Data.Boolean.SatSolver

This Haskell library provides an implementation of the Davis-Putnam-Logemann-Loveland algorithm (cf. http://en.wikipedia.org/wiki/DPLL_algorithm) for the boolean satisfiability problem. It not only allows to solve boolean formulas in one go but also to add constraints and query bindings of variables incrementally.

The implementation is not sophisticated at all but uses the basic DPLL algorithm with unit propagation.

Documentation

data Boolean

Boolean formulas are represented as values of type Boolean.

Constructors

Var Int

Variables are labeled with an Int,

Yes

Yes represents true,

No

No represents false,

Not Boolean

Not constructs negated formulas,

Boolean :&&: Boolean

and finally we provide conjunction

Boolean :||: Boolean

and disjunction of boolean formulas.

Instances

Show Boolean

data SatSolver

A SatSolver can be used to solve boolean formulas.

Instances

Show SatSolver

newSatSolver :: SatSolver

A new SAT solver without stored constraints.

isSolved :: SatSolver -> Bool

This predicate tells whether all constraints are solved.

lookupVar :: Int -> SatSolver -> Maybe Bool

We can lookup the binding of a variable according to the currently stored constraints. If the variable is unbound, the result is Nothing.

assertTrue :: MonadPlus m => Boolean -> SatSolver -> m SatSolver

We can assert boolean formulas to update a SatSolver. The assertion may fail if the resulting constraints are unsatisfiable.

branchOnVar :: MonadPlus m => Int -> SatSolver -> m SatSolver

This function guesses a value for the given variable, if it is currently unbound. As this is a non-deterministic operation, the resulting solvers are returned in an instance of MonadPlus.

selectBranchVar :: SatSolver -> Int

We select a variable from the shortest clause hoping to produce a unit clause.

solve :: MonadPlus m => SatSolver -> m SatSolver

This function guesses values for variables such that the stored constraints are satisfied. The result may be non-deterministic and is, hence, returned in an instance of MonadPlus.

isSolvable :: SatSolver -> Bool

This predicate tells whether the stored constraints are solvable. Use with care! This might be an inefficient operation. It tries to find a solution using backtracking and returns True if and only if that fails.