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{-# LANGUAGE RankNTypes #-}
module Memo where
import Data.Bits
type Memo a = forall r. (a -> r) -> (a -> r)
memo2 :: Memo a -> Memo b -> (a -> b -> r) -> (a -> b -> r)
memo2 a b = a . (b .)
wrap :: (a -> b) -> (b -> a) -> Memo a -> Memo b
wrap i j m f = m (f . i) . j
pair :: Memo a -> Memo b -> Memo (a,b)
pair m m' f = uncurry (m (\x -> m' (\y -> f (x,y))))
bits :: (Num a, Ord a, Bits a) => Memo a
bits f = apply (fmap f identity)
data IntTrie a = IntTrie (BitTrie a) a (BitTrie a) -- negative, 0, positive
data BitTrie a = BitTrie a (BitTrie a) (BitTrie a)
instance Functor BitTrie where
fmap f ~(BitTrie x l r) = BitTrie (f x) (fmap f l) (fmap f r)
instance Functor IntTrie where
fmap f ~(IntTrie neg z pos) = IntTrie (fmap f neg) (f z) (fmap f pos)
-- | Apply the trie to an argument. This is the semantic map.
apply :: (Ord b, Num b, Bits b) => IntTrie a -> b -> a
apply (IntTrie neg z pos) x =
case compare x 0 of
LT -> applyPositive neg (-x)
EQ -> z
GT -> applyPositive pos x
applyPositive :: (Num b, Bits b) => BitTrie a -> b -> a
applyPositive (BitTrie one eve od) x
| x == 1 = one
| testBit x 0 = applyPositive od (x `shiftR` 1)
| otherwise = applyPositive eve (x `shiftR` 1)
identity :: (Num a, Bits a) => IntTrie a
identity = IntTrie (fmap negate identityPositive) 0 identityPositive
identityPositive :: (Num a, Bits a) => BitTrie a
identityPositive = go
where
go = BitTrie 1 (fmap (`shiftL` 1) go) (fmap (\n -> (n `shiftL` 1) .|. 1) go)
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