Discrete constraint satisfaction problem (CSP) solver.

Constraint satisfaction problem (CSP) solvers

CSP

This package is available via Hackage where its documentation resides. It provides a solver for constraint satisfaction problems by implementing a CSP monad. Currently it only implements arc consistency but other kinds of constraints will be added.

Below is a Sudoku solver, project Euler problem 96.

import Data.List
import Control.Monad.CSP

mapAllPairsM_ :: Monad m => (a -> a -> m b) -> [a] -> m ()
mapAllPairsM_ f []     = return ()
mapAllPairsM_ f (_:[]) = return ()
mapAllPairsM_ f (a:l) = mapM_ (f a) l >> mapAllPairsM_ f l

solveSudoku :: (Enum a, Eq a, Num a) => [[a]] -> [[a]]
solveSudoku puzzle = oneCSPSolution $ do
  dvs <- mapM (mapM (\a -> mkDV $ if a == 0 then [1 .. 9] else [a])) puzzle
  mapM_ assertRowConstraints dvs
  mapM_ assertRowConstraints $ transpose dvs
  sequence_ [assertSquareConstraints dvs x y | x <- [0,3,6], y <- [0,3,6]]
  return dvs
      where assertRowConstraints =  mapAllPairsM_ (constraint2 (/=))
            assertSquareConstraints dvs i j = 
                mapAllPairsM_ (constraint2 (/=)) [(dvs !! x) !! y | x <- [i..i+2], y <- [j..j+2]]

sudoku3 = [[0,0,0,0,0,0,9,0,7],
           [0,0,0,4,2,0,1,8,0],
           [0,0,0,7,0,5,0,2,6],
           [1,0,0,9,0,4,0,0,0],
           [0,5,0,0,0,0,0,4,0],
           [0,0,0,5,0,7,0,0,9],
           [9,2,0,1,0,8,0,0,0],
           [0,3,4,0,5,9,0,0,0],
           [5,0,7,0,0,0,0,0,0]]

solveSudoku sudoku3

Future

• Allow a randomized execution order for CSPs
• CSPs don't need to use IO internally. ST is enough.
• Constraint synthesis. Already facilitated by the fact that constraints are internally nondeterministic
• Other constraint types for CSPs, right now only AC is implemented
• n-ary heterogeneous constraints.