Portability | portable |
---|---|

Stability | experimental |

Maintainer | Sebastian Fischer (sebf@informatik.uni-kiel.de) |

Safe Haskell | Safe-Inferred |

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.

- data Boolean
- data SatSolver
- data Literal
- literalVar :: Literal -> Int
- invLiteral :: Literal -> Literal
- isPositiveLiteral :: Literal -> Bool
- type CNF = [Clause]
- type Clause = [Literal]
- booleanToCNF :: Boolean -> CNF
- newSatSolver :: SatSolver
- isSolved :: SatSolver -> Bool
- lookupVar :: Int -> SatSolver -> Maybe Bool
- assertTrue :: MonadPlus m => Boolean -> SatSolver -> m SatSolver
- assertTrue' :: MonadPlus m => CNF -> SatSolver -> m SatSolver
- branchOnVar :: MonadPlus m => Int -> SatSolver -> m SatSolver
- selectBranchVar :: SatSolver -> Int
- solve :: MonadPlus m => SatSolver -> m SatSolver
- isSolvable :: SatSolver -> Bool

# Documentation

Boolean formulas are represented as values of type `Boolean`

.

Literals are variables that occur either positively or negatively.

literalVar :: Literal -> IntSource

This function returns the name of the variable in a literal.

invLiteral :: Literal -> LiteralSource

This function negates a literal.

isPositiveLiteral :: Literal -> BoolSource

This predicate checks whether the given literal is positive.

booleanToCNF :: Boolean -> CNFSource

We convert boolean formulas to conjunctive normal form by pushing negations down to variables and repeatedly applying the distributive laws.

newSatSolver :: SatSolverSource

A new SAT solver without stored constraints.

lookupVar :: Int -> SatSolver -> Maybe BoolSource

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 SatSolverSource

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 SatSolverSource

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 -> IntSource

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

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

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 -> BoolSource

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.