module TrieMap.TrieAlgebraic where
import Control.Arrow ((***))
import Data.Traversable
import Data.Foldable
import Data.Either
import Data.Sequence (Seq)
import Data.Maybe
import Data.Monoid
import Data.IntMap (IntMap)
import Data.Map (Map)
import qualified Data.Sequence as Seq
import qualified Data.IntMap as IMap
import qualified Data.Map as Map
import Control.Monad
import Control.Applicative hiding (Alternative(..), Const(..))
import GHC.Exts (build)
import TrieMap.Applicative
import TrieMap.MapTypes
import Prelude hiding (foldr, foldl, all, any)
newtype Ordered k = Ord {unOrd :: k} deriving (Eq, Ord)
instance Show k => Show (Ordered k) where
show = show . unOrd
showsPrec x = showsPrec x . unOrd
instance Functor Ordered where
fmap f (Ord x) = Ord (f x)
type L a = Fix (Const () :+: (Const a :*: Id))
class EqT f => TrieKeyT f t | f -> t, t -> f where
compareKeyT :: TrieKey k m => f k -> f k -> Ordering
emptyT :: (Sized a, TrieKey k m) => t k m a
nullT :: (Sized a, TrieKey k m) => t k m a -> Bool
guardNullT :: (Sized a, TrieKey k m) => t k m a -> Maybe (t k m a)
sizeT :: (Sized a, TrieKey k m) => t k m a -> Int
getSingleT :: (Sized a, TrieKey k m) => t k m a -> Maybe (f k, a)
alterLookupT :: (Sized a, TrieKey k m) =>
(Maybe a -> (b, Maybe a)) -> f k -> t k m a -> (b, t k m a)
lookupT :: (Sized a, TrieKey k m) => f k -> t k m a -> Maybe a
foldWithKeyT :: (TrieKey k m) => (f k -> a -> b -> b) -> b -> t k m a -> b
mapAppT :: (Applicative g, Sized a, Sized b, TrieKey k m) =>
(f k -> a -> g b) -> t k m a -> g (t k m b)
mapMaybeT :: (Sized a, Sized b, TrieKey k m) =>
(f k -> a -> Maybe b) -> t k m a -> t k m b
mapEitherT :: (Sized a, Sized b, Sized c, TrieKey k m) =>
(f k -> a -> (Maybe b, Maybe c)) -> t k m a -> (t k m b, t k m c)
unionT :: (Sized a, TrieKey k m) => (f k -> a -> a -> Maybe a) -> t k m a -> t k m a -> t k m a
intersectT :: (Sized a, Sized b, Sized c, TrieKey k m) =>
(f k -> a -> b -> Maybe c) -> t k m a -> t k m b -> t k m c
differenceT :: (Sized a, Sized b, TrieKey k m) => (f k -> a -> b -> Maybe a) -> t k m a -> t k m b -> t k m a
fromDistAscListT :: (Sized a, TrieKey k m) => [(f k, a)] -> t k m a
fromAscListT :: (Sized a, TrieKey k m) => (f k -> a -> a -> a) -> [(f k, a)] -> t k m a
fromListT :: (Sized a, TrieKey k m) => (f k -> a -> a -> a) -> [(f k, a)] -> t k m a
getMinT :: (Sized a, TrieKey k m) => t k m a -> Maybe ((f k, a), t k m a)
getMaxT :: (Sized a, TrieKey k m) => t k m a -> Maybe ((f k, a), t k m a)
updateMinT :: (Sized a, TrieKey k m) => (f k -> a -> (Bool, Maybe a)) -> t k m a -> (Bool, t k m a)
updateMaxT :: (Sized a, TrieKey k m) => (f k -> a -> (Bool, Maybe a)) -> t k m a -> (Bool, t k m a)
isSubmapT :: (Sized a, Sized b, TrieKey k m) => (a -> b -> Bool) -> t k m a -> t k m b -> Bool
splitLookupT :: (Sized a, TrieKey k m) => (a -> (Maybe a, Maybe b, Maybe a)) -> f k -> t k m a -> (t k m a, Maybe b, t k m a)
guardNullT m
| nullT m = Nothing
| otherwise = Just m
eqKey :: TrieKey k m => k -> k -> Bool
eqKey a b = compareKey a b == EQ
eqKeyT :: (TrieKey k m, TrieKeyT f t) => f k -> f k -> Bool
eqKeyT a b = compareKeyT a b == EQ
class Eq k => TrieKey k m | k -> m, m -> k where
compareKey :: k -> k -> Ordering
emptyAlg :: Sized a => m a
nullAlg :: Sized a => m a -> Bool
sizeAlg :: Sized a => m a -> Int
getSingleAlg :: Sized a => m a -> Maybe (k, a)
guardNullAlg :: Sized a => m a -> Maybe (m a)
alterLookupAlg :: Sized a => (Maybe a -> (b, Maybe a)) -> k -> m a -> (b, m a)
lookupAlg :: Sized a => k -> m a -> Maybe a
foldWithKeyAlg :: (k -> a -> b -> b) -> b -> m a -> b
mapAppAlg :: (Applicative f, Sized a, Sized b) => (k -> a -> f b) -> m a -> f (m b)
mapMaybeAlg :: (Sized a, Sized b) => (k -> a -> Maybe b) -> m a -> m b
mapEitherAlg :: (Sized a, Sized b, Sized c) => (k -> a -> (Maybe b, Maybe c)) -> m a -> (m b, m c)
unionMaybeAlg :: Sized a => (k -> a -> a -> Maybe a) -> m a -> m a -> m a
intersectAlg :: (Sized a, Sized b, Sized c) => (k -> a -> b -> Maybe c) -> m a -> m b -> m c
differenceAlg :: (Sized a, Sized b) => (k -> a -> b -> Maybe a) -> m a -> m b -> m a
fromDistAscListAlg :: Sized a => [(k, a)] -> m a
fromAscListAlg :: Sized a => (k -> a -> a -> a) -> [(k, a)] -> m a
fromListAlg :: Sized a => (k -> a -> a -> a) -> [(k, a)] -> m a
getMinAlg :: Sized a => m a -> Maybe ((k, a), m a)
getMaxAlg :: Sized a => m a -> Maybe ((k, a), m a)
updateMinAlg :: Sized a => (k -> a -> (Bool, Maybe a)) -> m a -> (Bool, m a)
updateMaxAlg :: Sized a => (k -> a -> (Bool, Maybe a)) -> m a -> (Bool, m a)
valid :: Sized a => m a -> Bool
isSubmapAlg :: (Sized a, Sized b) => (a -> b -> Bool) -> m a -> m b -> Bool
splitLookupAlg :: (Sized a) => (a -> (Maybe a, Maybe b, Maybe a)) -> k -> m a -> (m a, Maybe b, m a)
lookupAlg k = fst . alterLookupAlg (\ v -> (v, v)) k
guardNullAlg m
| nullAlg m = Nothing
| otherwise = Just m
getSingleAlg m = do
((k, v), m') <- getMinAlg m
guard (nullAlg m')
return (k, v)
fromListAlg f = foldr (\ (k, v) -> alterAlg (Just . maybe v (f k v)) k) emptyAlg
fromAscListAlg _ [] = emptyAlg
fromAscListAlg f ((k, v):xs) = fromDistAscListAlg (distinct k v xs) where
distinct k v ((k', v'):xs)
| k `eqKey` k' = distinct k (f k v v') xs
| otherwise = (k, v):distinct k' v' xs
distinct k v [] = [(k, v)]
fromDistAscListAlg = fromListAlg'
sizeAlg = foldWithKeyAlg (\ _ x n -> n + getSize x) 0
updateMinAlg f m = maybe (False, m) (\ ((k, v), m') -> maybe m' (\ v' -> insertAlg k v' m) <$> f k v) (getMinAlg m)
updateMaxAlg f m = maybe (False, m) (\ ((k, v), m') -> maybe m' (\ v' -> insertAlg k v' m) <$> f k v) (getMaxAlg m)
valid = (`seq` True)
instance TrieKeyT f t => TrieKey (Fix f) (FixMap f t) where
compareKey (Fix a) (Fix b) = compareKeyT a b
emptyAlg = FixMap emptyT
nullAlg (FixMap m) = nullT m
sizeAlg (FixMap m) = sizeT m
getSingleAlg (FixMap m) = do
(k, v) <- getSingleT m
return (Fix k, v)
lookupAlg (Fix k) (FixMap m) = lookupT k m
alterLookupAlg f (Fix k) (FixMap m) = FixMap <$> alterLookupT f k m
foldWithKeyAlg f z (FixMap m) = foldWithKeyT (f . Fix) z m
mapAppAlg f (FixMap m) = FixMap <$> mapAppT (f . Fix) m
mapMaybeAlg f (FixMap m) = FixMap (mapMaybeT (f . Fix) m)
mapEitherAlg f (FixMap m) = case mapEitherT (f . Fix) m of
(mL, mR) -> (FixMap mL, FixMap mR)
unionMaybeAlg f (FixMap m1) (FixMap m2) = FixMap (unionT (f . Fix) m1 m2)
intersectAlg f (FixMap m1) (FixMap m2) = FixMap (intersectT (f . Fix) m1 m2)
differenceAlg f (FixMap m1) (FixMap m2) = FixMap (differenceT (f . Fix) m1 m2)
getMinAlg (FixMap m) = do
(~(k, v), m') <- getMinT m
return ((Fix k, v), FixMap m')
getMaxAlg (FixMap m) = do
(~(k, v), m') <- getMaxT m
return ((Fix k, v), FixMap m')
updateMinAlg f (FixMap m) = FixMap <$> updateMinT (f . Fix) m
updateMaxAlg f (FixMap m) = FixMap <$> updateMaxT (f . Fix) m
isSubmapAlg (<=) (FixMap m1) (FixMap m2) = isSubmapT (<=) m1 m2
splitLookupAlg f (Fix k) (FixMap m) = case splitLookupT f k m of
(mL, ans, mR) -> (FixMap mL, ans, FixMap mR)
instance (Sized a, TrieKey k m) => Sized (m a) where
getSize = sizeAlg
instance (Sized a, TrieKey k m, TrieKeyT f t) => Sized (t k m a) where
getSize = sizeT
fromListAlg' :: (Sized v, TrieKey k m) => [(k, v)] -> m v
fromListAlg' = fromListAlg (const const)
singletonAlg :: (Sized v, TrieKey k m) => k -> v -> m v
singletonAlg k v = insertAlg k v emptyAlg
mapWithKeyAlg :: (Sized v, Sized w, TrieKey k m) => (k -> v -> w) -> m v -> m w
mapWithKeyAlg f m = unId (mapAppAlg (\ k v -> Id (f k v)) m)
mapWithKeyT :: (Sized v, Sized w, TrieKeyT f t, TrieKey k m) => (f k -> v -> w) -> t k m v -> t k m w
mapWithKeyT f m = unId (mapAppT (\ k v -> Id (f k v)) m)
mapAlg :: (Sized v, Sized w, TrieKey k m) => (v -> w) -> m v -> m w
mapAlg = mapWithKeyAlg . const
mapT :: (Sized v, Sized w, TrieKeyT f t, TrieKey k m) => (v -> w) -> t k m v -> t k m w
mapT = mapWithKeyT . const
insertAlg :: (Sized v, TrieKey k m) => k -> v -> m v -> m v
insertAlg k v = alterAlg (const (Just v)) k
insertT :: (Sized v, TrieKey k m, TrieKeyT f t) => f k -> v -> t k m v -> t k m v
insertT k v = alterT (const (Just v)) k
alterAlg :: (Sized v, TrieKey k m) => (Maybe v -> Maybe v) -> k -> m v -> m v
alterAlg f k = snd . alterLookupAlg (\ x -> ((), f x)) k
alterT :: (Sized v, TrieKey k m, TrieKeyT f t) => (Maybe v -> Maybe v) -> f k -> t k m v -> t k m v
alterT f k = snd . alterLookupT (\ x -> ((), f x)) k
foldrAlg :: (Sized a, TrieKey k m) => (a -> b -> b) -> b -> m a -> b
foldrAlg = foldWithKeyAlg . const
unionMaybe :: (a -> a -> Maybe a) -> Maybe a -> Maybe a -> Maybe a
unionMaybe f (Just x) (Just y) = f x y
unionMaybe _ Nothing y = y
unionMaybe _ x Nothing = x
intersectMaybe :: (a -> b -> Maybe c) -> Maybe a -> Maybe b -> Maybe c
intersectMaybe f (Just x) (Just y) = f x y
intersectMaybe _ _ _ = Nothing
differenceMaybe :: (a -> b -> Maybe a) -> Maybe a -> Maybe b -> Maybe a
differenceMaybe _ Nothing _ = Nothing
differenceMaybe _ x Nothing = x
differenceMaybe f (Just x) (Just y) = f x y
filterLeft :: a -> Either b c -> Maybe b
filterLeft _ (Left x) = Just x
filterLeft _ _ = Nothing
filterRight :: a -> Either b c -> Maybe c
filterRight _ (Right x) = Just x
filterRight _ _ = Nothing
assocsAlg :: (TrieKey k m) => m a -> [(k, a)]
assocsAlg m = build (\ c n -> foldWithKeyAlg (\ k v xs -> (k,v) `c` xs) n m)
instance (TrieKeyT f1 t1, TrieKeyT f2 t2) => TrieKeyT (f1 :*: f2) (t1 `ProdMap` t2) where
compareKeyT (a :*: x) (b :*: y) = compareKeyT a b `mappend` compareKeyT x y
emptyT = PMap emptyT
nullT (PMap m) = nullT m
sizeT (PMap m) = sizeT m
getSingleT (PMap m) = do
(k1, m') <- getSingleT m
(k2, v) <- getSingleT m'
return (k1 :*: k2, v)
lookupT (k1 :*: k2) (PMap m) = lookupT k1 m >>= lookupT k2
alterLookupT f (k1 :*: k2) (PMap m) = PMap <$> alterLookupT g k1 m where
g = fmap guardNullT . alterLookupT f k2 . fromMaybe emptyT
foldWithKeyT f z (PMap m) = foldWithKeyT (\ k1 -> flip (foldWithKeyT (\ k2 -> f (k1 :*: k2)))) z m
mapAppT f (PMap m) = PMap <$> mapAppT (\ k1 -> mapAppT (\ k2 -> f (k1 :*: k2))) m
mapMaybeT f (PMap m) = PMap (mapMaybeT (\ k1 -> guardNullT . mapMaybeT (\ k2 -> f (k1 :*: k2))) m)
mapEitherT f (PMap m) = (PMap *** PMap) (mapEitherT (\ k1 -> (guardNullT *** guardNullT) . mapEitherT (\ k2 -> f (k1 :*: k2))) m)
unionT f (PMap m1) (PMap m2) = PMap (unionT (\ k1 -> guardNullT .: unionT (\ k2 -> f (k1 :*: k2))) m1 m2)
intersectT f (PMap m1) (PMap m2) = PMap (intersectT (\ k1 -> guardNullT .: intersectT (\ k2 -> f (k1 :*: k2))) m1 m2)
differenceT f (PMap m1) (PMap m2) = PMap (differenceT (\ k1 -> guardNullT .: differenceT (\ k2 -> f (k1 :*: k2))) m1 m2)
fromListT f xs = PMap $ mapWithKeyT (\ k1 (Elem xs) -> fromListT (\ k2 -> f (k1 :*: k2)) xs) $
fromListT (\ _ (Elem x) (Elem y) -> Elem (x ++ y)) [(k1, Elem [(k2, v)]) | ((k1 :*: k2), v) <- xs]
fromDistAscListT xs = PMap $ fromDistAscListT [(k1, fromDistAscListT ys) | (k1, ys) <- breakFst eqKeyT xs]
fromAscListT f xs = PMap $ fromDistAscListT [(k1, fromAscListT (\ k2 -> f (k1 :*: k2)) ys) | (k1, ys) <- breakFst eqKeyT xs]
getMinT (PMap m) = do
((k1, m'), m1') <- getMinT m
((k2, v), m2') <- getMinT m'
return ((k1 :*: k2, v), PMap (maybe m1' (\ m2' -> insertT k1 m2' m) (guardNullT m2')))
getMaxT (PMap m) = do
((k1, m'), m1') <- getMaxT m
((k2, v), m2') <- getMaxT m'
return ((k1 :*: k2, v), PMap (maybe m1' (\ m2' -> insertT k1 m2' m) (guardNullT m2')))
updateMinT f (PMap m) =
PMap <$> updateMinT (\ k1 -> guardNullT <.> updateMinT (\ k2 -> f (k1 :*: k2))) m
updateMaxT f (PMap m) =
PMap <$> updateMaxT (\ k1 -> guardNullT <.> updateMaxT (\ k2 -> f (k1 :*: k2))) m
isSubmapT (<=) (PMap m1) (PMap m2) =
isSubmapT (isSubmapT (<=)) m1 m2
splitLookupT f (k1 :*: k2) (PMap m) = case splitLookupT g k1 m of
(mL, ans, mR) -> (PMap mL, ans, PMap mR)
where g m' = case splitLookupT f k2 m' of
(mL, ans, mR) -> (guardNullT mL, ans, guardNullT mR)
instance (Eq (f1 k), Eq (f2 k), TrieKey k m, TrieKeyT f1 t1, TrieKeyT f2 t2) => TrieKey ((f1 :*: f2) k) (ProdMap t1 t2 k m) where
compareKey = compareKeyT
emptyAlg = emptyT
nullAlg = nullT
getSingleAlg = getSingleT
guardNullAlg = guardNullT
sizeAlg = sizeT
lookupAlg = lookupT
alterLookupAlg = alterLookupT
mapAppAlg = mapAppT
mapMaybeAlg = mapMaybeT
mapEitherAlg = mapEitherT
foldWithKeyAlg = foldWithKeyT
unionMaybeAlg = unionT
intersectAlg = intersectT
differenceAlg = differenceT
getMinAlg = getMinT
getMaxAlg = getMaxT
updateMinAlg = updateMinT
updateMaxAlg = updateMaxT
isSubmapAlg = isSubmapT
splitLookupAlg = splitLookupT
breakFst :: (f1 k -> f1 k -> Bool) -> [((f1 :*: f2) k, v)] -> [(f1 k, [(f2 k, v)])]
breakFst _ [] = []
breakFst eq (((k1 :*: k2), x):xs) = breakFst' k1 (Seq.singleton (k2, x)) xs where
breakFst' k xs (((k' :*: k2), x):xss)
| k `eq` k' = breakFst' k ((Seq.|>) xs (k2, x)) xss
| otherwise = (k, toList xs):breakFst' k' (Seq.singleton (k2, x)) xss
breakFst' k xs [] = [(k, toList xs)]
instance (TrieKeyT f1 t1, TrieKeyT f2 t2) => TrieKeyT (f1 :+: f2) (UnionMap t1 t2) where
compareKeyT (A a) (A b) = compareKeyT a b
compareKeyT (B x) (B y) = compareKeyT x y
compareKeyT A{} B{} = LT
compareKeyT B{} A{} = GT
emptyT = UMap emptyT emptyT
nullT (UMap m1 m2) = nullT m1 && nullT m2
getSingleT (UMap m1 m2) = case (getSingleT m1, getSingleT m2) of
(Just (k, v), Nothing) -> Just (A k, v)
(Nothing, Just (k, v)) -> Just (B k, v)
_ -> Nothing
sizeT (UMap m1 m2) = sizeT m1 + sizeT m2
lookupT (A k) (UMap m1 _) = lookupT k m1
lookupT (B k) (UMap _ m2) = lookupT k m2
alterLookupT f (A k) (UMap m1 m2) = (`UMap` m2) <$> alterLookupT f k m1
alterLookupT f (B k) (UMap m1 m2) = UMap m1 <$> alterLookupT f k m2
foldWithKeyT f z (UMap m1 m2) = foldWithKeyT (f . A) (foldWithKeyT (f . B) z m2) m1
mapAppT f (UMap m1 m2) = UMap <$> mapAppT (f . A) m1 <*> mapAppT (f . B) m2
mapMaybeT f (UMap m1 m2) = UMap (mapMaybeT (f . A) m1) (mapMaybeT (f . B) m2)
mapEitherT f (UMap m1 m2) = (UMap m1L m2L, UMap m1R m2R)
where (m1L, m1R) = mapEitherT (f . A) m1
(m2L, m2R) = mapEitherT (f . B) m2
unionT f (UMap m11 m12) (UMap m21 m22) =
UMap (unionT (f . A) m11 m21) (unionT (f . B) m12 m22)
intersectT f (UMap m11 m12) (UMap m21 m22) =
UMap (intersectT (f . A) m11 m21) (intersectT (f . B) m12 m22)
differenceT f (UMap m11 m12) (UMap m21 m22) =
UMap (differenceT (f . A) m11 m21) (differenceT (f . B) m12 m22)
getMinT (UMap m1 m2)
| Just ~(~(k, v), m1') <- getMinT m1
= Just ((A k, v), UMap m1' m2)
| Just ~(~(k, v), m2') <- getMinT m2
= Just ((B k, v), UMap m1 m2')
| otherwise = Nothing
getMaxT (UMap m1 m2)
| Just ~(~(k, v), m2') <- getMaxT m2
= Just ((B k, v), UMap m1 m2')
| Just ~(~(k, v), m1') <- getMaxT m1
= Just ((A k, v), UMap m1' m2)
| otherwise = Nothing
updateMinT f (UMap m1 m2)
| nullT m1 = UMap m1 <$> updateMinT (f . B) m2
| otherwise = (`UMap` m2) <$> updateMinT (f . A) m1
updateMaxT f (UMap m1 m2)
| nullT m2 = (`UMap` m2) <$> updateMaxT (f . A) m1
| otherwise = UMap m1 <$> updateMaxT (f . B) m2
fromDistAscListT xs = UMap (fromDistAscListT ys) (fromDistAscListT zs)
where (ys, zs) = partitionEithers' (map pullEither xs)
fromAscListT f xs = UMap (fromAscListT (f . A) ys) (fromAscListT (f . B) zs)
where (ys, zs) = partitionEithers' (map pullEither xs)
fromListT f xs = UMap (fromListT (f . A) ys) (fromListT (f . B) zs)
where (ys, zs) = partitionEithers' (map pullEither xs)
isSubmapT (<=) (UMap m11 m12) (UMap m21 m22) = isSubmapT (<=) m11 m21 && isSubmapT (<=) m12 m22
splitLookupT f (A k) (UMap m1 m2) = case splitLookupT f k m1 of
(m1L, ans, m1R) -> (UMap m1L emptyT, ans, UMap m1R m2)
splitLookupT f (B k) (UMap m1 m2) = case splitLookupT f k m2 of
(m2L, ans, m2R) -> (UMap m1 m2L, ans, UMap emptyT m2R)
instance (Eq (f1 k), Eq (f2 k), TrieKey k m, TrieKeyT f1 t1, TrieKeyT f2 t2) => TrieKey ((f1 :+: f2) k) (UnionMap t1 t2 k m) where
compareKey = compareKeyT
emptyAlg = emptyT
nullAlg = nullT
getSingleAlg = getSingleT
guardNullAlg = guardNullT
sizeAlg = sizeT
lookupAlg = lookupT
alterLookupAlg = alterLookupT
mapAppAlg = mapAppT
mapMaybeAlg = mapMaybeT
mapEitherAlg = mapEitherT
foldWithKeyAlg = foldWithKeyT
unionMaybeAlg = unionT
intersectAlg = intersectT
differenceAlg = differenceT
getMinAlg = getMinT
getMaxAlg = getMaxT
updateMinAlg = updateMinT
updateMaxAlg = updateMaxT
isSubmapAlg = isSubmapT
splitLookupAlg = splitLookupT
instance TrieKey k m => TrieKeyT ((,) k) (CProdMap m) where
compareKeyT (a, x) (b, y) = compareKey a b `mappend` compareKey x y
emptyT = CPMap emptyAlg
nullT (CPMap m) = nullAlg m
getSingleT (CPMap m) = do
(k1, m') <- getSingleAlg m
(k2, v) <- getSingleAlg m'
return ((k1, k2), v)
guardNullT (CPMap m) = CPMap <$> guardNullAlg m
sizeT (CPMap m) = sizeAlg m
lookupT (k1, k2) (CPMap m) = lookupAlg k1 m >>= lookupAlg k2
alterLookupT f (k1, k2) (CPMap m) = CPMap <$> alterLookupAlg g k1 m where
g = guardNullAlg <.> alterLookupAlg f k2 . fromMaybe emptyAlg
foldWithKeyT f z (CPMap m) = foldWithKeyAlg (\ k1 -> flip $ foldWithKeyAlg (\ k2 -> f (k1, k2))) z m
mapAppT f (CPMap m) = CPMap <$> mapAppAlg (\ k1 -> mapAppAlg (\ k2 -> f (k1, k2))) m
mapMaybeT f (CPMap m) = CPMap (mapMaybeAlg (\ k1 -> guardNullAlg . mapMaybeAlg (\ k2 -> f (k1, k2))) m)
mapEitherT f (CPMap m) = (CPMap *** CPMap) (mapEitherAlg (\ k1 -> (guardNullAlg *** guardNullAlg) . mapEitherAlg (\ k2 -> f (k1, k2))) m)
unionT f (CPMap m1) (CPMap m2) =
CPMap (unionMaybeAlg (\ k1 -> guardNullAlg .: unionMaybeAlg (\ k2 -> f (k1, k2))) m1 m2)
intersectT f (CPMap m1) (CPMap m2) =
CPMap (intersectAlg (\ k1 -> guardNullAlg .: intersectAlg (\ k2 -> f (k1, k2))) m1 m2)
differenceT f (CPMap m1) (CPMap m2) =
CPMap (differenceAlg (\ k1 -> guardNullAlg .: differenceAlg (\ k2 -> f (k1, k2))) m1 m2)
getMinT (CPMap m) = do
((k1, m1), m') <- getMinAlg m
((k2, v), m1') <- getMinAlg m1
return (((k1, k2), v), CPMap $ maybe m' (\ m1' -> snd $ updateMinAlg (\ _ _ -> (False, Just m1')) m) (guardNullAlg m1'))
getMaxT (CPMap m) = do
((k1, m1), m') <- getMaxAlg m
((k2, v), m1') <- getMaxAlg m1
return (((k1, k2), v), CPMap $ maybe m' (\ m1' -> snd $ updateMaxAlg (\ _ _ -> (False, Just m1')) m) (guardNullAlg m1'))
updateMinT f (CPMap m) =
CPMap <$> updateMinAlg (\ k1 -> guardNullAlg <.> updateMinAlg (\ k2 -> f (k1, k2))) m
updateMaxT f (CPMap m) =
CPMap <$> updateMaxAlg (\ k1 -> guardNullAlg <.> updateMaxAlg (\ k2 -> f (k1, k2))) m
isSubmapT (<=) (CPMap m1) (CPMap m2) = isSubmapAlg (isSubmapAlg (<=)) m1 m2
splitLookupT f (k1, k2) (CPMap m) = case splitLookupAlg g k1 m of
(mL, ans, mR) -> (CPMap mL, ans, CPMap mR)
where g m = case splitLookupAlg f k2 m of
(mL, ans, mR) -> (guardNullAlg mL, ans, guardNullAlg mR)
fromDistAscListT xs = CPMap (fromDistAscListAlg [(k1, fromDistAscListAlg ys) | (k1, ys) <- breakFst' (==) xs])
fromAscListT f xs = CPMap (fromDistAscListAlg [(k1, fromAscListAlg (\ k2 -> f (k1, k2)) ys) | (k1, ys) <- breakFst' (==) xs])
fromListT f xs = CPMap (mapWithKeyAlg (\ k1 (Elem ys) -> fromListAlg (\ k2 -> f (k1, k2)) ys) $
fromListAlg (\ _ (Elem ys) (Elem zs) -> Elem (ys ++ zs)) [(k1, Elem [(k2, v)]) | ((k1, k2), v) <- xs])
breakFst' :: (k1 -> k1 -> Bool) -> [((k1, k2), v)] -> [(k1, [(k2, v)])]
breakFst' _ [] = []
breakFst' eq (((k1, k2), x):xs) = breakFst'' k1 (Seq.singleton (k2, x)) xs where
breakFst'' k xs (((k', k2), x):xss)
| k `eq` k' = breakFst'' k ((Seq.|>) xs (k2, x)) xss
| otherwise = (k, toList xs):breakFst'' k' (Seq.singleton (k2, x)) xss
breakFst'' k xs [] = [(k, toList xs)]
instance (TrieKey k1 m1, TrieKey k2 m2) => TrieKey (k1, k2) (CProdMap m1 k2 m2) where
compareKey = compareKeyT
emptyAlg = emptyT
nullAlg = nullT
getSingleAlg = getSingleT
guardNullAlg = guardNullT
sizeAlg = sizeT
lookupAlg = lookupT
alterLookupAlg = alterLookupT
mapAppAlg = mapAppT
mapMaybeAlg = mapMaybeT
mapEitherAlg = mapEitherT
foldWithKeyAlg = foldWithKeyT
unionMaybeAlg = unionT
intersectAlg = intersectT
differenceAlg = differenceT
getMinAlg = getMinT
getMaxAlg = getMaxT
updateMinAlg = updateMinT
updateMaxAlg = updateMaxT
isSubmapAlg = isSubmapT
splitLookupAlg = splitLookupT
instance TrieKey k m => TrieKeyT (Either k) (CUnionMap m) where
compareKeyT (Left a) (Left b) = compareKey a b
compareKeyT (Right a) (Right b) = compareKey a b
compareKeyT Left{} Right{} = LT
compareKeyT Right{} Left{} = GT
emptyT = CUMap emptyAlg emptyAlg
nullT (CUMap m1 m2) = nullAlg m1 && nullAlg m2
sizeT (CUMap m1 m2) = sizeAlg m1 + sizeAlg m2
getSingleT (CUMap m1 m2) = case (getSingleAlg m1, getSingleAlg m2) of
(Just (k, v), Nothing) -> Just (Left k, v)
(Nothing, Just (k, v)) -> Just (Right k, v)
_ -> Nothing
lookupT k (CUMap m1 m2) = either (`lookupAlg` m1) (`lookupAlg` m2) k
alterLookupT f (Left k) (CUMap m1 m2) = (`CUMap` m2) <$> alterLookupAlg f k m1
alterLookupT f (Right k) (CUMap m1 m2) = CUMap m1 <$> alterLookupAlg f k m2
foldWithKeyT f z (CUMap m1 m2) = foldWithKeyAlg (f . Left) (foldWithKeyAlg (f . Right) z m2) m1
mapAppT f (CUMap m1 m2) = CUMap <$> mapAppAlg (f . Left) m1 <*> mapAppAlg (f . Right) m2
mapMaybeT f (CUMap m1 m2) = CUMap (mapMaybeAlg (f . Left) m1) (mapMaybeAlg (f . Right) m2)
mapEitherT f (CUMap m1 m2) = (CUMap m1L m2L, CUMap m1R m2R)
where (m1L, m1R) = mapEitherAlg (f . Left) m1
(m2L, m2R) = mapEitherAlg (f . Right) m2
unionT f (CUMap m11 m12) (CUMap m21 m22) =
CUMap (unionMaybeAlg (f . Left) m11 m21) (unionMaybeAlg (f . Right) m12 m22)
intersectT f (CUMap m11 m12) (CUMap m21 m22) =
CUMap (intersectAlg (f . Left) m11 m21) (intersectAlg (f . Right) m12 m22)
differenceT f (CUMap m11 m12) (CUMap m21 m22) =
CUMap (differenceAlg (f . Left) m11 m21) (differenceAlg (f . Right) m12 m22)
isSubmapT (<=) (CUMap m11 m12) (CUMap m21 m22) =
isSubmapAlg (<=) m11 m21 && isSubmapAlg (<=) m12 m22
splitLookupT f (Left k) (CUMap m1 m2) = case splitLookupAlg f k m1 of
(m1L, ans, m1R) -> (CUMap m1L emptyAlg, ans, CUMap m1R m2)
splitLookupT f (Right k) (CUMap m1 m2) = case splitLookupAlg f k m2 of
(m2L, ans, m2R) -> (CUMap m1 m2L, ans, CUMap emptyAlg m2R)
getMinT (CUMap m1 m2) = case (getMinAlg m1, getMinAlg m2) of
(Just ((k, v), m1'), _) -> Just ((Left k, v), CUMap m1' m2)
(_, Just ((k, v), m2')) -> Just ((Right k, v), CUMap m1 m2')
_ -> Nothing
getMaxT (CUMap m1 m2) = case (getMaxAlg m1, getMaxAlg m2) of
(_, Just ((k, v), m2')) -> Just ((Right k, v), CUMap m1 m2')
(Just ((k, v), m1'), _) -> Just ((Left k, v), CUMap m1' m2)
_ -> Nothing
updateMinT f (CUMap m1 m2)
| nullAlg m1 = CUMap m1 <$> updateMinAlg (f . Right) m2
| otherwise = (`CUMap` m2) <$> updateMinAlg (f . Left) m1
updateMaxT f (CUMap m1 m2)
| nullAlg m2 = (`CUMap` m2) <$> updateMaxAlg (f . Left) m1
| otherwise = CUMap m1 <$> updateMaxAlg (f . Right) m2
fromListT f xs = CUMap (fromListAlg (f . Left) ys) (fromListAlg (f . Right) zs)
where (ys, zs) = partitionEithers (map pullEither' xs)
fromAscListT f xs = CUMap (fromAscListAlg (f . Left) ys) (fromAscListAlg (f . Right) zs)
where (ys, zs) = partitionEithers (map pullEither' xs)
fromDistAscListT xs = CUMap (fromDistAscListAlg ys) (fromDistAscListAlg zs)
where (ys, zs) = partitionEithers (map pullEither' xs)
instance (TrieKey k1 m1, TrieKey k2 m2) => TrieKey (Either k1 k2) (CUnionMap m1 k2 m2) where
compareKey = compareKeyT
emptyAlg = emptyT
nullAlg = nullT
getSingleAlg = getSingleT
guardNullAlg = guardNullT
sizeAlg = sizeT
lookupAlg = lookupT
alterLookupAlg = alterLookupT
mapAppAlg = mapAppT
mapMaybeAlg = mapMaybeT
mapEitherAlg = mapEitherT
foldWithKeyAlg = foldWithKeyT
unionMaybeAlg = unionT
intersectAlg = intersectT
differenceAlg = differenceT
getMinAlg = getMinT
getMaxAlg = getMaxT
updateMinAlg = updateMinT
updateMaxAlg = updateMaxT
isSubmapAlg = isSubmapT
splitLookupAlg = splitLookupT
partitionEithers' :: [Either a b] -> ([a], [b])
partitionEithers' = foldr part ([], []) where
part (Left x) (xs, ys) = (x:xs, ys)
part (Right y) (xs, ys) = (xs, y:ys)
pullEither :: ((f1 :+: f2) k, v) -> Either (f1 k, v) (f2 k, v)
pullEither (A k, v) = Left (k, v)
pullEither (B k, v) = Right (k, v)
pullEither' :: (Either k1 k2, v) -> Either (k1, v) (k2, v)
pullEither' (Left k, v) = Left (k, v)
pullEither' (Right k, v) = Right (k, v)
instance TrieKey k m => TrieKeyT (Const k) (ConstMap m) where
compareKeyT (Const a) (Const b) = compareKey a b
emptyT = ConstMap emptyAlg
nullT (ConstMap m) = nullAlg m
sizeT (ConstMap m) = sizeAlg m
getSingleT (ConstMap m) = do
(k, v) <- getSingleAlg m
return (Const k, v)
lookupT (Const k) (ConstMap m) = lookupAlg k m
alterLookupT f (Const k) (ConstMap m) = ConstMap <$> alterLookupAlg f k m
foldWithKeyT f z (ConstMap m) = foldWithKeyAlg (f . Const) z m
mapAppT f (ConstMap m) = ConstMap <$> mapAppAlg (f . Const) m
mapMaybeT f (ConstMap m) = ConstMap (mapMaybeAlg (f . Const) m)
mapEitherT f (ConstMap m) = case mapEitherAlg (f . Const) m of
(mL, mR) -> (ConstMap mL, ConstMap mR)
unionT f (ConstMap m1) (ConstMap m2) = ConstMap (unionMaybeAlg (f . Const) m1 m2)
intersectT f (ConstMap m1) (ConstMap m2) = ConstMap (intersectAlg (f . Const) m1 m2)
differenceT f (ConstMap m1) (ConstMap m2) = ConstMap (differenceAlg (f . Const) m1 m2)
fromDistAscListT xs = ConstMap (fromDistAscListAlg [(k, v) | (Const k, v) <- xs])
fromAscListT f xs = ConstMap (fromAscListAlg (f . Const) [(k, v) | (Const k, v) <- xs])
fromListT f xs = ConstMap (fromListAlg (f . Const) [(k, v) | (Const k, v) <- xs])
getMinT (ConstMap m) = do
(~(k, v), m') <- getMinAlg m
return ((Const k, v), ConstMap m')
getMaxT (ConstMap m) = do
(~(k, v), m') <- getMaxAlg m
return ((Const k, v), ConstMap m')
updateMinT f (ConstMap m) = ConstMap <$> updateMinAlg (f . Const) m
updateMaxT f (ConstMap m) = ConstMap <$> updateMaxAlg (f . Const) m
isSubmapT (<=) (ConstMap m1) (ConstMap m2) = isSubmapAlg (<=) m1 m2
splitLookupT f (Const k) (ConstMap m) = case splitLookupAlg f k m of
(mL, ans, mR) -> (ConstMap mL, ans, ConstMap mR)
instance (TrieKey k m, TrieKey k' m') => TrieKey (Const k k') (ConstMap m k' m') where
compareKey = compareKeyT
emptyAlg = emptyT
nullAlg = nullT
getSingleAlg = getSingleT
guardNullAlg = guardNullT
sizeAlg = sizeT
lookupAlg = lookupT
alterLookupAlg = alterLookupT
mapAppAlg = mapAppT
mapMaybeAlg = mapMaybeT
mapEitherAlg = mapEitherT
foldWithKeyAlg = foldWithKeyT
unionMaybeAlg = unionT
intersectAlg = intersectT
differenceAlg = differenceT
getMinAlg = getMinT
getMaxAlg = getMaxT
updateMinAlg = updateMinT
updateMaxAlg = updateMaxT
isSubmapAlg = isSubmapT
splitLookupAlg = splitLookupT
instance TrieKeyT Id IdMap where
compareKeyT (Id a) (Id b) = compareKey a b
emptyT = IdMap emptyAlg
nullT (IdMap m) = nullAlg m
sizeT (IdMap m) = sizeAlg m
getSingleT (IdMap m) = do
(k, v) <- getSingleAlg m
return (Id k, v)
lookupT (Id k) (IdMap m) = lookupAlg k m
alterLookupT f (Id k) (IdMap m) = IdMap <$> alterLookupAlg f k m
foldWithKeyT f z (IdMap m) = foldWithKeyAlg (f . Id) z m
mapAppT f (IdMap m) = IdMap <$> mapAppAlg (f . Id) m
mapMaybeT f (IdMap m) = IdMap (mapMaybeAlg (f . Id) m)
mapEitherT f (IdMap m) = case mapEitherAlg (f . Id) m of
(mL, mR) -> (IdMap mL, IdMap mR)
unionT f (IdMap m1) (IdMap m2) = IdMap (unionMaybeAlg (f . Id) m1 m2)
intersectT f (IdMap m1) (IdMap m2) = IdMap (intersectAlg (f . Id) m1 m2)
differenceT f (IdMap m1) (IdMap m2) = IdMap (differenceAlg (f . Id) m1 m2)
fromDistAscListT xs = IdMap (fromDistAscListAlg [(k, v) | (Id k, v) <- xs])
fromAscListT f xs = IdMap (fromAscListAlg (f . Id) [(k, v) | (Id k, v) <- xs])
fromListT f xs = IdMap (fromListAlg (f . Id) [(k, v) | (Id k, v) <- xs])
getMinT (IdMap m) = do
(~(k, v), m') <- getMinAlg m
return ((Id k, v), IdMap m')
getMaxT (IdMap m) = do
(~(k, v), m') <- getMaxAlg m
return ((Id k, v), IdMap m')
updateMinT f (IdMap m) = IdMap <$> updateMinAlg (f . Id) m
updateMaxT f (IdMap m) = IdMap <$> updateMaxAlg (f . Id) m
isSubmapT (<=) (IdMap m1) (IdMap m2) = isSubmapAlg (<=) m1 m2
splitLookupT f (Id k) (IdMap m) = case splitLookupAlg f k m of
(mL, ans, mR) -> (IdMap mL, ans, IdMap mR)
instance TrieKey k m => TrieKey (Id k) (IdMap k m) where
compareKey = compareKeyT
emptyAlg = emptyT
nullAlg = nullT
getSingleAlg = getSingleT
guardNullAlg = guardNullT
sizeAlg = sizeT
lookupAlg = lookupT
alterLookupAlg = alterLookupT
mapAppAlg = mapAppT
mapMaybeAlg = mapMaybeT
mapEitherAlg = mapEitherT
foldWithKeyAlg = foldWithKeyT
unionMaybeAlg = unionT
intersectAlg = intersectT
differenceAlg = differenceT
getMinAlg = getMinT
getMaxAlg = getMaxT
updateMinAlg = updateMinT
updateMaxAlg = updateMaxT
isSubmapAlg = isSubmapT
splitLookupAlg = splitLookupT
instance TrieKey Int IntMap where
compareKey = compare
emptyAlg = IMap.empty
nullAlg = IMap.null
getSingleAlg m
| IMap.size m == 1, [(k, v)] <- IMap.toList m
= Just (k, v)
getSingleAlg _ = Nothing
lookupAlg = IMap.lookup
alterLookupAlg f k m = fmap (\ v' -> IMap.alter (const v') k m) (f x)
where x = IMap.lookup k m
foldWithKeyAlg = IMap.foldWithKey
mapAppAlg = sequenceA .: IMap.mapWithKey
mapMaybeAlg = IMap.mapMaybeWithKey
mapEitherAlg f m = (IMap.mapMaybeWithKey (fst .: f) m, IMap.mapMaybeWithKey (snd .: f) m)
unionMaybeAlg f m1 m2 = IMap.mapMaybe (either Just id) (IMap.unionWithKey g (fmap Left m1) (fmap Left m2)) where
g k (Left v1) (Left v2) = Right (f k v1 v2)
g k (Right v) _ = Right v
g k _ (Right v) = Right v
intersectAlg f m1 m2 = IMap.mapMaybe (either (const Nothing) Just) $ IMap.intersectionWithKey g (fmap Left m1) m2 where
g k (Left x) = maybe (Left x) Right . f k x
g _ (Right x) = const (Right x)
differenceAlg = IMap.differenceWithKey
fromListAlg = IMap.fromListWithKey
fromAscListAlg = IMap.fromAscListWithKey
fromDistAscListAlg = IMap.fromDistinctAscList
getMinAlg = IMap.minViewWithKey
getMaxAlg = IMap.maxViewWithKey
updateMinAlg f m = case IMap.minViewWithKey m of
Just ((k, v), m') -> let (ans, v') = f k v in (ans, maybe m' (\ v' -> IMap.updateMin (const v') m) v')
_ -> (False, m)
updateMaxAlg f m = case IMap.maxViewWithKey m of
Just ((k, v), m') -> let (ans, v') = f k v in (ans, maybe m' (\ v' -> IMap.updateMax (const v') m) v')
_ -> (False, m)
isSubmapAlg = IMap.isSubmapOfBy
splitLookupAlg f k m = case IMap.splitLookup k m of
(mL, Nothing, mR) -> (mL, Nothing, mR)
(mL, Just v, mR) -> case f v of
(vL, ans, vR) -> (maybe mL (flip (IMap.insert k) mL) vL, ans, maybe mR (flip (IMap.insert k) mR) vR)
instance Ord k => TrieKey (Ordered k) (Map k) where
compareKey = compare
emptyAlg = Map.empty
nullAlg = Map.null
getSingleAlg m
| Map.size m == 1, (k, v) <- Map.findMin m
= Just (Ord k, v)
lookupAlg = Map.lookup . unOrd
alterLookupAlg f (Ord k) m = fmap (\ v -> Map.alter (const v) k m) (f x)
where x = Map.lookup k m
foldWithKeyAlg f = Map.foldWithKey (f . Ord)
mapAppAlg f = sequenceA . Map.mapWithKey (f . Ord)
mapMaybeAlg f = Map.mapMaybeWithKey (f . Ord)
mapEitherAlg f m = (Map.mapMaybeWithKey (fst .: f . Ord) m, Map.mapMaybeWithKey (snd .: f . Ord) m)
unionMaybeAlg f m1 m2 = Map.mapMaybe (either Just id) (Map.unionWithKey g (fmap Left m1) (fmap Left m2)) where
g k (Left v1) (Left v2) = Right (f (Ord k) v1 v2)
g k (Right v) _ = Right v
g k _ (Right v) = Right v
intersectAlg f = Map.mapMaybe id .: Map.intersectionWithKey (f . Ord)
differenceAlg f = Map.differenceWithKey (f . Ord)
fromListAlg f xs = Map.fromListWithKey (f . Ord) [(k, v) | (Ord k, v) <- xs]
fromAscListAlg f xs = Map.fromAscListWithKey (f . Ord) [(k, v) | (Ord k, v) <- xs]
fromDistAscListAlg xs = Map.fromDistinctAscList [(k, v) | (Ord k, v) <- xs]
getMinAlg m = do (~(k, v), m') <- Map.minViewWithKey m
return ((Ord k, v), m')
getMaxAlg m = do (~(k, v), m') <- Map.maxViewWithKey m
return ((Ord k, v), m')
updateMinAlg f m
| Map.null m = (False, m)
| otherwise = case Map.findMin m of
(k, v) -> let (ans, v') = f (Ord k) v in (ans, Map.updateMin (const v') m)
updateMaxAlg f m
| Map.null m = (False, m)
| otherwise = case Map.findMin m of
(k, v) -> let (ans, v') = f (Ord k) v in (ans, Map.updateMax (const v') m)
isSubmapAlg = Map.isSubmapOfBy
splitLookupAlg f (Ord k) m = case Map.splitLookup k m of
(mL, Nothing, mR) -> (mL, Nothing, mR)
(mL, Just v, mR) -> case f v of
(vL, ans, vR) -> (maybe mL (flip (Map.insert k) mL) vL, ans, maybe mR (flip (Map.insert k) mR) vR)
instance TrieKey () Maybe where
compareKey _ _ = EQ
emptyAlg = Nothing
nullAlg = isNothing
sizeAlg = maybe 0 getSize
getSingleAlg = fmap ((,) ())
lookupAlg _ = id
alterLookupAlg f _ = f
foldWithKeyAlg f = foldr (f ())
mapAppAlg f = traverse (f ())
mapMaybeAlg f = (>>= f ())
mapEitherAlg f = maybe (Nothing, Nothing) (f ())
unionMaybeAlg f = unionMaybe (f ())
intersectAlg f = intersectMaybe (f ())
differenceAlg f = differenceMaybe (f ())
fromListAlg _ [] = Nothing
fromListAlg f ((_, v):xs) = Just (foldr (f () . snd) v xs)
fromAscListAlg = fromListAlg
fromDistAscListAlg = fmap snd . listToMaybe
getMinAlg = fmap g where
g v = (((), v), Nothing)
getMaxAlg = fmap g where
g v = (((), v), Nothing)
updateMinAlg f = maybe (False, Nothing) (f ())
updateMaxAlg f = maybe (False, Nothing) (f ())
isSubmapAlg _ Nothing _ = True
isSubmapAlg _ _ Nothing = False
isSubmapAlg (<=) (Just x) (Just y) = x <= y
splitLookupAlg f _ = maybe (Nothing, Nothing, Nothing) f
instance (TrieKeyT f t, TrieKey k m) => TrieKey (App f k) (App (t k m)) where
compareKey (App a) (App b) = compareKeyT a b
emptyAlg = App emptyT
nullAlg (App m) = nullT m
getSingleAlg (App m) = do
(k, v) <- getSingleT m
return (App k, v)
alterLookupAlg f (App k) (App m) = App <$> alterLookupT f k m
foldWithKeyAlg f z (App m) = foldWithKeyT (f . App) z m
mapAppAlg f (App m) = App <$> mapAppT (f . App) m
mapMaybeAlg f (App m) = App (mapMaybeT (f . App) m)
mapEitherAlg f (App m) = (App *** App) (mapEitherT (f . App) m)
fromListAlg f xs = App (fromListT (f . App) [(k, v) | (App k, v) <- xs])
fromAscListAlg f xs = App (fromAscListT (f . App) [(k, v) | (App k, v) <- xs])
fromDistAscListAlg xs = App (fromDistAscListT [(k, v) | (App k, v) <- xs])
unionMaybeAlg f (App m1) (App m2) = App (unionT (f . App) m1 m2)
intersectAlg f (App m1) (App m2) = App (intersectT (f . App) m1 m2)
differenceAlg f (App m1) (App m2) = App (differenceT (f . App) m1 m2)
getMinAlg (App m) = do
((k, v), m') <- getMinT m
return ((App k, v), App m')
getMaxAlg (App m) = do
((k, v), m') <- getMaxT m
return ((App k, v), App m')
updateMinAlg f (App m) = App <$> updateMinT (f . App) m
updateMaxAlg f (App m) = App <$> updateMaxT (f . App) m
isSubmapAlg (<=) (App m1) (App m2) = isSubmapT (<=) m1 m2
splitLookupAlg f (App k) (App m) = case splitLookupT f k m of
(mL, ans, mR) -> (App mL, ans, App mR)
instance (TrieKeyT f1 t1, TrieKeyT f2 t2) => TrieKeyT (f1 `O` f2) (CompMap t1 f2 t2) where
compareKeyT (O a) (O b) = compareKeyT a b
emptyT = CompMap emptyT
nullT (CompMap m) = nullT m
guardNullT (CompMap m) = CompMap <$> guardNullT m
sizeT (CompMap m) = sizeT m
getSingleT (CompMap m) = do
(k, v) <- getSingleT m
return (O k, v)
lookupT (O k) (CompMap m) = lookupT k m
alterLookupT f (O k) (CompMap m) = CompMap <$> alterLookupT f k m
foldWithKeyT f z (CompMap m) = foldWithKeyT (f . O) z m
mapAppT f (CompMap m) = CompMap <$> mapAppT (f . O) m
mapMaybeT f (CompMap m) = CompMap (mapMaybeT (f . O) m)
mapEitherT f (CompMap m) = (CompMap *** CompMap) (mapEitherT (f . O) m)
unionT f (CompMap m1) (CompMap m2) = CompMap (unionT (f . O) m1 m2)
intersectT f (CompMap m1) (CompMap m2) = CompMap (intersectT (f . O) m1 m2)
differenceT f (CompMap m1) (CompMap m2) = CompMap (differenceT (f . O) m1 m2)
fromDistAscListT xs = CompMap (fromDistAscListT [(k, v) | (O k, v) <- xs])
fromAscListT f xs = CompMap (fromAscListT (f . O) [(k, v) | (O k, v) <- xs])
fromListT f xs = CompMap (fromListT (f . O) [(k, v) | (O k, v) <- xs])
getMinT (CompMap m) = do
((k, v), m') <- getMinT m
return ((O k, v), CompMap m')
getMaxT (CompMap m) = do
((k, v), m') <- getMaxT m
return ((O k, v), CompMap m')
updateMinT f (CompMap m) = CompMap <$> updateMinT (f . O) m
updateMaxT f (CompMap m) = CompMap <$> updateMaxT (f . O) m
isSubmapT (<=) (CompMap m1) (CompMap m2) = isSubmapT (<=) m1 m2
splitLookupT f (O k) (CompMap m) = case splitLookupT f k m of
(mL, ans, mR) -> (CompMap mL, ans, CompMap mR)
instance (TrieKey k m, TrieKeyT f1 t1, TrieKeyT f2 t2) => TrieKey ((f1 `O` f2) k) (CompMap t1 f2 t2 k m) where
compareKey = compareKeyT
emptyAlg = emptyT
nullAlg = nullT
getSingleAlg = getSingleT
guardNullAlg = guardNullT
sizeAlg = sizeT
lookupAlg = lookupT
alterLookupAlg = alterLookupT
mapAppAlg = mapAppT
mapMaybeAlg = mapMaybeT
mapEitherAlg = mapEitherT
foldWithKeyAlg = foldWithKeyT
unionMaybeAlg = unionT
intersectAlg = intersectT
differenceAlg = differenceT
getMinAlg = getMinT
getMaxAlg = getMaxT
updateMinAlg = updateMinT
updateMaxAlg = updateMaxT
isSubmapAlg = isSubmapT
splitLookupAlg = splitLookupT