{-# language TypeFamilies #-}
module Ersatz.Relation.Data (
Relation
, relation, symmetric_relation
, build
, buildFrom
, identity
, bounds, (!), indices, assocs, elems
, table
) where
import Prelude hiding ( and )
import Ersatz.Bit
import Ersatz.Codec
import Ersatz.Variable (exists)
import Ersatz.Problem (MonadSAT)
import Control.Monad (guard)
import qualified Data.Array as A
import Data.Array ( Array, Ix )
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 :: forall (f :: * -> *).
MonadPlus f =>
Solution -> Relation a b -> f (Decoded (Relation a b))
decode Solution
s (Relation Array (a, b) Bit
a) = forall a (f :: * -> *).
(Codec a, MonadPlus f) =>
Solution -> a -> f (Decoded a)
decode Solution
s Array (a, b) Bit
a
encode :: Decoded (Relation a b) -> Relation a b
encode Decoded (Relation a b)
a = forall a b. Array (a, b) Bit -> Relation a b
Relation forall a b. (a -> b) -> a -> b
$ forall a. Codec a => Decoded a -> a
encode Decoded (Relation a b)
a
relation :: ( Ix a, Ix b, MonadSAT s m ) =>
((a,b),(a,b))
-> m ( Relation a b )
relation :: forall a b s (m :: * -> *).
(Ix a, Ix b, MonadSAT s m) =>
((a, b), (a, b)) -> m (Relation a b)
relation ((a, b), (a, b))
bnd = do
[((a, b), Bit)]
pairs <- forall (t :: * -> *) (m :: * -> *) a.
(Traversable t, Monad m) =>
t (m a) -> m (t a)
sequence forall a b. (a -> b) -> a -> b
$ do
(a, b)
p <- forall a. Ix a => (a, a) -> [a]
A.range ((a, b), (a, b))
bnd
forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ do
Bit
x <- forall a s (m :: * -> *). (Variable a, MonadSAT s m) => m a
exists
forall (m :: * -> *) a. Monad m => a -> m a
return ( (a, b)
p, Bit
x )
forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ forall a b.
(Ix a, Ix b) =>
((a, b), (a, b)) -> [((a, b), Bit)] -> Relation a b
build ((a, b), (a, b))
bnd [((a, b), Bit)]
pairs
symmetric_relation ::
(MonadSAT s m, Ix b) =>
((b, b), (b, b))
-> m (Relation b b)
symmetric_relation :: forall s (m :: * -> *) b.
(MonadSAT s m, Ix b) =>
((b, b), (b, b)) -> m (Relation b b)
symmetric_relation ((b, b), (b, b))
bnd = do
[[((b, b), Bit)]]
pairs <- forall (t :: * -> *) (m :: * -> *) a.
(Traversable t, Monad m) =>
t (m a) -> m (t a)
sequence forall a b. (a -> b) -> a -> b
$ do
(b
p,b
q) <- forall a. Ix a => (a, a) -> [a]
A.range ((b, b), (b, b))
bnd
forall (f :: * -> *). Alternative f => Bool -> f ()
guard forall a b. (a -> b) -> a -> b
$ b
p forall a. Ord a => a -> a -> Bool
<= b
q
forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ do
Bit
x <- forall a s (m :: * -> *). (Variable a, MonadSAT s m) => m a
exists
forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ ((b
p,b
q), Bit
x)
forall a. a -> [a] -> [a]
: [ ((b
q,b
p), Bit
x) | b
p forall a. Eq a => a -> a -> Bool
/= b
q ]
forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ forall a b.
(Ix a, Ix b) =>
((a, b), (a, b)) -> [((a, b), Bit)] -> Relation a b
build ((b, b), (b, b))
bnd forall a b. (a -> b) -> a -> b
$ forall (t :: * -> *) a. Foldable t => t [a] -> [a]
concat [[((b, b), Bit)]]
pairs
build :: ( Ix a, Ix b )
=> ((a,b),(a,b))
-> [ ((a,b), Bit ) ]
-> Relation a b
build :: forall a b.
(Ix a, Ix b) =>
((a, b), (a, b)) -> [((a, b), Bit)] -> Relation a b
build ((a, b), (a, b))
bnd [((a, b), Bit)]
pairs = forall a b. Array (a, b) Bit -> Relation a b
Relation forall a b. (a -> b) -> a -> b
$ forall i e. Ix i => (i, i) -> [(i, e)] -> Array i e
A.array ((a, b), (a, b))
bnd [((a, b), Bit)]
pairs
buildFrom :: (Ix a, Ix b)
=> (a -> b -> Bit)
-> ((a,b),(a,b))
-> Relation a b
buildFrom :: forall a b.
(Ix a, Ix b) =>
(a -> b -> Bit) -> ((a, b), (a, b)) -> Relation a b
buildFrom a -> b -> Bit
p ((a, b), (a, b))
bnd = forall a b.
(Ix a, Ix b) =>
((a, b), (a, b)) -> [((a, b), Bit)] -> Relation a b
build ((a, b), (a, b))
bnd forall a b. (a -> b) -> a -> b
$ forall a b c. (a -> b -> c) -> b -> a -> c
flip forall a b. (a -> b) -> [a] -> [b]
map (forall a. Ix a => (a, a) -> [a]
A.range ((a, b), (a, b))
bnd) forall a b. (a -> b) -> a -> b
$ \ (a
i,b
j) -> ((a
i, b
j), a -> b -> Bit
p a
i b
j)
identity :: (Ix a)
=> ((a,a),(a,a))
-> Relation a a
identity :: forall a. Ix a => ((a, a), (a, a)) -> Relation a a
identity = forall a b.
(Ix a, Ix b) =>
(a -> b -> Bit) -> ((a, b), (a, b)) -> Relation a b
buildFrom (\ a
i a
j -> forall b. Boolean b => Bool -> b
bool forall a b. (a -> b) -> a -> b
$ a
i forall a. Eq a => a -> a -> Bool
== a
j)
bounds :: (Ix a, Ix b) => Relation a b -> ((a,b),(a,b))
bounds :: forall a b. (Ix a, Ix b) => Relation a b -> ((a, b), (a, b))
bounds ( Relation Array (a, b) Bit
r ) = forall i e. Array i e -> (i, i)
A.bounds Array (a, b) Bit
r
indices :: (Ix a, Ix b) => Relation a b -> [(a, b)]
indices :: forall a b. (Ix a, Ix b) => Relation a b -> [(a, b)]
indices ( Relation Array (a, b) Bit
r ) = forall i e. Ix i => Array i e -> [i]
A.indices Array (a, b) Bit
r
assocs :: (Ix a, Ix b) => Relation a b -> [((a, b), Bit)]
assocs :: forall a b. (Ix a, Ix b) => Relation a b -> [((a, b), Bit)]
assocs ( Relation Array (a, b) Bit
r ) = forall i e. Ix i => Array i e -> [(i, e)]
A.assocs Array (a, b) Bit
r
elems :: (Ix a, Ix b) => Relation a b -> [Bit]
elems :: forall a b. (Ix a, Ix b) => Relation a b -> [Bit]
elems ( Relation Array (a, b) Bit
r ) = forall i e. Array i e -> [e]
A.elems Array (a, b) Bit
r
(!) :: (Ix a, Ix b) => Relation a b -> (a, b) -> Bit
Relation Array (a, b) Bit
r ! :: forall a b. (Ix a, Ix b) => Relation a b -> (a, b) -> Bit
! (a, b)
p = Array (a, b) Bit
r forall i e. Ix i => Array i e -> i -> e
A.! (a, b)
p
table :: (Enum a, Ix a, Enum b, Ix b)
=> Array (a,b) Bool -> String
table :: forall a b.
(Enum a, Ix a, Enum b, Ix b) =>
Array (a, b) Bool -> String
table Array (a, b) Bool
r = [String] -> String
unlines forall a b. (a -> b) -> a -> b
$ do
let ((a
a,b
b),(a
c,b
d)) = forall i e. Array i e -> (i, i)
A.bounds Array (a, b) Bool
r
a
x <- [ a
a .. a
c ]
forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ [String] -> String
unwords forall a b. (a -> b) -> a -> b
$ do
b
y <- [ b
b .. b
d ]
forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ if Array (a, b) Bool
r forall i e. Ix i => Array i e -> i -> e
A.! (a
x,b
y) then String
"*" else String
"."