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Ambiguity

Ambiguity. Lecture 8. Announcement. Reading Assignment “Context-Free Grammars” (Sections 4.1, 4.2) Programming Assignment 2 due Friday! Homework 1 due in a week (Wed Feb 21) not Feb 25!. Ambiguity = program structure not defined. String id * id + id has two parse trees:. E. E. E.

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Ambiguity

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  1. Ambiguity Lecture 8 CS 536 Spring 2001

  2. Announcement • Reading Assignment • “Context-Free Grammars” (Sections 4.1, 4.2) • Programming Assignment 2 • due Friday! • Homework 1 • due in a week (Wed Feb 21) • not Feb 25! CS 536 Spring 2001

  3. Ambiguity = program structure not defined String id * id + id has two parse trees: E E E + E E E * E E id id E + E * id id id id CS 536 Spring 2001

  4. Ambiguity • A grammar is ambiguousif, for any string • it has more than one parse tree, or • there is more than one right-most derivation, or • there is more than one left-most derivation. (the three conditions are equivalent) • Ambiguity is BAD • Leaves meaning of some programs ill-defined CS 536 Spring 2001

  5. Dealing with Ambiguity • There are several ways to handle ambiguity • We’ll discuss two of them: • rewriting the grammar • parser-generator declarations CS 536 Spring 2001

  6. Outline • Rewriting: • Expression Grammars • precedence • associativity • IF-THEN-ELSE • the Dangling-ELSE problem • Declarations • Expression Grammars • precedence • associativity CS 536 Spring 2001

  7. Expression Grammars (precedence) • Rewrite the grammar • use a different nonterminal for each precedence level • start with the lowest precedence (MINUS) E  E - E|E / E | ( E ) |id rewrite to E  E - E| T T  T / T | F F  id | ( E ) CS 536 Spring 2001

  8. Example parse tree for id – id / id E  E - E| T T  T / T | F F  id | ( E ) E E E - T T / T T F F F id id id CS 536 Spring 2001

  9. TEST YOURSELF #1 • Attempt to construct a parse tree for id-id/id that shows the wrong precedence. • Question: • Why do you fail to construct this parse tree? CS 536 Spring 2001

  10. Associativity • The grammar captures operator precedence, but it is still ambiguous! • fails to express that both subtraction and division are left associative; • e.g., 5-3-2 is equivalent to: ((5-3)-2) and not to: (5-(3-2)). • TEST YOURSELF #3 • Draw two parse trees for the expression 5-3-2 using the grammar given above; one that correctly groups 5-3, and one that incorrectly groups 3-2. CS 536 Spring 2001

  11. Recursion • A grammar is recursive in nonterminal X if: • X + … X … • recall that + means “in one or more steps, X derives a sequence of symbols that includes an X” • A grammar is left recursive in X if: • X + X … • in one or more steps, X derives a sequence of symbols that starts with an X • A grammar is right recursive in X if: • X + … X • in one or more steps, X derives a sequence of symbols that ends with an X CS 536 Spring 2001

  12. How to fix associativity • The grammar given above is both left and right recursive in nonterminals exp and term • try at home: write the derivation steps that show this. • To correctly expresses operator associativity: • For left associativity, use left recursion. • For right associativity, use right recursion. • Here's the correct grammar: E  E – T | T T  T / F | F F  id | ( E ) CS 536 Spring 2001

  13. Ambiguity: The Dangling Else • Consider the grammar E  if E then E | if E then E else E | print • This grammar is also ambiguous CS 536 Spring 2001

  14. if if E1 if E1 E4 if E2 E3 E2 E3 E4 The Dangling Else: Example • The expression if E1 then if E2 then E3 else E4 has two parse trees • Typically we want the second form CS 536 Spring 2001

  15. The Dangling Else: A Fix • else matches the closest unmatched then • We can describe this in the grammar E  MIF /* all then are matched */ | UIF /* some then are unmatched */ MIF  if E then MIF else MIF | print UIF  if E then E | if E then MIF else UIF • Describes the same set of strings CS 536 Spring 2001

  16. if if E1 if E1 E4 if E2 E3 E2 E3 E4 The Dangling Else: Example Revisited • The expression if E1 then if E2 then E3 else E4 • A valid parse tree (for a UIF) • Not valid because the then expression is not a MIF CS 536 Spring 2001

  17. Precedence and Associativity Declarations • Instead of rewriting the grammar • Use the more natural (ambiguous) grammar • Along with disambiguating declarations • Most parser generators allow precedence and associativity declarations to disambiguate grammars • Examples … CS 536 Spring 2001

  18. E E E - E E E - E E int int E - E - int int int int Associativity Declarations • Consider the grammar E E - E | int • Ambiguous: two parse trees of int - int - int • Left associativity declaration: %left + CS 536 Spring 2001

  19. E E E * E E E + E E int int E * E + int int int int Precedence Declarations • Consider the grammar E E + E | E * E | int • And the string int + int * int • Precedence declarations: %left + • %left * CS 536 Spring 2001

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