1. Parsing Bottom Up
CMPS 450
J. Moloney
CMPS 450

2. We will examine “LR” parsers – Left-to-right, Rightmost derivation
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

3. Simple Expression Grammar Terminals: {id, +, *} Non-Terminals {E, T}
Example Stack Input
<empty> 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
<empty> 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’ <empty> R - 0
CMPS 450

4. <empty> id + id * id $ shift id + id * id $ R-4
Example Stack Input
<empty> 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’ $ <empty> 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

5. 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

6. num + * $ E T 1 s2 g3 g4 2 r(4) 3 s7 a 4 r(2) s5 5 s6 6 r(3) r(3)`` 7
Parse Table Example
num + * $ E T 1 s2 g3 g4 2
r(4) 3 s7 a 4
r(2) s5 5 s6 6
r(3)
r(3)`` 7 g8 8
r(1)
id + id$
id * id + id $
id id + $
id + * $
CMPS 450