module Satchmo.Boolean.Op
( constant
, and, or, xor
, fun2, fun3
, monadic
)
where
import Prelude hiding ( and, or, not )
import qualified Prelude
import Satchmo.MonadSAT
import Satchmo.Code
import Satchmo.Boolean.Data
import Control.Monad ( foldM )
and :: MonadSAT m => [ Boolean ] -> m Boolean
and [] = constant True
and [x]= return x
and xs = do
y <- boolean
sequence_ $ do
x <- xs
return $ assert [ not y, x ]
assert $ y : map not xs
return y
or :: MonadSAT m => [ Boolean ] -> m Boolean
or [] = constant False
or [x]= return x
or xs = do
y <- and $ map not xs
return $ not y
xor :: MonadSAT m => [ Boolean ] -> m Boolean
xor [] = constant False
xor (x:xs) = foldM xor2 x xs
fun2 :: MonadSAT m =>
( Bool -> Bool -> Bool )
-> Boolean -> Boolean
-> m Boolean
fun2 f x y = do
r <- boolean
sequence_ $ do
a <- [ False, True ]
b <- [ False, True ]
let pack flag var = if flag then not var else var
return $ assert
[ pack a x, pack b y, pack (Prelude.not $ f a b) r ]
return r
fun3 :: MonadSAT m =>
( Bool -> Bool -> Bool -> Bool )
-> Boolean -> Boolean -> Boolean
-> m Boolean
fun3 f x y z = do
r <- boolean
sequence_ $ do
a <- [ False, True ]
b <- [ False, True ]
c <- [ False, True ]
let pack flag var = if flag then not var else var
return $ assert
[ pack a x, pack b y, pack c z
, pack (Prelude.not $ f a b c) r
]
return r
xor2 :: MonadSAT m => Boolean -> Boolean -> m Boolean
xor2 = fun2 (/=)
xor2_orig :: MonadSAT m => Boolean -> Boolean -> m Boolean
xor2_orig x y = do
a <- and [ x, not y ]
b <- and [ not x, y ]
or [ a, b ]