module Ersatz.Relation.Data ( Relation
, relation, symmetric_relation
, build
, identity
, bounds, (!), indices, assocs, elems
, table
) where
import Ersatz.Bit
import Ersatz.Codec
import Ersatz.Variable (exists)
import Ersatz.Problem (HasSAT)
import qualified Data.Array as A
import Data.Array ( Array, Ix )
import Control.Monad.State
newtype Relation a b = Relation (A.Array (a, b) Bit)
instance (Ix a, Ix b) => Codec (Relation a b) where
type Decoded (Relation a b) = A.Array (a, b) Bool
decode s (Relation a) = decode s a
encode a = Relation $ encode a
relation :: ( Ix a, Ix b, MonadState s m, HasSAT s )
=> ((a,b),(a,b)) -> m ( Relation a b )
relation bnd = do
pairs <- sequence $ do
p <- A.range bnd
return $ do
x <- exists
return ( p, x )
return $ build bnd pairs
symmetric_relation ::
(HasSAT s, MonadState s m, Ix b) =>
((b, b), (b, b)) -> m (Relation b b)
symmetric_relation bnd = do
pairs <- sequence $ do
(p,q) <- A.range bnd
guard $ p <= q
return $ do
x <- exists
return $ [ ((p,q), x ) ]
++ [ ((q,p), x) | p /= q ]
return $ build bnd $ concat pairs
identity :: ( Ix a )
=> ((a,a),(a,a)) -> Relation a a
identity bnd = build bnd $ flip map (A.range bnd) $ \ (i,j) ->
((i,j), if i == j then true else false )
build :: ( Ix a, Ix b )
=> ((a,b),(a,b))
-> [ ((a,b), Bit ) ]
-> Relation a b
build bnd pairs = Relation $ A.array bnd pairs
bounds :: (Ix a, Ix b) => Relation a b -> ((a,b),(a,b))
bounds ( Relation r ) = A.bounds r
indices :: (Ix a, Ix b) => Relation a b -> [(a, b)]
indices ( Relation r ) = A.indices r
assocs :: (Ix a, Ix b) => Relation a b -> [((a, b), Bit)]
assocs ( Relation r ) = A.assocs r
elems :: (Ix a, Ix b) => Relation a b -> [Bit]
elems ( Relation r ) = A.elems r
(!) :: (Ix a, Ix b) => Relation a b -> (a, b) -> Bit
Relation r ! p = r A.! p
table :: (Enum a, Ix a, Enum b, Ix b)
=> Array (a,b) Bool -> String
table r = unlines $ do
let ((a,b),(c,d)) = A.bounds r
x <- [ a .. c ]
return $ unwords $ do
y <- [ b .. d ]
return $ if r A.! (x,y) then "*" else "."