eqbool

Testing boolean expressions for equivalence.

eqbool is a C++ and Python rewrite of code originally developed as part of a symbolic gate-level Z80 simulator in pure Python, where increasingly complex Boolean expressions representing gate states need to be repeatedly checked for equivalence. Z3 and several other existing libraries were tried and quickly proven too slow for such use, so a custom solution had to be developed.

The library is specifically designed to reduce overall equivalence-check times by simplifying expressions in ways that never increase the diversity of SAT clauses.

Where equivalence cannot be trivially established via simplifications, eqbool uses the CaDiCaL solver.

#include "eqbool.h"

int main() {
    eqbool::term_set<std::string> terms;
    eqbool::eqbool_context eqbools(terms);
    using eqbool::eqbool;

    eqbool eqfalse = eqbools.get_false();
    eqbool eqtrue = eqbools.get_true();

    // Constants are evaluated and eliminated right away.
    assert((eqfalse | ~eqfalse) == eqtrue);

    // Expressions get simplified on construction.
    eqbool a = eqbools.get(terms.add("a"));
    eqbool b = eqbools.get(terms.add("b"));
    assert((~b | ~eqbools.ifelse(a, b, ~b)) == (~a | ~b));

    // Identical, but differently spelled expressions are uniquified.
    eqbool c = eqbools.get(terms.add("c"));
    assert(((a | b) | c) == (a | (b | c)));

    // Speed is king, so simplifications that require deep traversals,
    // restructuring of existing nodes and increasing the diversity of
    // SAT clauses are intentionally omitted.
    eqbool d = eqbools.get(terms.add("d"));
    eqbool e1 = a & ((b | c) | (~a | ((~b | (d | ~c)) & (c | ~b))));
    eqbool e2 = a;
    assert(!eqbools.is_trivially_equiv(e1, e2));

    // The equivalence can still be established using SAT.
    assert(eqbools.is_equiv(e1, e2));

    // From there on, the expressions are considered identical.
    assert(eqbools.is_trivially_equiv(e1, e2));

    // They then can be propagated to their simplest known forms.
    assert(e1 != e2);

    e1.propagate();
    e2.propagate();
    assert(e1 == e2);
}

example.cpp

In Python

pip install eqbool

import eqbool


def main():
    # Undefined Bool objects have no associated value or context.
    assert eqbool.Bool().is_undef

    ctx = eqbool.Context()
    assert ctx.false | ~ctx.false == ctx.true

    # Terms can be any hashable objects.
    a = ctx.get('a')
    b = ctx.get('b')
    e = ~b | ~ctx.ifelse(a, b, ~b)
    assert e == ~a | ~b

    # Bool values can be verbalised as usual.
    print(e)

    c = ctx.get('c')
    assert (a | b) | c == a | (b | c)

    # In the Python API, all values get propagated automatically, so
    # simple equality can be used to test for trivial equivalence.
    d = ctx.get('d')
    e1 = a & ((b | c) | (~a | ((~b | (d | ~c)) & (c | ~b))))
    e2 = a
    assert e1 != e2

    assert ctx.is_equiv(e1, e2)

    assert e1 == e2

example.py