1. COP4620 – Programming Language Translators Dr. Manuel E. Bermudez
SLR(1) parsing
COP4620 – Programming Language Translators Dr. Manuel E. Bermudez

2. topics Conflicts in LR(0) Automata Using Follow sets for lookahead
SLR(1) examples

3. LR Parsing Operation of an LR parser Two moves: shift and reduce.
Shift: Advance from current state on Next_Token, push new state on stack.
Reduce: (on A → ω). Pop |ω| states from stack. Advance from new top state on A.
So far, we haven’t seen both apply in the same state.

4. SLR(1) parsing Grammar: S → E  T → P * T E → E + T → P → T P →(E) → i2
S → . E 
E → .E + T
E → .T
T → .P*T
T → .P
P →.i
P →.( E )
P → (.E)
E → .E + T
E → .T
T → .P*T
T → .P
P →.i
P →.( E ) 10 1 6 E
NOT LR(0)! T 3 T 3 T
T → P * .T
T → .P*T
T → .P
P →.i
P →.( E ) 12 P 4 P 4 9 P 4 i i 5 5 i 5 ( ( 6 6 ( 6
S → E .  7 7
S → E . 
E → E. + T 2 + ) T
P → (E.)
E → E. + T 8 11 13
E → E + .T
T → .P*T
T → .P
P →.i
P →.( E ) 10 8 P + 8 4 3
E → T. 11
E → E + T. i * 5 4
T →P.*T
T →P. 9 ( 12
T → P * T. 6 5
P → i.
P → (E).
Shift/reduce conflict. 13

5. SLR(1) parsing
Conflicts appear in the ACTION table, as multiple actions.
State + * i ( )  1
S/5
S/6 2
S/8
S/7 3
R/E→T 4
R/T→P
S/9 5
R/P→i 6 7
Accept 8 9 10
S/13 11
R/E→E+T 12
R/T→P*T 13
R/P→(E)

6. SLR(1) parsing Conflict Solution: Use lookahead!
Grammar:
S → E 
E → E + T
→ T
T → P * T
→ P
P →(E)
→ i
SLR(1) parsing
Conflict Solution: Use lookahead!
SLR(1): For each “conflict” state s,
Compute Follow(A) for each conflict production A → ω.
Place “R/A → ω” in ACTION[s,t], only if tFollow(A).
Need Follow(T)  Follow(E) = {+, ),  }. So, change row 4 to
State + * i ( )  4
R/T→P
S/9
State + * i ( )  4
R/T→P
S/9
Shift/reduce conflict solved! Grammar is SLR(1).

7. SLR(1) parsing ┴ Grammar: S’ → S  S → aSb → 1 2 4 3 5 6 2 S’ → .S 
ACTION
GOTO
State a b  S 1
R/S→
S/3 2
S/4 3 5 4
Accept 6
R/S→aSb S 5 3
S → a.Sb
S → .aSb
S → . a 3 4
S’ → S  . b 5 6
S →aS.b 6
S →aSb.
Two shift/reduce conflicts: need Follow(S)

8. SLR(1) parsing Grammar: S’ → S  S → aSb → SLR(1) Analysis:
State 1: Follow(S) = {b, }. Place ’S →’ only in
ACTION[1,b] and ACTION[1, ].
Since a ∉ Follow(S), the shift/reduce conflict is resolved.
State 3: Same story. Table (rows 1,3) changes
ACTION
State a b  1
R/S→
S/3 3
ACTION
State a b  1
S/3
R/S→ 3
from to
Conflicts solved.
Grammar is SLR(1).

9. summary Conflicts in LR(0) Automata Using Follow sets for lookahead
SLR(1) examples