# 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