Problems with follow sets, epsilon handling, LR0 table

[rick-masters]

There are some problems with follow sets, epsilon handling, and the lr0 action table which I have been able to identify fixes for.

But before that, thank you very much for writing this code. Your code is smaller and simpler than a lot of other projects and it has helped me to learn LR parsing better.

This grammar is not handled correctly:

S -> A B
A -> a
A -> epsilon
B -> b
B -> epsilon

The following test program demonstrates incorrect tables. The proper tables are shown down below further. They can also be computed online at https://mdaines.github.io/grammophone
(just add periods to the end of rules and remove the epsilons).

import util.*;
import lr1.*;
public class TestLR
{
    public static void main(String[] args) {
        String grammarText = "S -> A B  \n" +
                             "A -> a       \n" +
                             "A -> epsilon \n" +
                             "B -> b       \n" +
                             "B -> epsilon \n";
        LR1Parser lr1Parser = new LR1Parser(new Grammar(grammarText));
        if (lr1Parser.parseCLR1()) {
            System.out.println(lr1Parser.actionTableStr());
            System.out.println(lr1Parser.goToTableStr());
        }
        else {
            System.out.println("parse not ok");
        }
    }
}

$ java TestLR
Rules:
0 : S' -> S
1 : S -> A B
2 : A -> a
3 : A -> epsilon
4 : B -> b
5 : B -> epsilon
Action Table :
                epsilon   a         b         $
----------------------------------------------------
|0         |  SHIFT 1|  SHIFT 3|         |         |
----------------------------------------------------
|1         |         |         | REDUCE 3| REDUCE 3|
----------------------------------------------------
|2         |  SHIFT 5|         |  SHIFT 7|         |
----------------------------------------------------
|3         |         |         | REDUCE 2| REDUCE 2|
----------------------------------------------------
|4         |         |         |         |  ACCEPT |
----------------------------------------------------
|5         |         |         |         | REDUCE 5|
----------------------------------------------------
|6         |         |         |         | REDUCE 1|
----------------------------------------------------
|7         |         |         |         | REDUCE 4|
----------------------------------------------------
Go TO Table :
          A     B     S
--------------------------
|0     |    2|     |    4|
--------------------------
|1     |     |     |     |
--------------------------
|2     |     |    6|     |
--------------------------
|3     |     |     |     |
--------------------------
|4     |     |     |     |
--------------------------
|5     |     |     |     |
--------------------------
|6     |     |     |     |
--------------------------
|7     |     |     |     |
--------------------------

Epsilon should not be in the action table. Also, the action table is not correct. For example in state 0 an EOF ($) is valid, and should be a reduce of A to epsilon (rule 3).

This is the correct output:

$ java TestLR
Rules:
0 : S' -> S
1 : S -> A B
2 : A -> a
3 : A -> epsilon
4 : B -> b
5 : B -> epsilon
Action Table :
                a         b         $
------------------------------------------
|0         |  SHIFT 2| REDUCE 3| REDUCE 3|
------------------------------------------
|1         |         |  SHIFT 5| REDUCE 5|
------------------------------------------
|2         |         | REDUCE 2| REDUCE 2|
------------------------------------------
|3         |         |         |  ACCEPT |
------------------------------------------
|4         |         |         | REDUCE 1|
------------------------------------------
|5         |         |         | REDUCE 4|
------------------------------------------
Go TO Table :
         A     B     S
--------------------------
|0     |    1|     |    3|
--------------------------
|1     |     |    4|     |
--------------------------
|2     |     |     |     |
--------------------------
|3     |     |     |     |
--------------------------
|4     |     |     |     |
--------------------------
|5     |     |     |     |
--------------------------

I have prepared fixes and will send over a pull request.

I want to also let you know that I plan on using this code in a new project soon. It is much appreciated that you offered an MIT license.

[Amirhossein Hassankhani]

Thank you very much for your help.

[rick-masters]

This is resolved and can be closed.