Looking for advice on project. Parsing logical expression

Question

I'm looking for some advice on my school project. I am supposed to create a program that takes a logical expression and outputs a truth table for it. The actually creating of the truth table for me is not difficult at all and I've already wrote the methods in Java for it. I would like to know if there are any classes in java that I could use to parse the expression for me and put it into a stack. If not I'm looking for help on parsing the expression. It's the parentheses that get me whenever I try and think it through. Also if this would be easier in any other language I would be open to doing it in that. Perl is probably my next best language.

Some examples (P && Q) -> R

(P || Q || R) && ((P -> R) -> Q)

Answer 1

If you're allowed to use a parser generator tool like ANTLR, here's how you could get started. The grammar for a simple logic-language could look like this:

grammar Logic;

parse
  :  expression EOF
  ;

expression
  :  implication
  ;

implication
  :  or ('->' or)*
  ;

or
  :  and ('||' and)*
  ;

and
  :  not ('&&' not)*
  ;

not
  :  '~' atom
  |  atom
  ;

atom
  :  ID
  |  '(' expression ')'
  ;

ID    : ('a'..'z' | 'A'..'Z')+;
Space : (' ' | '\t' | '\r' | '\n')+ {$channel=HIDDEN;};

However, if you'd parse input like (P || Q || R) && ((P -> R) -> Q) with a parser generated from the grammar above, the parse tree would contain the parenthesis (something you're not interested in after parsing the expression) and the operators would not be the root of each sub-trees, which doesn't make your life any easier if you're interested in evaluating the expression.

You'll need to tell ANTLR to omit certain tokens from the AST (this can be done by placing a ! after the token/rule) and make certain tokens/rules the root of their (sub) tree (this can be done by placing a ^ after it). Finally, you need to indicate in the options section of your grammar that you want a proper AST to be created instead of a simple parse tree.

So, the grammar above would look like this:

// save it in a file called Logic.g
grammar Logic;

options {
  output=AST;
}

// parser/production rules start with a lower case letter
parse
  :  expression EOF!    // omit the EOF token
  ;

expression
  :  implication
  ;

implication
  :  or ('->'^ or)*    // make `->` the root
  ;

or
  :  and ('||'^ and)*    // make `||` the root
  ;

and
  :  not ('&&'^ not)*      // make `&&` the root
  ;

not
  :  '~'^ atom    // make `~` the root
  |  atom
  ;

atom
  :  ID
  |  '('! expression ')'!    // omit both `(` and `)`
  ;

// lexer/terminal rules start with an upper case letter
ID    : ('a'..'z' | 'A'..'Z')+;
Space : (' ' | '\t' | '\r' | '\n')+ {$channel=HIDDEN;};

You can test the parser with the following class:

import org.antlr.runtime.*;
import org.antlr.runtime.tree.*;
import org.antlr.stringtemplate.*;

public class Main {
  public static void main(String[] args) throws Exception {

    // the expression
    String src = "(P || Q || R) && ((P -> R) -> Q)";

    // create a lexer & parser
    LogicLexer lexer = new LogicLexer(new ANTLRStringStream(src));
    LogicParser parser = new LogicParser(new CommonTokenStream(lexer));

    // invoke the entry point of the parser (the parse() method) and get the AST
    CommonTree tree = (CommonTree)parser.parse().getTree();

    // print the DOT representation of the AST 
    DOTTreeGenerator gen = new DOTTreeGenerator();
    StringTemplate st = gen.toDOT(tree);
    System.out.println(st);
  }
}

Now to run the Main class, do:

*nix/MacOS

java -cp antlr-3.3.jar org.antlr.Tool Logic.g 
javac -cp antlr-3.3.jar *.java
java -cp .:antlr-3.3.jar Main

Windows

java -cp antlr-3.3.jar org.antlr.Tool Logic.g 
javac -cp antlr-3.3.jar *.java
java -cp .;antlr-3.3.jar Main

which will print a DOT source of the following AST:

(image produced with graphviz-dev.appspot.com)

Now all you need to do is evaluate this AST! :)

Answer 2

In Perl you can use Regexp::Grammars to do the parsing. It may be a little on the "grenade to kill an ant" side, but it should work.

Edit: Here is a (very quick) example which might get you going.

#!/usr/bin/env perl

use strict;
use warnings;

use Regexp::Grammars;
use Data::Dumper;

my $parser = qr/
  <nocontext:>

  <Logic>

  <rule: Logic>     <[Element]>*

  <rule: Element>   <Group> | <Operator> | <Item>

  <rule: Group>     \( <[Element]>* \)

  <rule: Operator>  (?:&&) | (?:\|\|) | (?:\-\>)

  <rule: Item>      \w+
/xms;                    #/ #Fix Syntax Highlight

my $text = '(P && Q) -> R';

print Dumper \%/ if $text =~ $parser; #/ #Fix Syntax Highlight