Simple Boolean Expression Manipulation in Java

I’ve worked on a couple projects recently where I needed to be able to do some lightweight propositional expression manipulation in Java.  Specifically, I wanted to be able to:

  • Let a user input simple logical expressions, and parse them into Java data structures
  • Evaluate the truth of the statement given values for each variable
  • Incrementally update the expression as values are assigned to the variables
  • If the statement given some variable assignments is not definitively true or false, show which terms remain.
  • Perform basic simplification of redundant terms (full satisfiability is of course NP hard, so this would only include basic simplification)

I couldn’t find a Java library which made this particularly easy; a couple stackoverflow questions I found didn’t have any particularly easy solutions.  I decided to take a shot at implementing a basic library.  The result is on GitHub as the jbool_expressions library.

(most of the rest of this is copied from the README, so feel free to read it there.)

Using the library, a basic propositional expression is built out of the types And, Or, Not, Variable and Literal. All of these extend the base type Expression.  An Expression can be built programatically:

    Expression expr = And.of(
        Or.of(Variable.of("C"), Not.of(Variable.of("C"))));

or by parsing a string:

    Expression expr =
        ExprParser.parse("( ( (! C) | C) & A & B)");

The expression is the same either way:

    ((!C | C) & A & B)

We can do some basic simplification to eliminate the redundant terms:

    Expression simplified = RuleSet.simplify(expr);

to see the redundant terms are simplified to “true”:

    (A & B)

We can assign a value to one of the variables, and see that the expression is simplified after assigning “A” a value:

    Expression halfAssigned = RuleSet.assign(
        Collections.singletonMap("A", true)

We can see the remaining expression:


If we assign a value to the remaining variable, we can see the expression evaluate to a literal:

    Expression resolved = RuleSet.assign(
         Collections.singletonMap("B", true)

All expressions are immutable (we got a new expression back each time we performed an operation), so we can see that the original expression is unmodified:

    ((!C | C) & A & B)

Expressions can also be converted to sum-of-products form:

    Expression nonStandard = PrefixParser.parse(
        "(* (+ A B) (+ C D))"


    Expression sopForm = RuleSet.toSop(nonStandard);
    ((A | B) & (C | D))
    ((A & C) | (A & D) | (B & C) | (B & D))

You can build the library yourself or grab it via maven:


Happy to hear any feedback / bugs / improvements etc. I’d also be interested in hearing how other people have dealt with this problem, and if there are any better libraries out there.

This entry was posted in Algorithms, Github, Open Source. Bookmark the permalink.

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