Programming Language Pragmatics, Fourth Edition
4th Edition
ISBN: 9780124104099
Author: Michael L. Scott
Publisher: Elsevier Science
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Expert Solution & Answer
Chapter 2, Problem 14E
Explanation of Solution
a.
Grammar for LL (1):
Consider the grammar for LL (1) as below:
Grammar for SLR (1):
Consider the grammar for SLR (1) as below:
Explanation of Solution
b.
Parsing table for LL (1) grammar:
| Top-of-stack non-terminal | ( | ) | [ | ] | $$ |
| P | 1 | - | 1 | - | 1 |
| S | 2 | 4 | 3 | 4 | 4 |
- The entries in the above table indicates the production of predict. The “-” means an error.
- If the top-of-stack is terminal, the appropriate action is always to match it against an incoming token from the scanner.
Parsing table for SLR (1) grammar:
| Top-of-stack | S | ( | ) | [ | ] | $$ |
| 0 | s1 | r4 | r4 | r4 | r4 | r4 |
| 1 | - | s2 | - | s3 | - | b1 |
| 2 | s4 | r4 | r4 | r4 | r4 | r4 |
| 3 | s5 | r4 | r4 | r4 | r4 | r4 |
| 4 | - | s2 | b2 | s3 | - | - |
| 5 | - | s2 | - | s3 | b3 | - |
- The entries in the above table indicates whether to shift (s), reduce (r), or shift and then reduce (d). The “-” means an error.
Explanation of Solution
c.
Parsing tree for LL (1):
Parsing tree for SLR (1):
Explanation of Solution
d.
LL (1) trace:
| Parse stack | Input stream | Comment |
| P | ( [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | |
| S $$ | ( [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | Predict P →S $$ |
| ( S ) S $$ | ( [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | Predict S →( S ) S |
| S ) S $$ | [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | Match ( |
| [ S ] S ) S $$ | [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | Predict S →[ S ] S |
| S ] S ) S $$ | ] ( [ ] ) ) [ ] ( ( ) ) $$ | Match [ |
| ] S ) S $$ | ] ( [ ] ) ) [ ] ( ( ) ) $$ | Predict S → ε |
| S ) S $$ | ( [ ] ) ) [ ] ( ( ) ) $$ | Match ] |
| ( S ) S ) S $$ | ( [ ] ) ) [ ] ( ( ) ) $$ | Predict S →( S ) S |
| S ) S ) S $$ | [ ] ) ) [ ] ( ( ) ) $$ | Match ( |
| [ S ] S ) S ) S $$ | [ ] ) ) [ ] ( ( ) ) $$ | Predict S →[ S ] S |
| S ] S ) S ) S $$ | ] ) ) [ ] ( ( ) ) $$ | Match [ |
| ] S ) S ) S $$ | ] ) ) [ ] ( ( ) ) $$ | Predict S → ε |
| S ) S ) S $$ | ) ) [ ] ( ( ) ) $$ | Match ] |
| ) S ) S $$ | ) ) [ ] ( ( ) ) $$ | Predict S → ε |
| S ) S $$ | ) [ ] ( ( ) ) $$ | Predict S → |
| ) S $$ | ) [ ] ( ( ) ) $$ | Predict S → ε |
| S $$ | [ ] ( ( ) ) $$ | Match ) |
| [ S ] S $$ | [ ] ( ( ) ) $$ | Predict S →[ S ] S |
| S ] S $$ | ] ( ( ) ) $$ | Match [ |
| ] S $$ | ] ( ( ) ) $$ | Predict S → ε |
| S $$ | ( ( ) ) $$ | Match ] |
| ( S ) S $$ | ( ( ) ) $$ | Predict S →( S ) S |
| S ) S $$ | ( ) ) $$ | Match ( |
| ( S ) S ) S $$ | ( ) ) $$ | Predict S →( S ) S |
| S ) S ) S $$ | ) ) $$ | Match ( |
| ) S ) S $$ | ) ) $$ | Predict S → ε |
| S ) S $$ | ) $$ | Match ) |
| ) S $$ | ) $$ | Predict S → ε |
| S $$ | $$ | Match ) |
| $$ | $$ | Predict S → ε |
SLR (1) trace:
| Parse stack | Input stream | Comment |
| 0 | ( [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | |
| 0 | S ( [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 | ( [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | Shift S |
| 0S1 ( 2 | [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | Shift ( |
| 0S1 ( 2 | S [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 ( 2 S 4 | [ ] ( [ ] ) ) [ ] ( ( ) ) $$ | Shift S |
| 0S1 ( 2 S 4 [ 3 | ] ( [ ] ) ) [ ] ( ( ) ) $$ | Shift [ |
| 0S1 ( 2 S 4 [ 3 | S ] ( [ ] ) ) [ ] ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 ( 2 S 4 [ 3 S 5 | ] ( [ ] ) ) [ ] ( ( ) ) $$ | Shift S |
| 0S1 ( 2 | ( [ ] ) ) [ ] ( ( ) ) $$ | Shift and reduce by S→ S [ S ] |
| 0S1 ( 2 | S ( [ ] ) ) [ ] ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 ( 2 S 4 | ( [ ] ) ) [ ] ( ( ) ) $$ | Shift S |
| 0S1 ( 2 S 4 ( 2 | [ ] ) ) [ ] ( ( ) ) $$ | Shift ( |
| 0S1 ( 2 S 4 ( 2 | S [ ] ) ) [ ] ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 ( 2 S 4 ( 2 S 4 | [ ] ) ) [ ] ( ( ) ) $$ | Shift S |
| 0S1 ( 2 S 4 ( 2 S 4 [ 3 | ] ) ) [ ] ( ( ) ) $$ | Shift [ |
| 0S1 ( 2 S 4 ( 2 S 4 [ 3 | S ] ) ) [ ] ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 ( 2 S 4 ( 2 S 4 [ 3 S 5 | ] ) ) [ ] ( ( ) ) $$ | Shift S |
| 0S1 ( 2 S 4 ( 2 | ) ) [ ] ( ( ) ) $$ | Shift and reduce by S→ S [ S ] |
| 0S1 ( 2 S 4 ( 2 | S ) ) [ ] ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 ( 2 S 4 ( 2 S 4 | ) ) [ ] ( ( ) ) $$ | Shift S |
| 0S1 ( 2 | ) [ ] ( ( ) ) $$ | Shift and reduce by S→ S ( S ) |
| 0S1 ( 2 | S ) [ ] ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 ( 2 S 4 | ) [ ] ( ( ) ) $$ | Shift S |
| 0 | [ ] ( ( ) ) $$ | Shift and reduce by S→ S ( S ) |
| 0 | S [ ] ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 | [ ] ( ( ) ) $$ | Shift S |
| 0S1 [ 3 | ] ( ( ) ) $$ | Shift [ |
| 0S1 [ 3 | S ] ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 [ 3 S 5 | ] ( ( ) ) $$ | Shift S |
| 0 | ( ( ) ) $$ | Shift and reduce by S→ S [ S ] |
| 0 | S ( ( ) ) $$ | Reduce by S→ ε |
| 0S1 | ( ( ) ) $$ | Shift S |
| 0S1 ( 2 | ( ) ) $$ | Shift ( |
| 0S1 ( 2 | S ( ) ) $$ | Reduce by S→ ε |
| 0S1 ( 2 S 4 | ( ) ) $$ | Shift S |
| 0S1 ( 2 S 4 ( 2 | ) ) $$ | Shift ( |
| 0S1 ( 2 S 4 ( 2 | S ) ) $$ | Reduce by S→ ε |
| 0S1 ( 2 S 4 ( 2 S 4 | ) ) $$ | Shift S |
| 0S1 ( 2 | ) $$ | Shift and reduce by S→ S ( S ) |
| 0S1 ( 2 | S ) $$ | Reduce by S→ ε |
| 0S1 ( 2 S 4 | ) $$ | Shift S |
| 0 | $$ | Shift and reduce by S→ S ( S ) |
| 0 | S $$ | Reduce by S→ ε |
| 0S1 | $$ | Shift S |
| 0 | P | Shift and reduce by S→ S ( S ) |
| [done] |
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Chapter 2 Solutions
Programming Language Pragmatics, Fourth Edition
Ch. 2.1 - Prob. 1CYUCh. 2.1 - Prob. 2CYUCh. 2.1 - Prob. 3CYUCh. 2.1 - Prob. 4CYUCh. 2.1 - Prob. 5CYUCh. 2.1 - Prob. 6CYUCh. 2.1 - Prob. 7CYUCh. 2.1 - Prob. 8CYUCh. 2.1 - Prob. 9CYUCh. 2.2 - Prob. 10CYU
Ch. 2.2 - Prob. 11CYUCh. 2.2 - Prob. 12CYUCh. 2.2 - Prob. 13CYUCh. 2.2 - Prob. 14CYUCh. 2.2 - Prob. 15CYUCh. 2.2 - Prob. 16CYUCh. 2.2 - Prob. 17CYUCh. 2.2 - Prob. 18CYUCh. 2.2 - Prob. 19CYUCh. 2.3 - Prob. 20CYUCh. 2.3 - Prob. 21CYUCh. 2.3 - Prob. 22CYUCh. 2.3 - Prob. 23CYUCh. 2.3 - Prob. 24CYUCh. 2.3 - Prob. 25CYUCh. 2.3 - Prob. 26CYUCh. 2.3 - Prob. 27CYUCh. 2.3 - Prob. 28CYUCh. 2.3 - Prob. 29CYUCh. 2.3 - Prob. 30CYUCh. 2.3 - Prob. 31CYUCh. 2.3 - Prob. 32CYUCh. 2.3 - Prob. 33CYUCh. 2.3 - Prob. 34CYUCh. 2.3 - Prob. 35CYUCh. 2.3 - Prob. 36CYUCh. 2.3 - Prob. 37CYUCh. 2.3 - Prob. 38CYUCh. 2.3 - Prob. 39CYUCh. 2.3 - Prob. 40CYUCh. 2.3 - Prob. 41CYUCh. 2.3 - Prob. 42CYUCh. 2.3 - Prob. 43CYUCh. 2.3 - Prob. 44CYUCh. 2 - Prob. 3ECh. 2 - Prob. 4ECh. 2 - Prob. 5ECh. 2 - Prob. 9ECh. 2 - Prob. 10ECh. 2 - Prob. 11ECh. 2 - Prob. 12ECh. 2 - Prob. 13ECh. 2 - Prob. 14ECh. 2 - Prob. 15ECh. 2 - Prob. 16ECh. 2 - Prob. 17ECh. 2 - Prob. 18ECh. 2 - Prob. 19ECh. 2 - Prob. 20ECh. 2 - Prob. 24ECh. 2 - Prob. 26ECh. 2 - Prob. 27ECh. 2 - Prob. 28ECh. 2 - Prob. 38EQCh. 2 - Prob. 40EQ
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