Haskell PicoSAT

haskell-picosat are Haskell bindings to the PicoSAT solver, written in C. It reads in clauses in CNF ( Conjunctive-Normal Form ) and returns a solution which satisfies the clauses.

The most notable distinction of this binding is that the SAT solver library is included with the cabal package so you shouldn't need to install anything but this package to get going. It's also notably faster than a pure Haskell solution at solving very large constraint problems.

Installing

$ cabal install picosat

Usage

If we have a table of variables representing logical statements we can enumerate them with integers.

A  1
B  2
C  3
D  4
E  5
F  6

Then the clause can be written as sequences of positive integers (assertion) and negative integers (negation):

(A v ¬B v C)
1 -2 3 0

(B v D v E)
2 4 5 0

(D V F)
4 6 0

Solutions to a statement of the form:

(A v ¬B v C) ∧ (B v D v E) ∧ (D v F)

Can be written as zero-terminated lists of integers:

1 -2 3 0
2 4 5 0
4 6 0

To use the Haskell bindings simply pass a list of clauses to the solve function, this will return either the solution or Unsatisfiable or Unknown.

import Picosat

main :: IO [Int]
main = do
  solve [[1, -2, 3], [2,4,5], [4,6]]
  -- Solution [1,-2,3,4,5,6]

The solution given we can interpret as:

1   A 
-2 ¬B 
3   C
4   D
5   E
6   F

To generate all possible solutions we repeatedly feed the negated solution to the solver yielding which is implemented with the solveAll function which yields a sequence of solutions.

import Picosat

main :: IO [Int]
main = solveAll [[1,2]]
  -- [Solution [1,2],Solution [-1,2],Solution [1,-2]]

For a more complicated example a Sudoku solver is included as an example.

License

PicoSAT itself is included and is also licensed the MIT license. Copyright (c) 2006 - 2012, Armin Biere, Johannes Kepler University.

Released under the MIT License. Copyright (c) 2013-2020, Stephen Diehl