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Parsing Bottom Up. CMPS 450 J. Moloney. Bottom Up Parsing. Parse tree build up from leaves We will examine “LR” parsers – L eft-to-right, R ightmost derivation. Rightmost Parsers Use a stack. Read input from left to right. Create a rightmost derivation.

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parsing bottom up

ParsingBottom Up

CMPS 450

J. Moloney

CMPS 450

slide2
Bottom Up Parsing
  • Parse tree build up from leaves
  • We will examine “LR” parsers – Left-to-right, Rightmost derivation
  • Rightmost Parsers
  • Use a stack.
  • Read input from left to right.
  • Create a rightmost derivation.
  • Reads input until entire right-hand side of a rule has been found, then reduce by that rule.
  • Process continues until entire input has been processed.

CMPS 450

slide3
Example Stack Input

abd$

a bd$

ab d$

abd $

S $

  • Simple Grammar
  • Terminals: {a,b,c,d}
  • Non-Terminals {S’, S}
  • (0) S’  S$
  • S  abc
  • S  abcd
  • Simple Expression Grammar
  • Terminals: {id, +, *}
  • Non-Terminals {E, T}
  • (0) E’  E$
  • E  E + T
  • E  T
  • T  T * id
  • T  id

Example Stack Input

id + id $

id + id $ shift

T + id $ R-4

E + id $ R-2

E + id $ shift

E + id $ Shift

E + T $ R – 4

E $ R – 1

E’ R - 0

CMPS 450

slide4
Example Stack Input

id + id * id $ shift

id + id * id $ R-4

T + id * id $ R - 2

E + id * id $ shift

E + * id $ shift

E + id * id $ R - 4

E + T * id $ shift

E + T * id $ shift E + T $ R – 1

E’ $ shift

E’ $ R - 0

  • Simple Expression Grammar
  • Terminals: {id, +, *}
  • Non-Terminals {E, T}
  • (0) E’  E$
  • E  E + T
  • E  T
  • T  T * id
  • T  id

Rightmost Derivation

E’  E$  E + T$  E + T * id  E + id * id$  T + id * id$ 

id + id * id$

CMPS 450

slide5
Shift/ Reduce – LR Parse Tables
  • Use DFA as well as past state to determine shift or reduce.
  • A stack holds terminals, nonterminals and state info.
    • Push State 1 on top of the stack.
    • According to the parse table – row of the state on the top of the stack, column of the next input symbol
      • If there is no entry parsing fails
      • If the entry is “accept” , then accept the string, parsing is successful
      • If entry is a shift – sn – push the next symbol and State n on the stack, and go back to step 2.
      • If the entry is a reduce – r(n) – pop off all the symbols (and associated states) form the stack that match the right-hand side of rule (n), to get a new state according to the parse table (row of the stare on top of the stack, column of the non-terminal on the left-hand side of rule (n)). Push the non-terminal on the left-hand side of the rule and the new state on top of the stack and go to step 2.

CMPS 450

slide6
Parse Table Example

id + id$

id * id + id $

id id + $

id + * $

CMPS 450

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