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Bottom-Up Parsing

Bottom-Up Parsing. David Woolbright. The Parsing Problem. Produce a parse tree starting at the leaves The order will be that of a rightmost derivation The most common bottom-up parsing algorithms are in the LR family L – Read the input left to right R – Trace out a rightmost parse tree.

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Bottom-Up Parsing

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  1. Bottom-Up Parsing David Woolbright

  2. The Parsing Problem • Produce a parse tree starting at the leaves • The order will be that of a rightmost derivation • The most common bottom-up parsing algorithms are in the LR family L – Read the input left to right R – Trace out a rightmost parse tree

  3. The Parsing Problem • Given a right sentential form, , determine what substring of  is the right-hand side of the rule in the grammar that must be reduced to produce the previous sentential form in the right derivation • The correct RHS is called the handle

  4. A Small example E  E + T | T T  T * F | F F  ( E ) | id A Rightmost Derivation: E  E + T  E + T * F  E + T * id  E + F * id  E + id * id  T + id * id  F + id * id  id + id * id

  5. Definition • Def:  is the handle of the right sentential form  = w if and only if S =>*rm Aw =>rm w E  E + T Let  = w be  E + T * F E + F * id  E + T * id What is  ?  E + F * id What is w ? What is  ? What is A?

  6. Definition • Def:  is a phrase of the right sentential form  if and only if S =>*  = 1A2 =>+ 12 E  E + T Let  = 1A2 be  E + T * FE + T  E + T * id Let A be T. What is 1 ?2 ? What can  be?

  7. Definition • Def:  is a simple phrase of the right sentential form  if and only if S =>*  = 1A2 => 12 E  E + T Let  = 1A2 be  E + T * FE + T  E + T * id Let A be T. What is 1 ?2 ? What can  be? • The handle of any rightmost sentential form is its leftmost simple phrase

  8. Think Parse Tree! E T F E + T * id T F Id id • Three internal nodes = three phrases in the sentential form E + T * id Phrases: Id T * id E + T * id

  9. LR Parsers • The handle of a right sentential form is its leftmost simple phrase • Given a parse tree, it is now easy to find the handle • Parsing can be thought of as handle pruning

  10. LR Parsers Use Shift-Reduce • Shift-Reduce Algorithms • Reduce: replace the handle on the top of the parse stack with its corresponding LHS • Shift: move the next token to the top of the parse stack

  11. LR Parsers • Advantages of LR parsers: • Work for most grammars that describe programming languages. • Detect syntax errors as soon as it is possible. • The LR class of grammars is a superset of the class of grammars parsable by LL parsers.

  12. The LR Algorithm • An LR configuration stores the state of an LR parser (S0X1S1X2S2…XmSm, aiai+1…an$) S0 = Start state Xm = symbol m Sm = state m ai = input symbol i

  13. Sebesta’s LR Diagram

  14. Sebesta’s LR Table

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