Grammars and ambiguity. CS164 3:305:00 TT 10 Evans. Prof. Bodik CS 164 Lecture 8 1


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1 Grammars and ambiguity CS164 3:305:00 TT 10 vans 1
2 Overview derivations and parse trees different derivations produce may produce same parse tree ambiguous grammars what they are and how to fix them 2
3 Recall: derivations and parse trees A derivation is a sequence of productions S A derivation can be drawn as a parse tree Start symbol is the tree s root For a production X Y 1 Y n add children Y 1,, Y n to node X You need parse trees to build ASTs 3
4 Derivation xample Grammar () id String id id id 4
5 Derivation xample (Cont.) id * id id id id id id id id 5
6 Derivation in Detail (1) 6
7 Derivation in Detail (2) 7
8 Derivation in Detail (3) * 8
9 Derivation in Detail (4) * id id 9
10 Derivation in Detail (5) id * id id id id 10
11 Derivation in Detail (6) id * id id id id id id id id 11
12 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 12
13 Leftmost and Rightmost Derivations The example is a leftmost derivation At each step, replace the leftmost nonterminal There is an equivalent notion of a rightmost derivation id id id id id id id 13
14 Rightmost Derivation in Detail (1) 14
15 Rightmost Derivation in Detail (2) 15
16 Rightmost Derivation in Detail (3) id id 16
17 Rightmost Derivation in Detail (4) id * id id 17
18 Rightmost Derivation in Detail (5) id id * id id id id 18
19 Rightmost Derivation in Detail (6) id id * id id id id id id id id 19
20 Derivations and Parse Trees Note that rightmost and leftmost derivations have the same parse tree The difference is only in the order in which branches are added 20
21 ambiguity
22 Ambiguity Grammar * ( ) Strings * 22
23 Ambiguity. xample This string has two parse trees is leftassociative 23
24 Ambiguity. xample This string has two parse trees * * * has higher precedence than 24
25 Ambiguity (Cont.) A grammar is ambiguous if 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 25
26 Dealing with Ambiguity There are several ways to handle ambiguity Most direct method is to rewrite the grammar unambiguously T T T T * ( ) nforces precedence of * over nforces leftassociativity of and * 26
27 Ambiguity. xample The * has ony one parse tree now T * T T * 27
28 Ambiguity: The Dangling lse Consider the grammar S if then S if then S else S OTHR This grammar is also ambiguous 28
29 The Dangling lse: xample The expression if 1 then if 2 then S 3 else S 4 has two parse trees if if 1 if S 4 1 if 2 S 3 2 S 3 S 4 Typically we want the second form 29
30 The Dangling lse: A Fix 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 if then MIF else MIF OTHR UIF if then S if then MIF else UIF Describes the same set of strings 30
31 The Dangling lse: xample Revisited The expression if 1 then if 2 then S 3 else S 4 if if 1 if 1 if S 4 2 S 3 S 4 2 S 3 A valid parse tree (for a UIF) Not valid because the then expression is not a MIF 31
32 Ambiguity No general techniques for handling ambiguity Impossible to convert automatically an ambiguous grammar to an unambiguous one Used with care, ambiguity can simplify the grammar Sometimes allows more natural definitions We need disambiguation mechanisms 32
33 Precedence and Associativity Declarations Instead of rewriting the grammar Use the more natural (ambiguous) grammar Along with disambiguating declarations LR (bottomup) parsers allow precedence and associativity declarations to disambiguate grammars xamples 33
34 Associativity Declarations Consider the grammar Ambiguous: two parse trees of Leftassociativity declaration: %left 34
35 Precedence Declarations Consider the grammar * And the string * * * Precedence declarations: %left %left * 35
36
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
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:
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