csp-haskell's Introduction

CSP

This package is now available via Hackage, and is primarily documented there.

A simple example which solves Sudoku puzzles, project Euler problem 96.

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]]

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 sudoku3

Future

Docs!
Allow a randomized execution order for CSPs
CSPs don't need 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

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