Module documentation for 1.3.1
This package is available via
Hackage where its documentation resides. It
provides a solver for constraint satisfaction problems by implementing
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
- 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