Safe Haskell | None |
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- mkDV :: [a] -> CSP r (DV r a)
- constraint1 :: (a -> Bool) -> DV r1 a -> CSP r ()
- constraint2 :: (a -> t1 -> Bool) -> DV t a -> DV t t1 -> CSP r ()
- constraint :: ([a] -> Bool) -> [DV r1 a] -> CSP r ()
- oneCSPSolution :: CSPResult a1 => CSP (Result a1) a1 -> Result a1
- allCSPSolutions :: CSPResult a1 => CSP (Result a1) a1 -> [Result a1]
- solveCSP :: CSPResult a1 => (AmbT r IO (Result a1) -> IO a) -> CSP r a1 -> a
- class CSPResult a where
- csp :: IO x -> CSP r x
- domain :: DV t t1 -> IO [t1]
- demons :: DV r a -> IO [Constraint r]
- isBound :: DV t t1 -> IO Bool
- domainSize :: DV t t1 -> IO Int
- localWriteIORef :: IORef a -> a -> AmbT r IO ()
- binding :: DV t b -> IO b
- addConstraint :: DV r1 a -> Constraint r1 -> CSP r ()
- restrictDomain :: DV r a -> ([a] -> IO [a]) -> AmbT r IO ()
- data DV r a = DV {
- dvDomain :: IORef [a]
- dvConstraints :: IORef [Constraint r]
- data DVContainer r = DVContainer {
- dvcIsBound :: AmbT r IO Bool
- dvcConstraints :: AmbT r IO ()
- dvcABinding :: AmbT r IO ()
- type Constraint r = AmbT r IO ()
- data CSP r x = CSP {
- unCSP :: IORef [DVContainer r] -> IO x
Overview
This constructs a discrete constraint satisfaction problem (CSP) and then solves it. A discrete CSP consists of a number of variables each having a discrete domain along with a number of constraints between those variables. Solving a CSP searches for assignments to the variables which satisfy those constraints. At the moment the only constraint propagation technique available is arc consistency.
Here is a simple example which solves Sudoku puzzles, project Euler problem 96.
import Data.List import Control.Monad.CSP 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]] 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 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
[[4,6,2,8,3,1,9,5,7],[7,9,5,4,2,6,1,8,3],[3,8,1,7,9,5,4,2,6],[1,7,3,9,8,4,2,6,5],[6,5,9,3,1,2,7,4,8],[2,4,8,5,6,7,3,1,9],[9,2,6,1,7,8,5,3,4],[8,3,4,2,5,9,6,7,1],[5,1,7,6,4,3,8,9,2]]
Building CSPs
constraint1 :: (a -> Bool) -> DV r1 a -> CSP r ()Source
Assert a unary constraint.
constraint2 :: (a -> t1 -> Bool) -> DV t a -> DV t t1 -> CSP r ()Source
Assert a binary constraint with arc consistency.
constraint :: ([a] -> Bool) -> [DV r1 a] -> CSP r ()Source
Assert an n-ary constraint with arc consistency. One day this will allow for a heterogeneous list of variables, but at the moment they must all be of the same type.
Solving CSPs
allCSPSolutions :: CSPResult a1 => CSP (Result a1) a1 -> [Result a1]Source
Return all solutions to the CSP. solveCSP
running with
allValuesT
solveCSP :: CSPResult a1 => (AmbT r IO (Result a1) -> IO a) -> CSP r a1 -> aSource
Solve the given CSP. The CSP solver is a nondeterministic function in IO and this is the generic interface which specifies how the nondeterministic computation should be carried out.
This extracts results from a CSP.
Low-level internal
Lift an IO computation into the CSP monad. CSPs are only in IO temporarily.
demons :: DV r a -> IO [Constraint r]Source
Extract the current constraints of a variable.
domainSize :: DV t t1 -> IO IntSource
Compute the size of the current domain of variable.
localWriteIORef :: IORef a -> a -> AmbT r IO ()Source
This performs a side-effect, writing to the given IORef but records this in the nondeterministic computation so that it can be undone when backtracking.
addConstraint :: DV r1 a -> Constraint r1 -> CSP r ()Source
Add a constraint to the given variable.
restrictDomain :: DV r a -> ([a] -> IO [a]) -> AmbT r IO ()Source
The low-level function out of which constraints are constructed. It modifies the domain of a variable.
Types
data DVContainer r Source
DVContainer | |
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type Constraint r = AmbT r IO ()Source