiguously d T T T d T ( ) nforces precedence of over nforces leftassociativity of and Ambiguity. xample Ambiguity: The Dangling lse The has ony one parse tree now T T T Conser the grammar S then S then S else S OTHR This grammar is also ambiguous The Dangling lse: xample The Dangling lse: A Fix The expression 1 then 2 then S 3 else S 4 has two parse trees 1 S 4 2 S 3 Typically we want the second form 1 2 S 3 S 4 29 else matches the closest unmatched then We can describe this in the grammar (distinguish between matched and unmatched then ) S MIF / all then are matched / UIF / some then are unmatched / MIF then MIF else MIF OTHR UIF then S then MIF else UIF Describes the same set of strings 30 5
6 The Dangling lse: xample Revisited The expression 1 then 2 then S 3 else S S 4 Ambiguity No general techniques for handling ambiguity Impossible to convert automatically an ambiguous grammar to an unambiguous one 2 S 3 S 4 A val parse tree (for a UIF) 2 S 3 Not val because the then expression is not a MIF Used with care, ambiguity can simply the grammar Sometimes allows more natural definitions We need disambiguation mechanisms Precedence and Associativity Declarations Associativity Declarations Instead of rewriting the grammar Use the more natural (ambiguous) grammar Along with disambiguating declarations Conser the grammar Ambiguous: two parse trees of LR (bottomup) parsers allow precedence and associativity declarations to disambiguate grammars xamples 33 Leftassociativity declaration: %left 34 Precedence Declarations Conser the grammar And the string Precedence declarations: %left %left 35 6
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