{-# language MultiParamTypeClasses #-}
module Satchmo.Binary.Data
( Number, bits, make
, width, number, constant
, equals, iszero
)
where
import Prelude hiding ( and, or, not )
import qualified Satchmo.Code as C
import Satchmo.Boolean hiding ( constant )
import qualified Satchmo.Boolean as B
import Satchmo.Counting
data Number = Number
{ bits :: [ Boolean ] -- lsb first
, decode :: C.Decoder Integer
}
instance C.Decode Number Integer where
decode = decode
width :: Number -> Int
width n = length $ bits n
-- | declare a number variable (bit width)
number :: Int -> SAT Number
number w = do
xs <- sequence $ replicate w boolean
return $ make xs
make :: [ Boolean ] -> Number
make xs = Number
{ bits = xs
, decode = do ys <- mapM C.decode xs ; return $ fromBinary ys
}
fromBinary :: [ Bool ] -> Integer
fromBinary xs = foldr ( \ x y -> 2*y + if x then 1 else 0 ) 0 xs
toBinary :: Integer -> [ Bool ]
toBinary 0 = []
toBinary n =
let (d,m) = divMod n 2
in toEnum ( fromIntegral m ) : toBinary d
-- | declare a number constant
constant :: Integer -> SAT Number
constant n = do
xs <- mapM B.constant $ toBinary n
return $ make xs
iszero :: Number -> SAT Boolean
iszero a = equals a $ make []
equals :: Number -> Number -> SAT Boolean
equals a b = do
equals' ( bits a ) ( bits b )
equals' :: Booleans -> Booleans -> SAT Boolean
equals' [] [] = B.constant True
equals' (x:xs) (y:ys) = do
z <- xor [x, y]
rest <- equals' xs ys
and [ not z, rest ]
equals' xs [] = and $ map not xs
equals' [] ys = and $ map not ys