# csp

Discrete constraint satisfaction problem (CSP) solver.

 Version on this page: 1.4.0 LTS Haskell 13.4: 1.4.0 Stackage Nightly 2019-01-23: 1.4.0 Latest on Hackage: 1.4.0

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LicenseRef-LGPL licensed and maintained by

#### Module documentation for 1.4.0

• Control
• Control.Monad

# 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 donâ€™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
Depends on 4 packages:
Used by 1 package:
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