module Satchmo.SMT.Exotic.Arctic where
import Satchmo.SMT.Exotic.Dict
import qualified Satchmo.SMT.Exotic.Domain
import qualified Data.Map as M
import qualified Satchmo.Unary.Op.Flexible as X
import qualified Satchmo.Unary as N
import qualified Satchmo.Boolean as B
import Satchmo.Code
import Satchmo.SAT.Mini (SAT)
import Control.Monad (forM, guard, when)
import qualified Satchmo.SMT.Exotic.Semiring.Arctic as A
data Arctic = Arctic { contents :: N.Number
}
minus_infinite = B.not . head . N.bits . contents
instance ( Decode m B.Boolean Bool )
=> Decode m Arctic ( A.Arctic Integer ) where
decode a = do
c <- decode $ contents a
return $ if 0 == c then A.Minus_Infinite else A.Finite (c1)
make c = do
return $ Arctic { contents = c }
dict :: Int
-> Dict SAT Arctic B.Boolean
dict bits = Dict { domain = Satchmo.SMT.Exotic.Domain.Arctic
, fresh = do
c <- N.number bits
make c
, finite = \ x -> return $ B.not $ minus_infinite x
, ge = \ l r -> N.ge ( contents l ) ( contents r )
, gg = \ l r ->
B.monadic B.or [ return $ minus_infinite r
, N.gt ( contents l ) ( contents r )
]
, plus = \ xs -> do
c <- X.maximum $ map contents xs
make c
, times = \ [s,t] -> do
m <- B.or [ minus_infinite s, minus_infinite t ]
let a = contents s ; b = contents t
let width = length $ N.bits a
when ( length ( N.bits b ) /= width )
$ error "Arctic.times: different bit widths"
pairs <- sequence $ do
(i,x) <- zip [0 .. ] $ N.bits a
(j,y) <- zip [0 .. ] $ N.bits b
guard $ i+j <= width
return $ do z <- B.and [x,y] ; return (i+j, [z])
cs <- forM ( map snd $ M.toAscList $ M.fromListWith (++) pairs ) B.or
B.assert [ B.not $ last cs ]
ds <- forM (init cs) $ \ c -> B.and [ B.not m, c ]
make $ N.make ds
}