[PATCH] Split Data.IntMap into Data.IntMap.Strict and Data.IntMap.Lazy.
Edward Z. Yang
ezyang at MIT.EDU
Fri Sep 16 21:53:21 CEST 2011
On request of Milan, this is a follow up proposal to
http://www.haskell.org/pipermail/libraries/2011-May/016362.html
Here is what this patch specifically implements:
- Shared representation between lazy and strict variants
- Lazy/Strict modules exporting appropriate operations for each
There is an alternative version of this patch which Milan favors, where we do
not have a separate Data.IntMap.Lazy, and all that code lives in
Data/IntMap.hs. This will require a circular import if we don't want to break
BC and not duplicate the strict functions which still need to be exported.
Please vote yes as is, yes with Milan's modification, or no. Discussion period:
two weeks.
Cheers,
Edward
Excerpts from Edward Z. Yang's message of Fri Sep 16 15:49:28 -0400 2011:
> From: "Edward Z. Yang" <ezyang at mit.edu>
>
> Deprecates insert' and insertWith', and adds a raft of new
> strict functions for manipulating IntMaps in Data.IntMap.Strict.
> Auxiliary module Data.IntMap.Common for defining bit manipulation
> and types.
>
> See libraries proposal:
> http://www.haskell.org/pipermail/libraries/2011-May/016362.html
>
> Signed-off-by: Edward Z. Yang <ezyang at mit.edu>
> ---
> Data/IntMap.hs | 1817 +------------------------------------------------
> Data/IntMap/Common.hs | 245 +++++++
> Data/IntMap/Lazy.hs | 1783 ++++++++++++++++++++++++++++++++++++++++++++++++
> Data/IntMap/Strict.hs | 883 ++++++++++++++++++++++++
> containers.cabal | 4 +
> 5 files changed, 2932 insertions(+), 1800 deletions(-)
> create mode 100644 Data/IntMap/Common.hs
> create mode 100644 Data/IntMap/Lazy.hs
> create mode 100644 Data/IntMap/Strict.hs
>
> diff --git a/Data/IntMap.hs b/Data/IntMap.hs
> index b214d90..1d8b0ce 100644
> --- a/Data/IntMap.hs
> +++ b/Data/IntMap.hs
> @@ -40,13 +40,11 @@
> -- This means that the operation can become linear in the number of
> -- elements with a maximum of /W/ -- the number of bits in an 'Int'
> -- (32 or 64).
> +--
> +-- This module is spine strict, but value lazy. If you require strict
> +-- operations on these maps, please use "Data.IntMap.Strict".
> -----------------------------------------------------------------------------
>
> --- It is essential that the bit fiddling functions like mask, zero, branchMask
> --- etc are inlined. If they do not, the memory allocation skyrockets. The GHC
> --- usually gets it right, but it is disastrous if it does not. Therefore we
> --- explicitly mark these functions INLINE.
> -
> module Data.IntMap (
> -- * Map type
> #if !defined(TESTING)
> @@ -187,1222 +185,25 @@ module Data.IntMap (
> ) where
>
> import Prelude hiding (lookup,map,filter,foldr,foldl,null)
> -import Data.Bits
> -import qualified Data.IntSet as IntSet
> -import Data.Monoid (Monoid(..))
> -import Data.Maybe (fromMaybe)
> -import Data.Typeable
> -import qualified Data.Foldable as Foldable
> -import Data.Traversable (Traversable(traverse))
> -import Control.Applicative (Applicative(pure,(<*>)),(<$>))
> -import Control.Monad ( liftM )
> -import Control.DeepSeq (NFData(rnf))
> -{-
> --- just for testing
> -import qualified Prelude
> -import Test.QuickCheck
> -import List (nub,sort)
> -import qualified List
> --}
> -
> -#if __GLASGOW_HASKELL__
> -import Text.Read
> -import Data.Data (Data(..), mkNoRepType)
> -#endif
> -
> -#if __GLASGOW_HASKELL__ >= 503
> -import GHC.Exts ( Word(..), Int(..), shiftRL# )
> -#elif __GLASGOW_HASKELL__
> -import Word
> -import GlaExts ( Word(..), Int(..), shiftRL# )
> -#else
> -import Data.Word
> -#endif
> -
> --- Use macros to define strictness of functions.
> --- STRICT_x_OF_y denotes an y-ary function strict in the x-th parameter.
> --- We do not use BangPatterns, because they are not in any standard and we
> --- want the compilers to be compiled by as many compilers as possible.
> -#define STRICT_1_OF_2(fn) fn arg _ | arg `seq` False = undefined
> -
> -infixl 9 \\{-This comment teaches CPP correct behaviour -}
> -
> --- A "Nat" is a natural machine word (an unsigned Int)
> -type Nat = Word
> -
> -natFromInt :: Key -> Nat
> -natFromInt = fromIntegral
> -{-# INLINE natFromInt #-}
> -
> -intFromNat :: Nat -> Key
> -intFromNat = fromIntegral
> -{-# INLINE intFromNat #-}
> -
> -shiftRL :: Nat -> Key -> Nat
> -#if __GLASGOW_HASKELL__
> -{--------------------------------------------------------------------
> - GHC: use unboxing to get @shiftRL@ inlined.
> ---------------------------------------------------------------------}
> -shiftRL (W# x) (I# i)
> - = W# (shiftRL# x i)
> -#else
> -shiftRL x i = shiftR x i
> -{-# INLINE shiftRL #-}
> -#endif
> -
> -{--------------------------------------------------------------------
> - Operators
> ---------------------------------------------------------------------}
> -
> --- | /O(min(n,W))/. Find the value at a key.
> --- Calls 'error' when the element can not be found.
> ---
> --- > fromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map
> --- > fromList [(5,'a'), (3,'b')] ! 5 == 'a'
> -
> -(!) :: IntMap a -> Key -> a
> -m ! k = find k m
> -
> --- | Same as 'difference'.
> -(\\) :: IntMap a -> IntMap b -> IntMap a
> -m1 \\ m2 = difference m1 m2
> -
> -{--------------------------------------------------------------------
> - Types
> ---------------------------------------------------------------------}
> -
> --- The order of constructors of IntMap matters when considering performance.
> --- Currently in GHC 7.0, when type has 3 constructors, they are matched from
> --- the first to the last -- the best performance is achieved when the
> --- constructors are ordered by frequency.
> --- On GHC 7.0, reordering constructors from Nil | Tip | Bin to Bin | Tip | Nil
> --- improves the containers_benchmark by 9.5% on x86 and by 8% on x86_64.
> -
> --- | A map of integers to values @a at .
> -data IntMap a = Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !(IntMap a) !(IntMap a)
> - | Tip {-# UNPACK #-} !Key a
> - | Nil
> -
> -type Prefix = Int
> -type Mask = Int
> -type Key = Int
> -
> -instance Monoid (IntMap a) where
> - mempty = empty
> - mappend = union
> - mconcat = unions
> -
> -instance Foldable.Foldable IntMap where
> - fold Nil = mempty
> - fold (Tip _ v) = v
> - fold (Bin _ _ l r) = Foldable.fold l `mappend` Foldable.fold r
> - foldr = foldr
> - foldl = foldl
> - foldMap _ Nil = mempty
> - foldMap f (Tip _k v) = f v
> - foldMap f (Bin _ _ l r) = Foldable.foldMap f l `mappend` Foldable.foldMap f r
> -
> -instance Traversable IntMap where
> - traverse _ Nil = pure Nil
> - traverse f (Tip k v) = Tip k <$> f v
> - traverse f (Bin p m l r) = Bin p m <$> traverse f l <*> traverse f r
> -
> -instance NFData a => NFData (IntMap a) where
> - rnf Nil = ()
> - rnf (Tip _ v) = rnf v
> - rnf (Bin _ _ l r) = rnf l `seq` rnf r
> -
> -#if __GLASGOW_HASKELL__
> -
> -{--------------------------------------------------------------------
> - A Data instance
> ---------------------------------------------------------------------}
> -
> --- This instance preserves data abstraction at the cost of inefficiency.
> --- We omit reflection services for the sake of data abstraction.
> -
> -instance Data a => Data (IntMap a) where
> - gfoldl f z im = z fromList `f` (toList im)
> - toConstr _ = error "toConstr"
> - gunfold _ _ = error "gunfold"
> - dataTypeOf _ = mkNoRepType "Data.IntMap.IntMap"
> - dataCast1 f = gcast1 f
> -
> -#endif
> -
> -{--------------------------------------------------------------------
> - Query
> ---------------------------------------------------------------------}
> --- | /O(1)/. Is the map empty?
> ---
> --- > Data.IntMap.null (empty) == True
> --- > Data.IntMap.null (singleton 1 'a') == False
> -
> -null :: IntMap a -> Bool
> -null Nil = True
> -null _ = False
> -
> --- | /O(n)/. Number of elements in the map.
> ---
> --- > size empty == 0
> --- > size (singleton 1 'a') == 1
> --- > size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3
> -size :: IntMap a -> Int
> -size t
> - = case t of
> - Bin _ _ l r -> size l + size r
> - Tip _ _ -> 1
> - Nil -> 0
> -
> --- | /O(min(n,W))/. Is the key a member of the map?
> ---
> --- > member 5 (fromList [(5,'a'), (3,'b')]) == True
> --- > member 1 (fromList [(5,'a'), (3,'b')]) == False
> -
> -member :: Key -> IntMap a -> Bool
> -member k m
> - = case lookup k m of
> - Nothing -> False
> - Just _ -> True
> -
> --- | /O(log n)/. Is the key not a member of the map?
> ---
> --- > notMember 5 (fromList [(5,'a'), (3,'b')]) == False
> --- > notMember 1 (fromList [(5,'a'), (3,'b')]) == True
> -
> -notMember :: Key -> IntMap a -> Bool
> -notMember k m = not $ member k m
> -
> --- The 'go' function in the lookup causes 10% speedup, but also an increased
> --- memory allocation. It does not cause speedup with other methods like insert
> --- and delete, so it is present only in lookup.
> -
> --- | /O(min(n,W))/. Lookup the value at a key in the map. See also 'Data.Map.lookup'.
> -lookup :: Key -> IntMap a -> Maybe a
> -lookup k = k `seq` go
> - where
> - go (Bin _ m l r)
> - | zero k m = go l
> - | otherwise = go r
> - go (Tip kx x)
> - | k == kx = Just x
> - | otherwise = Nothing
> - go Nil = Nothing
> -
> -
> -find :: Key -> IntMap a -> a
> -find k m
> - = case lookup k m of
> - Nothing -> error ("IntMap.find: key " ++ show k ++ " is not an element of the map")
> - Just x -> x
> -
> --- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@
> --- returns the value at key @k@ or returns @def@ when the key is not an
> --- element of the map.
> ---
> --- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x'
> --- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a'
> -
> -findWithDefault :: a -> Key -> IntMap a -> a
> -findWithDefault def k m
> - = case lookup k m of
> - Nothing -> def
> - Just x -> x
> -
> -{--------------------------------------------------------------------
> - Construction
> ---------------------------------------------------------------------}
> --- | /O(1)/. The empty map.
> ---
> --- > empty == fromList []
> --- > size empty == 0
> -
> -empty :: IntMap a
> -empty
> - = Nil
> -
> --- | /O(1)/. A map of one element.
> ---
> --- > singleton 1 'a' == fromList [(1, 'a')]
> --- > size (singleton 1 'a') == 1
> -
> -singleton :: Key -> a -> IntMap a
> -singleton k x
> - = Tip k x
> -
> -{--------------------------------------------------------------------
> - Insert
> ---------------------------------------------------------------------}
> --- | /O(min(n,W))/. Insert a new key\/value pair in the map.
> --- If the key is already present in the map, the associated value is
> --- replaced with the supplied value, i.e. 'insert' is equivalent to
> --- @'insertWith' 'const'@.
> ---
> --- > insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')]
> --- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')]
> --- > insert 5 'x' empty == singleton 5 'x'
> -
> -insert :: Key -> a -> IntMap a -> IntMap a
> -insert k x t = k `seq`
> - case t of
> - Bin p m l r
> - | nomatch k p m -> join k (Tip k x) p t
> - | zero k m -> Bin p m (insert k x l) r
> - | otherwise -> Bin p m l (insert k x r)
> - Tip ky _
> - | k==ky -> Tip k x
> - | otherwise -> join k (Tip k x) ky t
> - Nil -> Tip k x
> -
> --- right-biased insertion, used by 'union'
> --- | /O(min(n,W))/. Insert with a combining function.
> --- @'insertWith' f key value mp@
> --- will insert the pair (key, value) into @mp@ if key does
> --- not exist in the map. If the key does exist, the function will
> --- insert @f new_value old_value at .
> ---
> --- > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")]
> --- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
> --- > insertWith (++) 5 "xxx" empty == singleton 5 "xxx"
> -
> -insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
> -insertWith f k x t
> - = insertWithKey (\_ x' y' -> f x' y') k x t
> +import Data.IntMap.Lazy
> +import qualified Data.IntMap.Strict as S
>
> -- | Same as 'insertWith', but the combining function is applied strictly.
> +-- This function is deprecated, use 'insertWith' in "Data.IntMap.Strict"
> +-- instead.
> insertWith' :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
> -insertWith' f k x t
> - = insertWithKey' (\_ x' y' -> f x' y') k x t
> -
> --- | /O(min(n,W))/. Insert with a combining function.
> --- @'insertWithKey' f key value mp@
> --- will insert the pair (key, value) into @mp@ if key does
> --- not exist in the map. If the key does exist, the function will
> --- insert @f key new_value old_value at .
> ---
> --- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
> --- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")]
> --- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
> --- > insertWithKey f 5 "xxx" empty == singleton 5 "xxx"
> -
> -insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
> -insertWithKey f k x t = k `seq`
> - case t of
> - Bin p m l r
> - | nomatch k p m -> join k (Tip k x) p t
> - | zero k m -> Bin p m (insertWithKey f k x l) r
> - | otherwise -> Bin p m l (insertWithKey f k x r)
> - Tip ky y
> - | k==ky -> Tip k (f k x y)
> - | otherwise -> join k (Tip k x) ky t
> - Nil -> Tip k x
> +insertWith' = S.insertWith
> +{-# INLINE insertWith' #-}
> +-- {-# DEPRECATED insertWith' "Use insertWith in Data.IntMap.Strict instead" #-}
>
> -- | Same as 'insertWithKey', but the combining function is applied strictly.
> +-- This function is deprecated, use 'insertWithKey' in "Data.IntMap.Strict"
> +-- instead.
> insertWithKey' :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
> -insertWithKey' f k x t = k `seq`
> - case t of
> - Bin p m l r
> - | nomatch k p m -> join k (Tip k x) p t
> - | zero k m -> Bin p m (insertWithKey' f k x l) r
> - | otherwise -> Bin p m l (insertWithKey' f k x r)
> - Tip ky y
> - | k==ky -> let x' = f k x y in seq x' (Tip k x')
> - | otherwise -> join k (Tip k x) ky t
> - Nil -> Tip k x
> -
> --- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@)
> --- is a pair where the first element is equal to (@'lookup' k map@)
> --- and the second element equal to (@'insertWithKey' f k x map@).
> ---
> --- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
> --- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
> --- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")])
> --- > insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx")
> ---
> --- This is how to define @insertLookup@ using @insertLookupWithKey@:
> ---
> --- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t
> --- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")])
> --- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")])
> -
> -insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
> -insertLookupWithKey f k x t = k `seq`
> - case t of
> - Bin p m l r
> - | nomatch k p m -> (Nothing,join k (Tip k x) p t)
> - | zero k m -> let (found,l') = insertLookupWithKey f k x l in (found,Bin p m l' r)
> - | otherwise -> let (found,r') = insertLookupWithKey f k x r in (found,Bin p m l r')
> - Tip ky y
> - | k==ky -> (Just y,Tip k (f k x y))
> - | otherwise -> (Nothing,join k (Tip k x) ky t)
> - Nil -> (Nothing,Tip k x)
> -
> -
> -{--------------------------------------------------------------------
> - Deletion
> - [delete] is the inlined version of [deleteWith (\k x -> Nothing)]
> ---------------------------------------------------------------------}
> --- | /O(min(n,W))/. Delete a key and its value from the map. When the key is not
> --- a member of the map, the original map is returned.
> ---
> --- > delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
> --- > delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> --- > delete 5 empty == empty
> -
> -delete :: Key -> IntMap a -> IntMap a
> -delete k t = k `seq`
> - case t of
> - Bin p m l r
> - | nomatch k p m -> t
> - | zero k m -> bin p m (delete k l) r
> - | otherwise -> bin p m l (delete k r)
> - Tip ky _
> - | k==ky -> Nil
> - | otherwise -> t
> - Nil -> Nil
> -
> --- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
> --- a member of the map, the original map is returned.
> ---
> --- > adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
> --- > adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> --- > adjust ("new " ++) 7 empty == empty
> -
> -adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
> -adjust f k m
> - = adjustWithKey (\_ x -> f x) k m
> -
> --- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
> --- a member of the map, the original map is returned.
> ---
> --- > let f key x = (show key) ++ ":new " ++ x
> --- > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
> --- > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> --- > adjustWithKey f 7 empty == empty
> -
> -adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
> -adjustWithKey f
> - = updateWithKey (\k' x -> Just (f k' x))
> -
> --- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
> --- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
> --- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y at .
> ---
> --- > let f x = if x == "a" then Just "new a" else Nothing
> --- > update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
> --- > update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> --- > update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> -
> -update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
> -update f
> - = updateWithKey (\_ x -> f x)
> -
> --- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
> --- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is
> --- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y at .
> ---
> --- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
> --- > updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
> --- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> --- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> -
> -updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
> -updateWithKey f k t = k `seq`
> - case t of
> - Bin p m l r
> - | nomatch k p m -> t
> - | zero k m -> bin p m (updateWithKey f k l) r
> - | otherwise -> bin p m l (updateWithKey f k r)
> - Tip ky y
> - | k==ky -> case (f k y) of
> - Just y' -> Tip ky y'
> - Nothing -> Nil
> - | otherwise -> t
> - Nil -> Nil
> -
> --- | /O(min(n,W))/. Lookup and update.
> --- The function returns original value, if it is updated.
> --- This is different behavior than 'Data.Map.updateLookupWithKey'.
> --- Returns the original key value if the map entry is deleted.
> ---
> --- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
> --- > updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:new a")])
> --- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")])
> --- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a")
> -
> -updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a)
> -updateLookupWithKey f k t = k `seq`
> - case t of
> - Bin p m l r
> - | nomatch k p m -> (Nothing,t)
> - | zero k m -> let (found,l') = updateLookupWithKey f k l in (found,bin p m l' r)
> - | otherwise -> let (found,r') = updateLookupWithKey f k r in (found,bin p m l r')
> - Tip ky y
> - | k==ky -> case (f k y) of
> - Just y' -> (Just y,Tip ky y')
> - Nothing -> (Just y,Nil)
> - | otherwise -> (Nothing,t)
> - Nil -> (Nothing,Nil)
> -
> -
> -
> --- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof.
> --- 'alter' can be used to insert, delete, or update a value in an 'IntMap'.
> --- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@.
> -alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap a
> -alter f k t = k `seq`
> - case t of
> - Bin p m l r
> - | nomatch k p m -> case f Nothing of
> - Nothing -> t
> - Just x -> join k (Tip k x) p t
> - | zero k m -> bin p m (alter f k l) r
> - | otherwise -> bin p m l (alter f k r)
> - Tip ky y
> - | k==ky -> case f (Just y) of
> - Just x -> Tip ky x
> - Nothing -> Nil
> - | otherwise -> case f Nothing of
> - Just x -> join k (Tip k x) ky t
> - Nothing -> Tip ky y
> - Nil -> case f Nothing of
> - Just x -> Tip k x
> - Nothing -> Nil
> -
> -
> -{--------------------------------------------------------------------
> - Union
> ---------------------------------------------------------------------}
> --- | The union of a list of maps.
> ---
> --- > unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
> --- > == fromList [(3, "b"), (5, "a"), (7, "C")]
> --- > unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])]
> --- > == fromList [(3, "B3"), (5, "A3"), (7, "C")]
> -
> -unions :: [IntMap a] -> IntMap a
> -unions xs
> - = foldlStrict union empty xs
> -
> --- | The union of a list of maps, with a combining operation.
> ---
> --- > unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
> --- > == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")]
> -
> -unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a
> -unionsWith f ts
> - = foldlStrict (unionWith f) empty ts
> -
> --- | /O(n+m)/. The (left-biased) union of two maps.
> --- It prefers the first map when duplicate keys are encountered,
> --- i.e. (@'union' == 'unionWith' 'const'@).
> ---
> --- > union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")]
> -
> -union :: IntMap a -> IntMap a -> IntMap a
> -union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> - | shorter m1 m2 = union1
> - | shorter m2 m1 = union2
> - | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
> - | otherwise = join p1 t1 p2 t2
> - where
> - union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
> - | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
> - | otherwise = Bin p1 m1 l1 (union r1 t2)
> -
> - union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
> - | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
> - | otherwise = Bin p2 m2 l2 (union t1 r2)
> -
> -union (Tip k x) t = insert k x t
> -union t (Tip k x) = insertWith (\_ y -> y) k x t -- right bias
> -union Nil t = t
> -union t Nil = t
> -
> --- | /O(n+m)/. The union with a combining function.
> ---
> --- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]
> -
> -unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
> -unionWith f m1 m2
> - = unionWithKey (\_ x y -> f x y) m1 m2
> -
> --- | /O(n+m)/. The union with a combining function.
> ---
> --- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value
> --- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")]
> -
> -unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
> -unionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> - | shorter m1 m2 = union1
> - | shorter m2 m1 = union2
> - | p1 == p2 = Bin p1 m1 (unionWithKey f l1 l2) (unionWithKey f r1 r2)
> - | otherwise = join p1 t1 p2 t2
> - where
> - union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
> - | zero p2 m1 = Bin p1 m1 (unionWithKey f l1 t2) r1
> - | otherwise = Bin p1 m1 l1 (unionWithKey f r1 t2)
> -
> - union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
> - | zero p1 m2 = Bin p2 m2 (unionWithKey f t1 l2) r2
> - | otherwise = Bin p2 m2 l2 (unionWithKey f t1 r2)
> -
> -unionWithKey f (Tip k x) t = insertWithKey f k x t
> -unionWithKey f t (Tip k x) = insertWithKey (\k' x' y' -> f k' y' x') k x t -- right bias
> -unionWithKey _ Nil t = t
> -unionWithKey _ t Nil = t
> -
> -{--------------------------------------------------------------------
> - Difference
> ---------------------------------------------------------------------}
> --- | /O(n+m)/. Difference between two maps (based on keys).
> ---
> --- > difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b"
> -
> -difference :: IntMap a -> IntMap b -> IntMap a
> -difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> - | shorter m1 m2 = difference1
> - | shorter m2 m1 = difference2
> - | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
> - | otherwise = t1
> - where
> - difference1 | nomatch p2 p1 m1 = t1
> - | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
> - | otherwise = bin p1 m1 l1 (difference r1 t2)
> -
> - difference2 | nomatch p1 p2 m2 = t1
> - | zero p1 m2 = difference t1 l2
> - | otherwise = difference t1 r2
> -
> -difference t1@(Tip k _) t2
> - | member k t2 = Nil
> - | otherwise = t1
> -
> -difference Nil _ = Nil
> -difference t (Tip k _) = delete k t
> -difference t Nil = t
> -
> --- | /O(n+m)/. Difference with a combining function.
> ---
> --- > let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing
> --- > differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")])
> --- > == singleton 3 "b:B"
> -
> -differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
> -differenceWith f m1 m2
> - = differenceWithKey (\_ x y -> f x y) m1 m2
> -
> --- | /O(n+m)/. Difference with a combining function. When two equal keys are
> --- encountered, the combining function is applied to the key and both values.
> --- If it returns 'Nothing', the element is discarded (proper set difference).
> --- If it returns (@'Just' y@), the element is updated with a new value @y at .
> ---
> --- > let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing
> --- > differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")])
> --- > == singleton 3 "3:b|B"
> -
> -differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
> -differenceWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> - | shorter m1 m2 = difference1
> - | shorter m2 m1 = difference2
> - | p1 == p2 = bin p1 m1 (differenceWithKey f l1 l2) (differenceWithKey f r1 r2)
> - | otherwise = t1
> - where
> - difference1 | nomatch p2 p1 m1 = t1
> - | zero p2 m1 = bin p1 m1 (differenceWithKey f l1 t2) r1
> - | otherwise = bin p1 m1 l1 (differenceWithKey f r1 t2)
> -
> - difference2 | nomatch p1 p2 m2 = t1
> - | zero p1 m2 = differenceWithKey f t1 l2
> - | otherwise = differenceWithKey f t1 r2
> -
> -differenceWithKey f t1@(Tip k x) t2
> - = case lookup k t2 of
> - Just y -> case f k x y of
> - Just y' -> Tip k y'
> - Nothing -> Nil
> - Nothing -> t1
> -
> -differenceWithKey _ Nil _ = Nil
> -differenceWithKey f t (Tip k y) = updateWithKey (\k' x -> f k' x y) k t
> -differenceWithKey _ t Nil = t
> -
> -
> -{--------------------------------------------------------------------
> - Intersection
> ---------------------------------------------------------------------}
> --- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys).
> ---
> --- > intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a"
> -
> -intersection :: IntMap a -> IntMap b -> IntMap a
> -intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> - | shorter m1 m2 = intersection1
> - | shorter m2 m1 = intersection2
> - | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
> - | otherwise = Nil
> - where
> - intersection1 | nomatch p2 p1 m1 = Nil
> - | zero p2 m1 = intersection l1 t2
> - | otherwise = intersection r1 t2
> -
> - intersection2 | nomatch p1 p2 m2 = Nil
> - | zero p1 m2 = intersection t1 l2
> - | otherwise = intersection t1 r2
> -
> -intersection t1@(Tip k _) t2
> - | member k t2 = t1
> - | otherwise = Nil
> -intersection t (Tip k _)
> - = case lookup k t of
> - Just y -> Tip k y
> - Nothing -> Nil
> -intersection Nil _ = Nil
> -intersection _ Nil = Nil
> -
> --- | /O(n+m)/. The intersection with a combining function.
> ---
> --- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA"
> -
> -intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
> -intersectionWith f m1 m2
> - = intersectionWithKey (\_ x y -> f x y) m1 m2
> -
> --- | /O(n+m)/. The intersection with a combining function.
> ---
> --- > let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar
> --- > intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A"
> -
> -intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
> -intersectionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> - | shorter m1 m2 = intersection1
> - | shorter m2 m1 = intersection2
> - | p1 == p2 = bin p1 m1 (intersectionWithKey f l1 l2) (intersectionWithKey f r1 r2)
> - | otherwise = Nil
> - where
> - intersection1 | nomatch p2 p1 m1 = Nil
> - | zero p2 m1 = intersectionWithKey f l1 t2
> - | otherwise = intersectionWithKey f r1 t2
> -
> - intersection2 | nomatch p1 p2 m2 = Nil
> - | zero p1 m2 = intersectionWithKey f t1 l2
> - | otherwise = intersectionWithKey f t1 r2
> -
> -intersectionWithKey f (Tip k x) t2
> - = case lookup k t2 of
> - Just y -> Tip k (f k x y)
> - Nothing -> Nil
> -intersectionWithKey f t1 (Tip k y)
> - = case lookup k t1 of
> - Just x -> Tip k (f k x y)
> - Nothing -> Nil
> -intersectionWithKey _ Nil _ = Nil
> -intersectionWithKey _ _ Nil = Nil
> -
> -
> -{--------------------------------------------------------------------
> - Min\/Max
> ---------------------------------------------------------------------}
> -
> --- | /O(log n)/. Update the value at the minimal key.
> ---
> --- > updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")]
> --- > updateMinWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> -
> -updateMinWithKey :: (Key -> a -> a) -> IntMap a -> IntMap a
> -updateMinWithKey f t
> - = case t of
> - Bin p m l r | m < 0 -> let t' = updateMinWithKeyUnsigned f r in Bin p m l t'
> - Bin p m l r -> let t' = updateMinWithKeyUnsigned f l in Bin p m t' r
> - Tip k y -> Tip k (f k y)
> - Nil -> error "maxView: empty map has no maximal element"
> -
> -updateMinWithKeyUnsigned :: (Key -> a -> a) -> IntMap a -> IntMap a
> -updateMinWithKeyUnsigned f t
> - = case t of
> - Bin p m l r -> let t' = updateMinWithKeyUnsigned f l in Bin p m t' r
> - Tip k y -> Tip k (f k y)
> - Nil -> error "updateMinWithKeyUnsigned Nil"
> -
> --- | /O(log n)/. Update the value at the maximal key.
> ---
> --- > updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")]
> --- > updateMaxWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
> -
> -updateMaxWithKey :: (Key -> a -> a) -> IntMap a -> IntMap a
> -updateMaxWithKey f t
> - = case t of
> - Bin p m l r | m < 0 -> let t' = updateMaxWithKeyUnsigned f l in Bin p m t' r
> - Bin p m l r -> let t' = updateMaxWithKeyUnsigned f r in Bin p m l t'
> - Tip k y -> Tip k (f k y)
> - Nil -> error "maxView: empty map has no maximal element"
> -
> -updateMaxWithKeyUnsigned :: (Key -> a -> a) -> IntMap a -> IntMap a
> -updateMaxWithKeyUnsigned f t
> - = case t of
> - Bin p m l r -> let t' = updateMaxWithKeyUnsigned f r in Bin p m l t'
> - Tip k y -> Tip k (f k y)
> - Nil -> error "updateMaxWithKeyUnsigned Nil"
> -
> -
> --- | /O(log n)/. Retrieves the maximal (key,value) pair of the map, and
> --- the map stripped of that element, or 'Nothing' if passed an empty map.
> ---
> --- > maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b")
> --- > maxViewWithKey empty == Nothing
> -
> -maxViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a)
> -maxViewWithKey t
> - = case t of
> - Bin p m l r | m < 0 -> let (result, t') = maxViewUnsigned l in Just (result, bin p m t' r)
> - Bin p m l r -> let (result, t') = maxViewUnsigned r in Just (result, bin p m l t')
> - Tip k y -> Just ((k,y), Nil)
> - Nil -> Nothing
> -
> -maxViewUnsigned :: IntMap a -> ((Key, a), IntMap a)
> -maxViewUnsigned t
> - = case t of
> - Bin p m l r -> let (result,t') = maxViewUnsigned r in (result,bin p m l t')
> - Tip k y -> ((k,y), Nil)
> - Nil -> error "maxViewUnsigned Nil"
> -
> --- | /O(log n)/. Retrieves the minimal (key,value) pair of the map, and
> --- the map stripped of that element, or 'Nothing' if passed an empty map.
> ---
> --- > minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a")
> --- > minViewWithKey empty == Nothing
> -
> -minViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a)
> -minViewWithKey t
> - = case t of
> - Bin p m l r | m < 0 -> let (result, t') = minViewUnsigned r in Just (result, bin p m l t')
> - Bin p m l r -> let (result, t') = minViewUnsigned l in Just (result, bin p m t' r)
> - Tip k y -> Just ((k,y),Nil)
> - Nil -> Nothing
> -
> -minViewUnsigned :: IntMap a -> ((Key, a), IntMap a)
> -minViewUnsigned t
> - = case t of
> - Bin p m l r -> let (result,t') = minViewUnsigned l in (result,bin p m t' r)
> - Tip k y -> ((k,y),Nil)
> - Nil -> error "minViewUnsigned Nil"
> -
> -
> --- | /O(log n)/. Update the value at the maximal key.
> ---
> --- > updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")]
> --- > updateMax (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
> -
> -updateMax :: (a -> a) -> IntMap a -> IntMap a
> -updateMax f = updateMaxWithKey (const f)
> -
> --- | /O(log n)/. Update the value at the minimal key.
> ---
> --- > updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")]
> --- > updateMin (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> -
> -updateMin :: (a -> a) -> IntMap a -> IntMap a
> -updateMin f = updateMinWithKey (const f)
> -
> --- Similar to the Arrow instance.
> -first :: (a -> c) -> (a, b) -> (c, b)
> -first f (x,y) = (f x,y)
> -
> --- | /O(log n)/. Retrieves the maximal key of the map, and the map
> --- stripped of that element, or 'Nothing' if passed an empty map.
> -maxView :: IntMap a -> Maybe (a, IntMap a)
> -maxView t = liftM (first snd) (maxViewWithKey t)
> -
> --- | /O(log n)/. Retrieves the minimal key of the map, and the map
> --- stripped of that element, or 'Nothing' if passed an empty map.
> -minView :: IntMap a -> Maybe (a, IntMap a)
> -minView t = liftM (first snd) (minViewWithKey t)
> -
> --- | /O(log n)/. Delete and find the maximal element.
> -deleteFindMax :: IntMap a -> (a, IntMap a)
> -deleteFindMax = fromMaybe (error "deleteFindMax: empty map has no maximal element") . maxView
> -
> --- | /O(log n)/. Delete and find the minimal element.
> -deleteFindMin :: IntMap a -> (a, IntMap a)
> -deleteFindMin = fromMaybe (error "deleteFindMin: empty map has no minimal element") . minView
> -
> --- | /O(log n)/. The minimal key of the map.
> -findMin :: IntMap a -> (Key, a)
> -findMin Nil = error $ "findMin: empty map has no minimal element"
> -findMin (Tip k v) = (k,v)
> -findMin (Bin _ m l r)
> - | m < 0 = go r
> - | otherwise = go l
> - where go (Tip k v) = (k,v)
> - go (Bin _ _ l' _) = go l'
> - go Nil = error "findMax Nil"
> +insertWithKey' = S.insertWithKey
> +{-# INLINE insertWithKey' #-}
> +-- {-# DEPRECATED insertWithKey' "Use insertWithKey in Data.IntMap.Strict instead" #-}
>
> --- | /O(log n)/. The maximal key of the map.
> -findMax :: IntMap a -> (Key, a)
> -findMax Nil = error $ "findMax: empty map has no maximal element"
> -findMax (Tip k v) = (k,v)
> -findMax (Bin _ m l r)
> - | m < 0 = go l
> - | otherwise = go r
> - where go (Tip k v) = (k,v)
> - go (Bin _ _ _ r') = go r'
> - go Nil = error "findMax Nil"
> -
> --- | /O(log n)/. Delete the minimal key. An error is thrown if the IntMap is already empty.
> --- Note, this is not the same behavior Map.
> -deleteMin :: IntMap a -> IntMap a
> -deleteMin = maybe (error "deleteMin: empty map has no minimal element") snd . minView
> -
> --- | /O(log n)/. Delete the maximal key. An error is thrown if the IntMap is already empty.
> --- Note, this is not the same behavior Map.
> -deleteMax :: IntMap a -> IntMap a
> -deleteMax = maybe (error "deleteMax: empty map has no maximal element") snd . maxView
> -
> -
> -{--------------------------------------------------------------------
> - Submap
> ---------------------------------------------------------------------}
> --- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
> --- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
> -isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
> -isProperSubmapOf m1 m2
> - = isProperSubmapOfBy (==) m1 m2
> -
> -{- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
> - The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
> - @m1@ and @m2@ are not equal,
> - all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
> - applied to their respective values. For example, the following
> - expressions are all 'True':
> -
> - > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> - > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> -
> - But the following are all 'False':
> -
> - > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
> - > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
> - > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> --}
> -isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
> -isProperSubmapOfBy predicate t1 t2
> - = case submapCmp predicate t1 t2 of
> - LT -> True
> - _ -> False
> -
> -submapCmp :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
> -submapCmp predicate t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
> - | shorter m1 m2 = GT
> - | shorter m2 m1 = submapCmpLt
> - | p1 == p2 = submapCmpEq
> - | otherwise = GT -- disjoint
> - where
> - submapCmpLt | nomatch p1 p2 m2 = GT
> - | zero p1 m2 = submapCmp predicate t1 l2
> - | otherwise = submapCmp predicate t1 r2
> - submapCmpEq = case (submapCmp predicate l1 l2, submapCmp predicate r1 r2) of
> - (GT,_ ) -> GT
> - (_ ,GT) -> GT
> - (EQ,EQ) -> EQ
> - _ -> LT
> -
> -submapCmp _ (Bin _ _ _ _) _ = GT
> -submapCmp predicate (Tip kx x) (Tip ky y)
> - | (kx == ky) && predicate x y = EQ
> - | otherwise = GT -- disjoint
> -submapCmp predicate (Tip k x) t
> - = case lookup k t of
> - Just y | predicate x y -> LT
> - _ -> GT -- disjoint
> -submapCmp _ Nil Nil = EQ
> -submapCmp _ Nil _ = LT
> -
> --- | /O(n+m)/. Is this a submap?
> --- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
> -isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
> -isSubmapOf m1 m2
> - = isSubmapOfBy (==) m1 m2
> -
> -{- | /O(n+m)/.
> - The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if
> - all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
> - applied to their respective values. For example, the following
> - expressions are all 'True':
> -
> - > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> - > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> - > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
> -
> - But the following are all 'False':
> -
> - > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
> - > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> - > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
> --}
> -isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
> -isSubmapOfBy predicate t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
> - | shorter m1 m2 = False
> - | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubmapOfBy predicate t1 l2
> - else isSubmapOfBy predicate t1 r2)
> - | otherwise = (p1==p2) && isSubmapOfBy predicate l1 l2 && isSubmapOfBy predicate r1 r2
> -isSubmapOfBy _ (Bin _ _ _ _) _ = False
> -isSubmapOfBy predicate (Tip k x) t = case lookup k t of
> - Just y -> predicate x y
> - Nothing -> False
> -isSubmapOfBy _ Nil _ = True
> -
> -{--------------------------------------------------------------------
> - Mapping
> ---------------------------------------------------------------------}
> --- | /O(n)/. Map a function over all values in the map.
> ---
> --- > map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]
> -
> -map :: (a -> b) -> IntMap a -> IntMap b
> -map f = mapWithKey (\_ x -> f x)
> -
> --- | /O(n)/. Map a function over all values in the map.
> ---
> --- > let f key x = (show key) ++ ":" ++ x
> --- > mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")]
> -
> -mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
> -mapWithKey f t
> - = case t of
> - Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r)
> - Tip k x -> Tip k (f k x)
> - Nil -> Nil
> -
> --- | /O(n)/. The function @'mapAccum'@ threads an accumulating
> --- argument through the map in ascending order of keys.
> ---
> --- > let f a b = (a ++ b, b ++ "X")
> --- > mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")])
> -
> -mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> -mapAccum f = mapAccumWithKey (\a' _ x -> f a' x)
> -
> --- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
> --- argument through the map in ascending order of keys.
> ---
> --- > let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X")
> --- > mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")])
> -
> -mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> -mapAccumWithKey f a t
> - = mapAccumL f a t
> -
> --- | /O(n)/. The function @'mapAccumL'@ threads an accumulating
> --- argument through the map in ascending order of keys.
> -mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> -mapAccumL f a t
> - = case t of
> - Bin p m l r -> let (a1,l') = mapAccumL f a l
> - (a2,r') = mapAccumL f a1 r
> - in (a2,Bin p m l' r')
> - Tip k x -> let (a',x') = f a k x in (a',Tip k x')
> - Nil -> (a,Nil)
> -
> --- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
> --- argument through the map in descending order of keys.
> -mapAccumRWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> -mapAccumRWithKey f a t
> - = case t of
> - Bin p m l r -> let (a1,r') = mapAccumRWithKey f a r
> - (a2,l') = mapAccumRWithKey f a1 l
> - in (a2,Bin p m l' r')
> - Tip k x -> let (a',x') = f a k x in (a',Tip k x')
> - Nil -> (a,Nil)
> -
> -{--------------------------------------------------------------------
> - Filter
> ---------------------------------------------------------------------}
> --- | /O(n)/. Filter all values that satisfy some predicate.
> ---
> --- > filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
> --- > filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty
> --- > filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty
> -
> -filter :: (a -> Bool) -> IntMap a -> IntMap a
> -filter p m
> - = filterWithKey (\_ x -> p x) m
> -
> --- | /O(n)/. Filter all keys\/values that satisfy some predicate.
> ---
> --- > filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> -
> -filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
> -filterWithKey predicate t
> - = case t of
> - Bin p m l r
> - -> bin p m (filterWithKey predicate l) (filterWithKey predicate r)
> - Tip k x
> - | predicate k x -> t
> - | otherwise -> Nil
> - Nil -> Nil
> -
> --- | /O(n)/. Partition the map according to some predicate. The first
> --- map contains all elements that satisfy the predicate, the second all
> --- elements that fail the predicate. See also 'split'.
> ---
> --- > partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
> --- > partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
> --- > partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])
> -
> -partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
> -partition p m
> - = partitionWithKey (\_ x -> p x) m
> -
> --- | /O(n)/. Partition the map according to some predicate. The first
> --- map contains all elements that satisfy the predicate, the second all
> --- elements that fail the predicate. See also 'split'.
> ---
> --- > partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b")
> --- > partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
> --- > partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])
> -
> -partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
> -partitionWithKey predicate t
> - = case t of
> - Bin p m l r
> - -> let (l1,l2) = partitionWithKey predicate l
> - (r1,r2) = partitionWithKey predicate r
> - in (bin p m l1 r1, bin p m l2 r2)
> - Tip k x
> - | predicate k x -> (t,Nil)
> - | otherwise -> (Nil,t)
> - Nil -> (Nil,Nil)
> -
> --- | /O(n)/. Map values and collect the 'Just' results.
> ---
> --- > let f x = if x == "a" then Just "new a" else Nothing
> --- > mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a"
> -
> -mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b
> -mapMaybe f = mapMaybeWithKey (\_ x -> f x)
> -
> --- | /O(n)/. Map keys\/values and collect the 'Just' results.
> ---
> --- > let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing
> --- > mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3"
> -
> -mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b
> -mapMaybeWithKey f (Bin p m l r)
> - = bin p m (mapMaybeWithKey f l) (mapMaybeWithKey f r)
> -mapMaybeWithKey f (Tip k x) = case f k x of
> - Just y -> Tip k y
> - Nothing -> Nil
> -mapMaybeWithKey _ Nil = Nil
> -
> --- | /O(n)/. Map values and separate the 'Left' and 'Right' results.
> ---
> --- > let f a = if a < "c" then Left a else Right a
> --- > mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> --- > == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")])
> --- >
> --- > mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> --- > == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> -
> -mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
> -mapEither f m
> - = mapEitherWithKey (\_ x -> f x) m
> -
> --- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results.
> ---
> --- > let f k a = if k < 5 then Left (k * 2) else Right (a ++ a)
> --- > mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> --- > == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")])
> --- >
> --- > mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> --- > == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")])
> -
> -mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
> -mapEitherWithKey f (Bin p m l r)
> - = (bin p m l1 r1, bin p m l2 r2)
> - where
> - (l1,l2) = mapEitherWithKey f l
> - (r1,r2) = mapEitherWithKey f r
> -mapEitherWithKey f (Tip k x) = case f k x of
> - Left y -> (Tip k y, Nil)
> - Right z -> (Nil, Tip k z)
> -mapEitherWithKey _ Nil = (Nil, Nil)
> -
> --- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@
> --- where all keys in @map1@ are lower than @k@ and all keys in
> --- @map2@ larger than @k at . Any key equal to @k@ is found in neither @map1@ nor @map2 at .
> ---
> --- > split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")])
> --- > split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a")
> --- > split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
> --- > split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty)
> --- > split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty)
> -
> -split :: Key -> IntMap a -> (IntMap a,IntMap a)
> -split k t
> - = case t of
> - Bin _ m l r
> - | m < 0 -> (if k >= 0 -- handle negative numbers.
> - then let (lt,gt) = split' k l in (union r lt, gt)
> - else let (lt,gt) = split' k r in (lt, union gt l))
> - | otherwise -> split' k t
> - Tip ky _
> - | k>ky -> (t,Nil)
> - | k<ky -> (Nil,t)
> - | otherwise -> (Nil,Nil)
> - Nil -> (Nil,Nil)
> -
> -split' :: Key -> IntMap a -> (IntMap a,IntMap a)
> -split' k t
> - = case t of
> - Bin p m l r
> - | nomatch k p m -> if k>p then (t,Nil) else (Nil,t)
> - | zero k m -> let (lt,gt) = split k l in (lt,union gt r)
> - | otherwise -> let (lt,gt) = split k r in (union l lt,gt)
> - Tip ky _
> - | k>ky -> (t,Nil)
> - | k<ky -> (Nil,t)
> - | otherwise -> (Nil,Nil)
> - Nil -> (Nil,Nil)
> -
> --- | /O(log n)/. Performs a 'split' but also returns whether the pivot
> --- key was found in the original map.
> ---
> --- > splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")])
> --- > splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a")
> --- > splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a")
> --- > splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty)
> --- > splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty)
> -
> -splitLookup :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
> -splitLookup k t
> - = case t of
> - Bin _ m l r
> - | m < 0 -> (if k >= 0 -- handle negative numbers.
> - then let (lt,found,gt) = splitLookup' k l in (union r lt,found, gt)
> - else let (lt,found,gt) = splitLookup' k r in (lt,found, union gt l))
> - | otherwise -> splitLookup' k t
> - Tip ky y
> - | k>ky -> (t,Nothing,Nil)
> - | k<ky -> (Nil,Nothing,t)
> - | otherwise -> (Nil,Just y,Nil)
> - Nil -> (Nil,Nothing,Nil)
> -
> -splitLookup' :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
> -splitLookup' k t
> - = case t of
> - Bin p m l r
> - | nomatch k p m -> if k>p then (t,Nothing,Nil) else (Nil,Nothing,t)
> - | zero k m -> let (lt,found,gt) = splitLookup k l in (lt,found,union gt r)
> - | otherwise -> let (lt,found,gt) = splitLookup k r in (union l lt,found,gt)
> - Tip ky y
> - | k>ky -> (t,Nothing,Nil)
> - | k<ky -> (Nil,Nothing,t)
> - | otherwise -> (Nil,Just y,Nil)
> - Nil -> (Nil,Nothing,Nil)
> -
> -{--------------------------------------------------------------------
> - Fold
> ---------------------------------------------------------------------}
> -- | /O(n)/. Fold the values in the map using the given right-associative
> -- binary operator. This function is an equivalent of 'foldr' and is present
> -- for compatibility only.
> @@ -1411,72 +212,7 @@ splitLookup' k t
> fold :: (a -> b -> b) -> b -> IntMap a -> b
> fold = foldr
> {-# INLINE fold #-}
> -
> --- | /O(n)/. Fold the values in the map using the given right-associative
> --- binary operator, such that @'foldr' f z == 'Prelude.foldr' f z . 'elems'@.
> ---
> --- For example,
> ---
> --- > elems map = foldr (:) [] map
> ---
> --- > let f a len = len + (length a)
> --- > foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
> -foldr :: (a -> b -> b) -> b -> IntMap a -> b
> -foldr f z t =
> - case t of Bin 0 m l r | m < 0 -> go (go z l) r -- put negative numbers before
> - _ -> go z t
> - where
> - go z' Nil = z'
> - go z' (Tip _ x) = f x z'
> - go z' (Bin _ _ l r) = go (go z' r) l
> -{-# INLINE foldr #-}
> -
> --- | /O(n)/. A strict version of 'foldr'. Each application of the operator is
> --- evaluated before using the result in the next application. This
> --- function is strict in the starting value.
> -foldr' :: (a -> b -> b) -> b -> IntMap a -> b
> -foldr' f z t =
> - case t of Bin 0 m l r | m < 0 -> go (go z l) r -- put negative numbers before
> - _ -> go z t
> - where
> - STRICT_1_OF_2(go)
> - go z' Nil = z'
> - go z' (Tip _ x) = f x z'
> - go z' (Bin _ _ l r) = go (go z' r) l
> -{-# INLINE foldr' #-}
> -
> --- | /O(n)/. Fold the values in the map using the given left-associative
> --- binary operator, such that @'foldl' f z == 'Prelude.foldl' f z . 'elems'@.
> ---
> --- For example,
> ---
> --- > elems = reverse . foldl (flip (:)) []
> ---
> --- > let f len a = len + (length a)
> --- > foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
> -foldl :: (a -> b -> a) -> a -> IntMap b -> a
> -foldl f z t =
> - case t of Bin 0 m l r | m < 0 -> go (go z r) l -- put negative numbers before
> - _ -> go z t
> - where
> - go z' Nil = z'
> - go z' (Tip _ x) = f z' x
> - go z' (Bin _ _ l r) = go (go z' l) r
> -{-# INLINE foldl #-}
> -
> --- | /O(n)/. A strict version of 'foldl'. Each application of the operator is
> --- evaluated before using the result in the next application. This
> --- function is strict in the starting value.
> -foldl' :: (a -> b -> a) -> a -> IntMap b -> a
> -foldl' f z t =
> - case t of Bin 0 m l r | m < 0 -> go (go z r) l -- put negative numbers before
> - _ -> go z t
> - where
> - STRICT_1_OF_2(go)
> - go z' Nil = z'
> - go z' (Tip _ x) = f z' x
> - go z' (Bin _ _ l r) = go (go z' l) r
> -{-# INLINE foldl' #-}
> +-- {-# DEPRECATED fold "Use foldr instead." #-}
>
> -- | /O(n)/. Fold the keys and values in the map using the given right-associative
> -- binary operator. This function is an equivalent of 'foldrWithKey' and is present
> @@ -1486,523 +222,4 @@ foldl' f z t =
> foldWithKey :: (Int -> a -> b -> b) -> b -> IntMap a -> b
> foldWithKey = foldrWithKey
> {-# INLINE foldWithKey #-}
> -
> --- | /O(n)/. Fold the keys and values in the map using the given right-associative
> --- binary operator, such that
> --- @'foldrWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
> ---
> --- For example,
> ---
> --- > keys map = foldrWithKey (\k x ks -> k:ks) [] map
> ---
> --- > let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
> --- > foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"
> -foldrWithKey :: (Int -> a -> b -> b) -> b -> IntMap a -> b
> -foldrWithKey f z t =
> - case t of Bin 0 m l r | m < 0 -> go (go z l) r -- put negative numbers before
> - _ -> go z t
> - where
> - go z' Nil = z'
> - go z' (Tip kx x) = f kx x z'
> - go z' (Bin _ _ l r) = go (go z' r) l
> -{-# INLINE foldrWithKey #-}
> -
> --- | /O(n)/. A strict version of 'foldrWithKey'. Each application of the operator is
> --- evaluated before using the result in the next application. This
> --- function is strict in the starting value.
> -foldrWithKey' :: (Int -> a -> b -> b) -> b -> IntMap a -> b
> -foldrWithKey' f z t =
> - case t of Bin 0 m l r | m < 0 -> go (go z l) r -- put negative numbers before
> - _ -> go z t
> - where
> - STRICT_1_OF_2(go)
> - go z' Nil = z'
> - go z' (Tip kx x) = f kx x z'
> - go z' (Bin _ _ l r) = go (go z' r) l
> -{-# INLINE foldrWithKey' #-}
> -
> --- | /O(n)/. Fold the keys and values in the map using the given left-associative
> --- binary operator, such that
> --- @'foldlWithKey' f z == 'Prelude.foldl' (\\z' (kx, x) -> f z' kx x) z . 'toAscList'@.
> ---
> --- For example,
> ---
> --- > keys = reverse . foldlWithKey (\ks k x -> k:ks) []
> ---
> --- > let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
> --- > foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)"
> -foldlWithKey :: (a -> Int -> b -> a) -> a -> IntMap b -> a
> -foldlWithKey f z t =
> - case t of Bin 0 m l r | m < 0 -> go (go z r) l -- put negative numbers before
> - _ -> go z t
> - where
> - go z' Nil = z'
> - go z' (Tip kx x) = f z' kx x
> - go z' (Bin _ _ l r) = go (go z' l) r
> -{-# INLINE foldlWithKey #-}
> -
> --- | /O(n)/. A strict version of 'foldlWithKey'. Each application of the operator is
> --- evaluated before using the result in the next application. This
> --- function is strict in the starting value.
> -foldlWithKey' :: (a -> Int -> b -> a) -> a -> IntMap b -> a
> -foldlWithKey' f z t =
> - case t of Bin 0 m l r | m < 0 -> go (go z r) l -- put negative numbers before
> - _ -> go z t
> - where
> - STRICT_1_OF_2(go)
> - go z' Nil = z'
> - go z' (Tip kx x) = f z' kx x
> - go z' (Bin _ _ l r) = go (go z' l) r
> -{-# INLINE foldlWithKey' #-}
> -
> -{--------------------------------------------------------------------
> - List variations
> ---------------------------------------------------------------------}
> --- | /O(n)/.
> --- Return all elements of the map in the ascending order of their keys.
> ---
> --- > elems (fromList [(5,"a"), (3,"b")]) == ["b","a"]
> --- > elems empty == []
> -
> -elems :: IntMap a -> [a]
> -elems
> - = foldr (:) []
> -
> --- | /O(n)/. Return all keys of the map in ascending order.
> ---
> --- > keys (fromList [(5,"a"), (3,"b")]) == [3,5]
> --- > keys empty == []
> -
> -keys :: IntMap a -> [Key]
> -keys
> - = foldrWithKey (\k _ ks -> k:ks) []
> -
> --- | /O(n*min(n,W))/. The set of all keys of the map.
> ---
> --- > keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5]
> --- > keysSet empty == Data.IntSet.empty
> -
> -keysSet :: IntMap a -> IntSet.IntSet
> -keysSet m = IntSet.fromDistinctAscList (keys m)
> -
> -
> --- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
> ---
> --- > assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
> --- > assocs empty == []
> -
> -assocs :: IntMap a -> [(Key,a)]
> -assocs m
> - = toList m
> -
> -
> -{--------------------------------------------------------------------
> - Lists
> ---------------------------------------------------------------------}
> --- | /O(n)/. Convert the map to a list of key\/value pairs.
> ---
> --- > toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
> --- > toList empty == []
> -
> -toList :: IntMap a -> [(Key,a)]
> -toList
> - = foldrWithKey (\k x xs -> (k,x):xs) []
> -
> --- | /O(n)/. Convert the map to a list of key\/value pairs where the
> --- keys are in ascending order.
> ---
> --- > toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
> -
> -toAscList :: IntMap a -> [(Key,a)]
> -toAscList t
> - = -- NOTE: the following algorithm only works for big-endian trees
> - let (pos,neg) = span (\(k,_) -> k >=0) (foldrWithKey (\k x xs -> (k,x):xs) [] t) in neg ++ pos
> -
> --- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs.
> ---
> --- > fromList [] == empty
> --- > fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")]
> --- > fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")]
> -
> -fromList :: [(Key,a)] -> IntMap a
> -fromList xs
> - = foldlStrict ins empty xs
> - where
> - ins t (k,x) = insert k x t
> -
> --- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
> ---
> --- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")]
> --- > fromListWith (++) [] == empty
> -
> -fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
> -fromListWith f xs
> - = fromListWithKey (\_ x y -> f x y) xs
> -
> --- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
> ---
> --- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")]
> --- > fromListWith (++) [] == empty
> -
> -fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
> -fromListWithKey f xs
> - = foldlStrict ins empty xs
> - where
> - ins t (k,x) = insertWithKey f k x t
> -
> --- | /O(n)/. Build a map from a list of key\/value pairs where
> --- the keys are in ascending order.
> ---
> --- > fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
> --- > fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")]
> -
> -fromAscList :: [(Key,a)] -> IntMap a
> -fromAscList xs
> - = fromAscListWithKey (\_ x _ -> x) xs
> -
> --- | /O(n)/. Build a map from a list of key\/value pairs where
> --- the keys are in ascending order, with a combining function on equal keys.
> --- /The precondition (input list is ascending) is not checked./
> ---
> --- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]
> -
> -fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
> -fromAscListWith f xs
> - = fromAscListWithKey (\_ x y -> f x y) xs
> -
> --- | /O(n)/. Build a map from a list of key\/value pairs where
> --- the keys are in ascending order, with a combining function on equal keys.
> --- /The precondition (input list is ascending) is not checked./
> ---
> --- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]
> -
> -fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
> -fromAscListWithKey _ [] = Nil
> -fromAscListWithKey f (x0 : xs0) = fromDistinctAscList (combineEq x0 xs0)
> - where
> - -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs]
> - combineEq z [] = [z]
> - combineEq z@(kz,zz) (x@(kx,xx):xs)
> - | kx==kz = let yy = f kx xx zz in combineEq (kx,yy) xs
> - | otherwise = z:combineEq x xs
> -
> --- | /O(n)/. Build a map from a list of key\/value pairs where
> --- the keys are in ascending order and all distinct.
> --- /The precondition (input list is strictly ascending) is not checked./
> ---
> --- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
> -
> -#ifdef __GLASGOW_HASKELL__
> -fromDistinctAscList :: forall a. [(Key,a)] -> IntMap a
> -#else
> -fromDistinctAscList :: [(Key,a)] -> IntMap a
> -#endif
> -fromDistinctAscList [] = Nil
> -fromDistinctAscList (z0 : zs0) = work z0 zs0 Nada
> - where
> - work (kx,vx) [] stk = finish kx (Tip kx vx) stk
> - work (kx,vx) (z@(kz,_):zs) stk = reduce z zs (branchMask kx kz) kx (Tip kx vx) stk
> -
> -#ifdef __GLASGOW_HASKELL__
> - reduce :: (Key,a) -> [(Key,a)] -> Mask -> Prefix -> IntMap a -> Stack a -> IntMap a
> -#endif
> - reduce z zs _ px tx Nada = work z zs (Push px tx Nada)
> - reduce z zs m px tx stk@(Push py ty stk') =
> - let mxy = branchMask px py
> - pxy = mask px mxy
> - in if shorter m mxy
> - then reduce z zs m pxy (Bin pxy mxy ty tx) stk'
> - else work z zs (Push px tx stk)
> -
> - finish _ t Nada = t
> - finish px tx (Push py ty stk) = finish p (join py ty px tx) stk
> - where m = branchMask px py
> - p = mask px m
> -
> -data Stack a = Push {-# UNPACK #-} !Prefix !(IntMap a) !(Stack a) | Nada
> -
> -
> -{--------------------------------------------------------------------
> - Eq
> ---------------------------------------------------------------------}
> -instance Eq a => Eq (IntMap a) where
> - t1 == t2 = equal t1 t2
> - t1 /= t2 = nequal t1 t2
> -
> -equal :: Eq a => IntMap a -> IntMap a -> Bool
> -equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
> - = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
> -equal (Tip kx x) (Tip ky y)
> - = (kx == ky) && (x==y)
> -equal Nil Nil = True
> -equal _ _ = False
> -
> -nequal :: Eq a => IntMap a -> IntMap a -> Bool
> -nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
> - = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
> -nequal (Tip kx x) (Tip ky y)
> - = (kx /= ky) || (x/=y)
> -nequal Nil Nil = False
> -nequal _ _ = True
> -
> -{--------------------------------------------------------------------
> - Ord
> ---------------------------------------------------------------------}
> -
> -instance Ord a => Ord (IntMap a) where
> - compare m1 m2 = compare (toList m1) (toList m2)
> -
> -{--------------------------------------------------------------------
> - Functor
> ---------------------------------------------------------------------}
> -
> -instance Functor IntMap where
> - fmap = map
> -
> -{--------------------------------------------------------------------
> - Show
> ---------------------------------------------------------------------}
> -
> -instance Show a => Show (IntMap a) where
> - showsPrec d m = showParen (d > 10) $
> - showString "fromList " . shows (toList m)
> -
> -{-
> -XXX unused code
> -
> -showMap :: (Show a) => [(Key,a)] -> ShowS
> -showMap []
> - = showString "{}"
> -showMap (x:xs)
> - = showChar '{' . showElem x . showTail xs
> - where
> - showTail [] = showChar '}'
> - showTail (x':xs') = showChar ',' . showElem x' . showTail xs'
> -
> - showElem (k,v) = shows k . showString ":=" . shows v
> --}
> -
> -{--------------------------------------------------------------------
> - Read
> ---------------------------------------------------------------------}
> -instance (Read e) => Read (IntMap e) where
> -#ifdef __GLASGOW_HASKELL__
> - readPrec = parens $ prec 10 $ do
> - Ident "fromList" <- lexP
> - xs <- readPrec
> - return (fromList xs)
> -
> - readListPrec = readListPrecDefault
> -#else
> - readsPrec p = readParen (p > 10) $ \ r -> do
> - ("fromList",s) <- lex r
> - (xs,t) <- reads s
> - return (fromList xs,t)
> -#endif
> -
> -{--------------------------------------------------------------------
> - Typeable
> ---------------------------------------------------------------------}
> -
> -#include "Typeable.h"
> -INSTANCE_TYPEABLE1(IntMap,intMapTc,"IntMap")
> -
> -{--------------------------------------------------------------------
> - Debugging
> ---------------------------------------------------------------------}
> --- | /O(n)/. Show the tree that implements the map. The tree is shown
> --- in a compressed, hanging format.
> -showTree :: Show a => IntMap a -> String
> -showTree s
> - = showTreeWith True False s
> -
> -
> -{- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
> - the tree that implements the map. If @hang@ is
> - 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
> - @wide@ is 'True', an extra wide version is shown.
> --}
> -showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
> -showTreeWith hang wide t
> - | hang = (showsTreeHang wide [] t) ""
> - | otherwise = (showsTree wide [] [] t) ""
> -
> -showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS
> -showsTree wide lbars rbars t
> - = case t of
> - Bin p m l r
> - -> showsTree wide (withBar rbars) (withEmpty rbars) r .
> - showWide wide rbars .
> - showsBars lbars . showString (showBin p m) . showString "\n" .
> - showWide wide lbars .
> - showsTree wide (withEmpty lbars) (withBar lbars) l
> - Tip k x
> - -> showsBars lbars . showString " " . shows k . showString ":=" . shows x . showString "\n"
> - Nil -> showsBars lbars . showString "|\n"
> -
> -showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS
> -showsTreeHang wide bars t
> - = case t of
> - Bin p m l r
> - -> showsBars bars . showString (showBin p m) . showString "\n" .
> - showWide wide bars .
> - showsTreeHang wide (withBar bars) l .
> - showWide wide bars .
> - showsTreeHang wide (withEmpty bars) r
> - Tip k x
> - -> showsBars bars . showString " " . shows k . showString ":=" . shows x . showString "\n"
> - Nil -> showsBars bars . showString "|\n"
> -
> -showBin :: Prefix -> Mask -> String
> -showBin _ _
> - = "*" -- ++ show (p,m)
> -
> -showWide :: Bool -> [String] -> String -> String
> -showWide wide bars
> - | wide = showString (concat (reverse bars)) . showString "|\n"
> - | otherwise = id
> -
> -showsBars :: [String] -> ShowS
> -showsBars bars
> - = case bars of
> - [] -> id
> - _ -> showString (concat (reverse (tail bars))) . showString node
> -
> -node :: String
> -node = "+--"
> -
> -withBar, withEmpty :: [String] -> [String]
> -withBar bars = "| ":bars
> -withEmpty bars = " ":bars
> -
> -
> -{--------------------------------------------------------------------
> - Helpers
> ---------------------------------------------------------------------}
> -{--------------------------------------------------------------------
> - Join
> ---------------------------------------------------------------------}
> -join :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
> -join p1 t1 p2 t2
> - | zero p1 m = Bin p m t1 t2
> - | otherwise = Bin p m t2 t1
> - where
> - m = branchMask p1 p2
> - p = mask p1 m
> -{-# INLINE join #-}
> -
> -{--------------------------------------------------------------------
> - @bin@ assures that we never have empty trees within a tree.
> ---------------------------------------------------------------------}
> -bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
> -bin _ _ l Nil = l
> -bin _ _ Nil r = r
> -bin p m l r = Bin p m l r
> -{-# INLINE bin #-}
> -
> -
> -{--------------------------------------------------------------------
> - Endian independent bit twiddling
> ---------------------------------------------------------------------}
> -zero :: Key -> Mask -> Bool
> -zero i m
> - = (natFromInt i) .&. (natFromInt m) == 0
> -{-# INLINE zero #-}
> -
> -nomatch,match :: Key -> Prefix -> Mask -> Bool
> -nomatch i p m
> - = (mask i m) /= p
> -{-# INLINE nomatch #-}
> -
> -match i p m
> - = (mask i m) == p
> -{-# INLINE match #-}
> -
> -mask :: Key -> Mask -> Prefix
> -mask i m
> - = maskW (natFromInt i) (natFromInt m)
> -{-# INLINE mask #-}
> -
> -
> -{--------------------------------------------------------------------
> - Big endian operations
> ---------------------------------------------------------------------}
> -maskW :: Nat -> Nat -> Prefix
> -maskW i m
> - = intFromNat (i .&. (complement (m-1) `xor` m))
> -{-# INLINE maskW #-}
> -
> -shorter :: Mask -> Mask -> Bool
> -shorter m1 m2
> - = (natFromInt m1) > (natFromInt m2)
> -{-# INLINE shorter #-}
> -
> -branchMask :: Prefix -> Prefix -> Mask
> -branchMask p1 p2
> - = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
> -{-# INLINE branchMask #-}
> -
> -{----------------------------------------------------------------------
> - Finding the highest bit (mask) in a word [x] can be done efficiently in
> - three ways:
> - * convert to a floating point value and the mantissa tells us the
> - [log2(x)] that corresponds with the highest bit position. The mantissa
> - is retrieved either via the standard C function [frexp] or by some bit
> - twiddling on IEEE compatible numbers (float). Note that one needs to
> - use at least [double] precision for an accurate mantissa of 32 bit
> - numbers.
> - * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
> - * use processor specific assembler instruction (asm).
> -
> - The most portable way would be [bit], but is it efficient enough?
> - I have measured the cycle counts of the different methods on an AMD
> - Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
> -
> - highestBitMask: method cycles
> - --------------
> - frexp 200
> - float 33
> - bit 11
> - asm 12
> -
> - highestBit: method cycles
> - --------------
> - frexp 195
> - float 33
> - bit 11
> - asm 11
> -
> - Wow, the bit twiddling is on today's RISC like machines even faster
> - than a single CISC instruction (BSR)!
> -----------------------------------------------------------------------}
> -
> -{----------------------------------------------------------------------
> - [highestBitMask] returns a word where only the highest bit is set.
> - It is found by first setting all bits in lower positions than the
> - highest bit and than taking an exclusive or with the original value.
> - Allthough the function may look expensive, GHC compiles this into
> - excellent C code that subsequently compiled into highly efficient
> - machine code. The algorithm is derived from Jorg Arndt's FXT library.
> -----------------------------------------------------------------------}
> -highestBitMask :: Nat -> Nat
> -highestBitMask x0
> - = case (x0 .|. shiftRL x0 1) of
> - x1 -> case (x1 .|. shiftRL x1 2) of
> - x2 -> case (x2 .|. shiftRL x2 4) of
> - x3 -> case (x3 .|. shiftRL x3 8) of
> - x4 -> case (x4 .|. shiftRL x4 16) of
> - x5 -> case (x5 .|. shiftRL x5 32) of -- for 64 bit platforms
> - x6 -> (x6 `xor` (shiftRL x6 1))
> -{-# INLINE highestBitMask #-}
> -
> -
> -{--------------------------------------------------------------------
> - Utilities
> ---------------------------------------------------------------------}
> -
> -foldlStrict :: (a -> b -> a) -> a -> [b] -> a
> -foldlStrict f = go
> - where
> - go z [] = z
> - go z (x:xs) = let z' = f z x in z' `seq` go z' xs
> -{-# INLINE foldlStrict #-}
> +-- {-# DEPRECATED foldWithKey "Use foldrWithKey instead." #-}
> diff --git a/Data/IntMap/Common.hs b/Data/IntMap/Common.hs
> new file mode 100644
> index 0000000..a61dc51
> --- /dev/null
> +++ b/Data/IntMap/Common.hs
> @@ -0,0 +1,245 @@
> +{-# LANGUAGE CPP, NoBangPatterns, MagicHash, ScopedTypeVariables #-}
> +-----------------------------------------------------------------------------
> +-- |
> +-- Module : Data.IntMap.Common
> +-- Copyright : (c) Daan Leijen 2002
> +-- (c) Andriy Palamarchuk 2008
> +-- License : BSD-style
> +-- Maintainer : libraries at haskell.org
> +-- Stability : provisional
> +-- Portability : portable
> +--
> +-- An efficient implementation of maps from integer keys to values.
> +--
> +-- The implementation is based on /big-endian patricia trees/. This data
> +-- structure performs especially well on binary operations like 'union'
> +-- and 'intersection'. However, my benchmarks show that it is also
> +-- (much) faster on insertions and deletions when compared to a generic
> +-- size-balanced map implementation (see "Data.Map").
> +--
> +-- * Chris Okasaki and Andy Gill, \"/Fast Mergeable Integer Maps/\",
> +-- Workshop on ML, September 1998, pages 77-86,
> +-- <http://citeseer.ist.psu.edu/okasaki98fast.html>
> +--
> +-- * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve
> +-- Information Coded In Alphanumeric/\", Journal of the ACM, 15(4),
> +-- October 1968, pages 514-534.
> +--
> +-- This defines the data structures and core (hidden) manipulations
> +-- on representations.
> +-----------------------------------------------------------------------------
> +
> +-- It is essential that the bit fiddling functions like mask, zero, branchMask
> +-- etc are inlined. If they do not, the memory allocation skyrockets. The GHC
> +-- usually gets it right, but it is disastrous if it does not. Therefore we
> +-- explicitly mark these functions INLINE.
> +
> +module Data.IntMap.Common (
> + -- * Map type
> + IntMap(..), Key -- instance Eq,Show
> +
> + -- * Internal types
> + , Mask, Prefix, Nat
> +
> + -- * Utility
> + , natFromInt
> + , intFromNat
> + , shiftRL
> + , join
> + , bin
> + , zero
> + , nomatch
> + , match
> + , mask
> + , maskW
> + , shorter
> + , branchMask
> + , highestBitMask
> + , foldlStrict
> + ) where
> +
> +import Prelude hiding (lookup,map,filter,foldr,foldl,null)
> +import Data.Bits
> +
> +#if __GLASGOW_HASKELL__ >= 503
> +import GHC.Exts ( Word(..), Int(..), shiftRL# )
> +#elif __GLASGOW_HASKELL__
> +import Word
> +import GlaExts ( Word(..), Int(..), shiftRL# )
> +#else
> +import Data.Word
> +#endif
> +
> +-- A "Nat" is a natural machine word (an unsigned Int)
> +type Nat = Word
> +
> +natFromInt :: Key -> Nat
> +natFromInt = fromIntegral
> +{-# INLINE natFromInt #-}
> +
> +intFromNat :: Nat -> Key
> +intFromNat = fromIntegral
> +{-# INLINE intFromNat #-}
> +
> +shiftRL :: Nat -> Key -> Nat
> +#if __GLASGOW_HASKELL__
> +{--------------------------------------------------------------------
> + GHC: use unboxing to get @shiftRL@ inlined.
> +--------------------------------------------------------------------}
> +shiftRL (W# x) (I# i)
> + = W# (shiftRL# x i)
> +#else
> +shiftRL x i = shiftR x i
> +{-# INLINE shiftRL #-}
> +#endif
> +
> +{--------------------------------------------------------------------
> + Types
> +--------------------------------------------------------------------}
> +
> +-- The order of constructors of IntMap matters when considering performance.
> +-- Currently in GHC 7.0, when type has 3 constructors, they are matched from
> +-- the first to the last -- the best performance is achieved when the
> +-- constructors are ordered by frequency.
> +-- On GHC 7.0, reordering constructors from Nil | Tip | Bin to Bin | Tip | Nil
> +-- improves the containers_benchmark by 9.5% on x86 and by 8% on x86_64.
> +
> +-- | A map of integers to values @a at .
> +data IntMap a = Bin {-# UNPACK #-} !Prefix {-# UNPACK #-} !Mask !(IntMap a) !(IntMap a)
> + | Tip {-# UNPACK #-} !Key a
> + | Nil
> +
> +type Prefix = Int
> +type Mask = Int
> +type Key = Int
> +
> +{--------------------------------------------------------------------
> + Helpers
> +--------------------------------------------------------------------}
> +{--------------------------------------------------------------------
> + Join
> +--------------------------------------------------------------------}
> +join :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
> +join p1 t1 p2 t2
> + | zero p1 m = Bin p m t1 t2
> + | otherwise = Bin p m t2 t1
> + where
> + m = branchMask p1 p2
> + p = mask p1 m
> +{-# INLINE join #-}
> +
> +{--------------------------------------------------------------------
> + @bin@ assures that we never have empty trees within a tree.
> +--------------------------------------------------------------------}
> +bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
> +bin _ _ l Nil = l
> +bin _ _ Nil r = r
> +bin p m l r = Bin p m l r
> +{-# INLINE bin #-}
> +
> +
> +{--------------------------------------------------------------------
> + Endian independent bit twiddling
> +--------------------------------------------------------------------}
> +zero :: Key -> Mask -> Bool
> +zero i m
> + = (natFromInt i) .&. (natFromInt m) == 0
> +{-# INLINE zero #-}
> +
> +nomatch,match :: Key -> Prefix -> Mask -> Bool
> +nomatch i p m
> + = (mask i m) /= p
> +{-# INLINE nomatch #-}
> +
> +match i p m
> + = (mask i m) == p
> +{-# INLINE match #-}
> +
> +mask :: Key -> Mask -> Prefix
> +mask i m
> + = maskW (natFromInt i) (natFromInt m)
> +{-# INLINE mask #-}
> +
> +
> +{--------------------------------------------------------------------
> + Big endian operations
> +--------------------------------------------------------------------}
> +maskW :: Nat -> Nat -> Prefix
> +maskW i m
> + = intFromNat (i .&. (complement (m-1) `xor` m))
> +{-# INLINE maskW #-}
> +
> +shorter :: Mask -> Mask -> Bool
> +shorter m1 m2
> + = (natFromInt m1) > (natFromInt m2)
> +{-# INLINE shorter #-}
> +
> +branchMask :: Prefix -> Prefix -> Mask
> +branchMask p1 p2
> + = intFromNat (highestBitMask (natFromInt p1 `xor` natFromInt p2))
> +{-# INLINE branchMask #-}
> +
> +{----------------------------------------------------------------------
> + Finding the highest bit (mask) in a word [x] can be done efficiently in
> + three ways:
> + * convert to a floating point value and the mantissa tells us the
> + [log2(x)] that corresponds with the highest bit position. The mantissa
> + is retrieved either via the standard C function [frexp] or by some bit
> + twiddling on IEEE compatible numbers (float). Note that one needs to
> + use at least [double] precision for an accurate mantissa of 32 bit
> + numbers.
> + * use bit twiddling, a logarithmic sequence of bitwise or's and shifts (bit).
> + * use processor specific assembler instruction (asm).
> +
> + The most portable way would be [bit], but is it efficient enough?
> + I have measured the cycle counts of the different methods on an AMD
> + Athlon-XP 1800 (~ Pentium III 1.8Ghz) using the RDTSC instruction:
> +
> + highestBitMask: method cycles
> + --------------
> + frexp 200
> + float 33
> + bit 11
> + asm 12
> +
> + highestBit: method cycles
> + --------------
> + frexp 195
> + float 33
> + bit 11
> + asm 11
> +
> + Wow, the bit twiddling is on today's RISC like machines even faster
> + than a single CISC instruction (BSR)!
> +----------------------------------------------------------------------}
> +
> +{----------------------------------------------------------------------
> + [highestBitMask] returns a word where only the highest bit is set.
> + It is found by first setting all bits in lower positions than the
> + highest bit and than taking an exclusive or with the original value.
> + Allthough the function may look expensive, GHC compiles this into
> + excellent C code that subsequently compiled into highly efficient
> + machine code. The algorithm is derived from Jorg Arndt's FXT library.
> +----------------------------------------------------------------------}
> +highestBitMask :: Nat -> Nat
> +highestBitMask x0
> + = case (x0 .|. shiftRL x0 1) of
> + x1 -> case (x1 .|. shiftRL x1 2) of
> + x2 -> case (x2 .|. shiftRL x2 4) of
> + x3 -> case (x3 .|. shiftRL x3 8) of
> + x4 -> case (x4 .|. shiftRL x4 16) of
> + x5 -> case (x5 .|. shiftRL x5 32) of -- for 64 bit platforms
> + x6 -> (x6 `xor` (shiftRL x6 1))
> +{-# INLINE highestBitMask #-}
> +
> +
> +{--------------------------------------------------------------------
> + Utilities
> +--------------------------------------------------------------------}
> +
> +foldlStrict :: (a -> b -> a) -> a -> [b] -> a
> +foldlStrict f = go
> + where
> + go z [] = z
> + go z (x:xs) = let z' = f z x in z' `seq` go z' xs
> +{-# INLINE foldlStrict #-}
> diff --git a/Data/IntMap/Lazy.hs b/Data/IntMap/Lazy.hs
> new file mode 100644
> index 0000000..efe6d8e
> --- /dev/null
> +++ b/Data/IntMap/Lazy.hs
> @@ -0,0 +1,1783 @@
> +{-# LANGUAGE CPP, NoBangPatterns, MagicHash, ScopedTypeVariables #-}
> +{-# OPTIONS_GHC -fno-warn-orphans #-}
> +-----------------------------------------------------------------------------
> +-- |
> +-- Module : Data.IntMap.Lazy
> +-- Copyright : (c) Daan Leijen 2002
> +-- (c) Andriy Palamarchuk 2008
> +-- License : BSD-style
> +-- Maintainer : libraries at haskell.org
> +-- Stability : provisional
> +-- Portability : portable
> +--
> +-- An efficient implementation of maps from integer keys to lazy values.
> +--
> +-- Since many function names (but not the type name) clash with
> +-- "Prelude" names, this module is usually imported @qualified@, e.g.
> +--
> +-- > import Data.IntMap (IntMap)
> +-- > import qualified Data.IntMap as IntMap
> +--
> +-- The implementation is based on /big-endian patricia trees/. This data
> +-- structure performs especially well on binary operations like 'union'
> +-- and 'intersection'. However, my benchmarks show that it is also
> +-- (much) faster on insertions and deletions when compared to a generic
> +-- size-balanced map implementation (see "Data.Map").
> +--
> +-- * Chris Okasaki and Andy Gill, \"/Fast Mergeable Integer Maps/\",
> +-- Workshop on ML, September 1998, pages 77-86,
> +-- <http://citeseer.ist.psu.edu/okasaki98fast.html>
> +--
> +-- * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve
> +-- Information Coded In Alphanumeric/\", Journal of the ACM, 15(4),
> +-- October 1968, pages 514-534.
> +--
> +-- Operation comments contain the operation time complexity in
> +-- the Big-O notation <http://en.wikipedia.org/wiki/Big_O_notation>.
> +-- Many operations have a worst-case complexity of /O(min(n,W))/.
> +-- This means that the operation can become linear in the number of
> +-- elements with a maximum of /W/ -- the number of bits in an 'Int'
> +-- (32 or 64).
> +--
> +-- If you need value-strict maps, try "Data.IntMap.Strict" instead.
> +-----------------------------------------------------------------------------
> +
> +module Data.IntMap.Lazy (
> + -- * Map type
> +#if !defined(TESTING)
> + IntMap, Key -- instance Eq,Show
> +#else
> + IntMap(..), Key -- instance Eq,Show
> +#endif
> +
> + -- * Operators
> + , (!), (\\)
> +
> + -- * Query
> + , null
> + , size
> + , member
> + , notMember
> + , lookup
> + , findWithDefault
> +
> + -- * Construction
> + , empty
> + , singleton
> +
> + -- ** Insertion
> + , insert
> + , insertWith
> + , insertWithKey
> + , insertLookupWithKey
> +
> + -- ** Delete\/Update
> + , delete
> + , adjust
> + , adjustWithKey
> + , update
> + , updateWithKey
> + , updateLookupWithKey
> + , alter
> +
> + -- * Combine
> +
> + -- ** Union
> + , union
> + , unionWith
> + , unionWithKey
> + , unions
> + , unionsWith
> +
> + -- ** Difference
> + , difference
> + , differenceWith
> + , differenceWithKey
> +
> + -- ** Intersection
> + , intersection
> + , intersectionWith
> + , intersectionWithKey
> +
> + -- * Traversal
> + -- ** Map
> + , map
> + , mapWithKey
> + , mapAccum
> + , mapAccumWithKey
> + , mapAccumRWithKey
> +
> + -- * Folds
> + , foldr
> + , foldl
> + , foldrWithKey
> + , foldlWithKey
> + -- ** Strict folds
> + , foldr'
> + , foldl'
> + , foldrWithKey'
> + , foldlWithKey'
> +
> + -- * Conversion
> + , elems
> + , keys
> + , keysSet
> + , assocs
> +
> + -- ** Lists
> + , toList
> + , fromList
> + , fromListWith
> + , fromListWithKey
> +
> + -- ** Ordered lists
> + , toAscList
> + , fromAscList
> + , fromAscListWith
> + , fromAscListWithKey
> + , fromDistinctAscList
> +
> + -- * Filter
> + , filter
> + , filterWithKey
> + , partition
> + , partitionWithKey
> +
> + , mapMaybe
> + , mapMaybeWithKey
> + , mapEither
> + , mapEitherWithKey
> +
> + , split
> + , splitLookup
> +
> + -- * Submap
> + , isSubmapOf, isSubmapOfBy
> + , isProperSubmapOf, isProperSubmapOfBy
> +
> + -- * Min\/Max
> + , findMin
> + , findMax
> + , deleteMin
> + , deleteMax
> + , deleteFindMin
> + , deleteFindMax
> + , updateMin
> + , updateMax
> + , updateMinWithKey
> + , updateMaxWithKey
> + , minView
> + , maxView
> + , minViewWithKey
> + , maxViewWithKey
> +
> + -- * Debugging
> + , showTree
> + , showTreeWith
> + ) where
> +
> +import Prelude hiding (lookup,map,filter,foldr,foldl,null)
> +import qualified Data.IntSet as IntSet
> +import Data.Monoid (Monoid(..))
> +import Data.Maybe (fromMaybe)
> +import Data.Typeable
> +import qualified Data.Foldable as Foldable
> +import Data.Traversable (Traversable(traverse))
> +import Control.Applicative (Applicative(pure,(<*>)),(<$>))
> +import Control.Monad ( liftM )
> +import Control.DeepSeq (NFData(rnf))
> +{-
> +-- just for testing
> +import qualified Prelude
> +import Test.QuickCheck
> +import List (nub,sort)
> +import qualified List
> +-}
> +
> +#if __GLASGOW_HASKELL__
> +import Text.Read
> +import Data.Data (Data(..), mkNoRepType)
> +#endif
> +
> +import Data.IntMap.Common
> +
> +-- Use macros to define strictness of functions.
> +-- STRICT_x_OF_y denotes an y-ary function strict in the x-th parameter.
> +-- We do not use BangPatterns, because they are not in any standard and we
> +-- want the compilers to be compiled by as many compilers as possible.
> +#define STRICT_1_OF_2(fn) fn arg _ | arg `seq` False = undefined
> +
> +infixl 9 \\{-This comment teaches CPP correct behaviour -}
> +
> +{--------------------------------------------------------------------
> + Operators
> +--------------------------------------------------------------------}
> +
> +-- | /O(min(n,W))/. Find the value at a key.
> +-- Calls 'error' when the element can not be found.
> +--
> +-- > fromList [(5,'a'), (3,'b')] ! 1 Error: element not in the map
> +-- > fromList [(5,'a'), (3,'b')] ! 5 == 'a'
> +
> +(!) :: IntMap a -> Key -> a
> +m ! k = find k m
> +
> +-- | Same as 'difference'.
> +(\\) :: IntMap a -> IntMap b -> IntMap a
> +m1 \\ m2 = difference m1 m2
> +
> +{--------------------------------------------------------------------
> + Types
> +--------------------------------------------------------------------}
> +
> +instance Monoid (IntMap a) where
> + mempty = empty
> + mappend = union
> + mconcat = unions
> +
> +instance Foldable.Foldable IntMap where
> + fold Nil = mempty
> + fold (Tip _ v) = v
> + fold (Bin _ _ l r) = Foldable.fold l `mappend` Foldable.fold r
> + foldr = foldr
> + foldl = foldl
> + foldMap _ Nil = mempty
> + foldMap f (Tip _k v) = f v
> + foldMap f (Bin _ _ l r) = Foldable.foldMap f l `mappend` Foldable.foldMap f r
> +
> +instance Traversable IntMap where
> + traverse _ Nil = pure Nil
> + traverse f (Tip k v) = Tip k <$> f v
> + traverse f (Bin p m l r) = Bin p m <$> traverse f l <*> traverse f r
> +
> +instance NFData a => NFData (IntMap a) where
> + rnf Nil = ()
> + rnf (Tip _ v) = rnf v
> + rnf (Bin _ _ l r) = rnf l `seq` rnf r
> +
> +#if __GLASGOW_HASKELL__
> +
> +{--------------------------------------------------------------------
> + A Data instance
> +--------------------------------------------------------------------}
> +
> +-- This instance preserves data abstraction at the cost of inefficiency.
> +-- We omit reflection services for the sake of data abstraction.
> +
> +instance Data a => Data (IntMap a) where
> + gfoldl f z im = z fromList `f` (toList im)
> + toConstr _ = error "toConstr"
> + gunfold _ _ = error "gunfold"
> + dataTypeOf _ = mkNoRepType "Data.IntMap.IntMap"
> + dataCast1 f = gcast1 f
> +
> +#endif
> +
> +{--------------------------------------------------------------------
> + Query
> +--------------------------------------------------------------------}
> +-- | /O(1)/. Is the map empty?
> +--
> +-- > Data.IntMap.null (empty) == True
> +-- > Data.IntMap.null (singleton 1 'a') == False
> +
> +null :: IntMap a -> Bool
> +null Nil = True
> +null _ = False
> +
> +-- | /O(n)/. Number of elements in the map.
> +--
> +-- > size empty == 0
> +-- > size (singleton 1 'a') == 1
> +-- > size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3
> +size :: IntMap a -> Int
> +size t
> + = case t of
> + Bin _ _ l r -> size l + size r
> + Tip _ _ -> 1
> + Nil -> 0
> +
> +-- | /O(min(n,W))/. Is the key a member of the map?
> +--
> +-- > member 5 (fromList [(5,'a'), (3,'b')]) == True
> +-- > member 1 (fromList [(5,'a'), (3,'b')]) == False
> +
> +member :: Key -> IntMap a -> Bool
> +member k m
> + = case lookup k m of
> + Nothing -> False
> + Just _ -> True
> +
> +-- | /O(log n)/. Is the key not a member of the map?
> +--
> +-- > notMember 5 (fromList [(5,'a'), (3,'b')]) == False
> +-- > notMember 1 (fromList [(5,'a'), (3,'b')]) == True
> +
> +notMember :: Key -> IntMap a -> Bool
> +notMember k m = not $ member k m
> +
> +-- The 'go' function in the lookup causes 10% speedup, but also an increased
> +-- memory allocation. It does not cause speedup with other methods like insert
> +-- and delete, so it is present only in lookup.
> +
> +-- | /O(min(n,W))/. Lookup the value at a key in the map. See also 'Data.Map.lookup'.
> +lookup :: Key -> IntMap a -> Maybe a
> +lookup k = k `seq` go
> + where
> + go (Bin _ m l r)
> + | zero k m = go l
> + | otherwise = go r
> + go (Tip kx x)
> + | k == kx = Just x
> + | otherwise = Nothing
> + go Nil = Nothing
> +
> +
> +find :: Key -> IntMap a -> a
> +find k m
> + = case lookup k m of
> + Nothing -> error ("IntMap.find: key " ++ show k ++ " is not an element of the map")
> + Just x -> x
> +
> +-- | /O(min(n,W))/. The expression @('findWithDefault' def k map)@
> +-- returns the value at key @k@ or returns @def@ when the key is not an
> +-- element of the map.
> +--
> +-- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x'
> +-- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a'
> +
> +findWithDefault :: a -> Key -> IntMap a -> a
> +findWithDefault def k m
> + = case lookup k m of
> + Nothing -> def
> + Just x -> x
> +
> +{--------------------------------------------------------------------
> + Construction
> +--------------------------------------------------------------------}
> +-- | /O(1)/. The empty map.
> +--
> +-- > empty == fromList []
> +-- > size empty == 0
> +
> +empty :: IntMap a
> +empty
> + = Nil
> +
> +-- | /O(1)/. A map of one element.
> +--
> +-- > singleton 1 'a' == fromList [(1, 'a')]
> +-- > size (singleton 1 'a') == 1
> +
> +singleton :: Key -> a -> IntMap a
> +singleton k x
> + = Tip k x
> +
> +{--------------------------------------------------------------------
> + Insert
> +--------------------------------------------------------------------}
> +-- | /O(min(n,W))/. Insert a new key\/value pair in the map.
> +-- If the key is already present in the map, the associated value is
> +-- replaced with the supplied value, i.e. 'insert' is equivalent to
> +-- @'insertWith' 'const'@.
> +--
> +-- > insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')]
> +-- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')]
> +-- > insert 5 'x' empty == singleton 5 'x'
> +
> +insert :: Key -> a -> IntMap a -> IntMap a
> +insert k x t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> join k (Tip k x) p t
> + | zero k m -> Bin p m (insert k x l) r
> + | otherwise -> Bin p m l (insert k x r)
> + Tip ky _
> + | k==ky -> Tip k x
> + | otherwise -> join k (Tip k x) ky t
> + Nil -> Tip k x
> +
> +-- right-biased insertion, used by 'union'
> +-- | /O(min(n,W))/. Insert with a combining function.
> +-- @'insertWith' f key value mp@
> +-- will insert the pair (key, value) into @mp@ if key does
> +-- not exist in the map. If the key does exist, the function will
> +-- insert @f new_value old_value at .
> +--
> +-- > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")]
> +-- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
> +-- > insertWith (++) 5 "xxx" empty == singleton 5 "xxx"
> +
> +insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
> +insertWith f k x t
> + = insertWithKey (\_ x' y' -> f x' y') k x t
> +
> +-- | /O(min(n,W))/. Insert with a combining function.
> +-- @'insertWithKey' f key value mp@
> +-- will insert the pair (key, value) into @mp@ if key does
> +-- not exist in the map. If the key does exist, the function will
> +-- insert @f key new_value old_value at .
> +--
> +-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
> +-- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")]
> +-- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
> +-- > insertWithKey f 5 "xxx" empty == singleton 5 "xxx"
> +
> +insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
> +insertWithKey f k x t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> join k (Tip k x) p t
> + | zero k m -> Bin p m (insertWithKey f k x l) r
> + | otherwise -> Bin p m l (insertWithKey f k x r)
> + Tip ky y
> + | k==ky -> Tip k (f k x y)
> + | otherwise -> join k (Tip k x) ky t
> + Nil -> Tip k x
> +
> +-- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@)
> +-- is a pair where the first element is equal to (@'lookup' k map@)
> +-- and the second element equal to (@'insertWithKey' f k x map@).
> +--
> +-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
> +-- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
> +-- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")])
> +-- > insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx")
> +--
> +-- This is how to define @insertLookup@ using @insertLookupWithKey@:
> +--
> +-- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t
> +-- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")])
> +-- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")])
> +
> +insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
> +insertLookupWithKey f k x t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> (Nothing,join k (Tip k x) p t)
> + | zero k m -> let (found,l') = insertLookupWithKey f k x l in (found,Bin p m l' r)
> + | otherwise -> let (found,r') = insertLookupWithKey f k x r in (found,Bin p m l r')
> + Tip ky y
> + | k==ky -> (Just y,Tip k (f k x y))
> + | otherwise -> (Nothing,join k (Tip k x) ky t)
> + Nil -> (Nothing,Tip k x)
> +
> +
> +{--------------------------------------------------------------------
> + Deletion
> + [delete] is the inlined version of [deleteWith (\k x -> Nothing)]
> +--------------------------------------------------------------------}
> +-- | /O(min(n,W))/. Delete a key and its value from the map. When the key is not
> +-- a member of the map, the original map is returned.
> +--
> +-- > delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
> +-- > delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> +-- > delete 5 empty == empty
> +
> +delete :: Key -> IntMap a -> IntMap a
> +delete k t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> t
> + | zero k m -> bin p m (delete k l) r
> + | otherwise -> bin p m l (delete k r)
> + Tip ky _
> + | k==ky -> Nil
> + | otherwise -> t
> + Nil -> Nil
> +
> +-- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
> +-- a member of the map, the original map is returned.
> +--
> +-- > adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
> +-- > adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> +-- > adjust ("new " ++) 7 empty == empty
> +
> +adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
> +adjust f k m
> + = adjustWithKey (\_ x -> f x) k m
> +
> +-- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
> +-- a member of the map, the original map is returned.
> +--
> +-- > let f key x = (show key) ++ ":new " ++ x
> +-- > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
> +-- > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> +-- > adjustWithKey f 7 empty == empty
> +
> +adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
> +adjustWithKey f
> + = updateWithKey (\k' x -> Just (f k' x))
> +
> +-- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
> +-- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
> +-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y at .
> +--
> +-- > let f x = if x == "a" then Just "new a" else Nothing
> +-- > update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
> +-- > update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> +-- > update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> +
> +update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
> +update f
> + = updateWithKey (\_ x -> f x)
> +
> +-- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
> +-- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is
> +-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y at .
> +--
> +-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
> +-- > updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
> +-- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> +-- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> +
> +updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
> +updateWithKey f k t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> t
> + | zero k m -> bin p m (updateWithKey f k l) r
> + | otherwise -> bin p m l (updateWithKey f k r)
> + Tip ky y
> + | k==ky -> case (f k y) of
> + Just y' -> Tip ky y'
> + Nothing -> Nil
> + | otherwise -> t
> + Nil -> Nil
> +
> +-- | /O(min(n,W))/. Lookup and update.
> +-- The function returns original value, if it is updated.
> +-- This is different behavior than 'Data.Map.updateLookupWithKey'.
> +-- Returns the original key value if the map entry is deleted.
> +--
> +-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
> +-- > updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:new a")])
> +-- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")])
> +-- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a")
> +
> +updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a)
> +updateLookupWithKey f k t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> (Nothing,t)
> + | zero k m -> let (found,l') = updateLookupWithKey f k l in (found,bin p m l' r)
> + | otherwise -> let (found,r') = updateLookupWithKey f k r in (found,bin p m l r')
> + Tip ky y
> + | k==ky -> case (f k y) of
> + Just y' -> (Just y,Tip ky y')
> + Nothing -> (Just y,Nil)
> + | otherwise -> (Nothing,t)
> + Nil -> (Nothing,Nil)
> +
> +
> +
> +-- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof.
> +-- 'alter' can be used to insert, delete, or update a value in an 'IntMap'.
> +-- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@.
> +alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap a
> +alter f k t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> case f Nothing of
> + Nothing -> t
> + Just x -> join k (Tip k x) p t
> + | zero k m -> bin p m (alter f k l) r
> + | otherwise -> bin p m l (alter f k r)
> + Tip ky y
> + | k==ky -> case f (Just y) of
> + Just x -> Tip ky x
> + Nothing -> Nil
> + | otherwise -> case f Nothing of
> + Just x -> join k (Tip k x) ky t
> + Nothing -> Tip ky y
> + Nil -> case f Nothing of
> + Just x -> Tip k x
> + Nothing -> Nil
> +
> +
> +{--------------------------------------------------------------------
> + Union
> +--------------------------------------------------------------------}
> +-- | The union of a list of maps.
> +--
> +-- > unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
> +-- > == fromList [(3, "b"), (5, "a"), (7, "C")]
> +-- > unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])]
> +-- > == fromList [(3, "B3"), (5, "A3"), (7, "C")]
> +
> +unions :: [IntMap a] -> IntMap a
> +unions xs
> + = foldlStrict union empty xs
> +
> +-- | The union of a list of maps, with a combining operation.
> +--
> +-- > unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
> +-- > == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")]
> +
> +unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a
> +unionsWith f ts
> + = foldlStrict (unionWith f) empty ts
> +
> +-- | /O(n+m)/. The (left-biased) union of two maps.
> +-- It prefers the first map when duplicate keys are encountered,
> +-- i.e. (@'union' == 'unionWith' 'const'@).
> +--
> +-- > union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")]
> +
> +union :: IntMap a -> IntMap a -> IntMap a
> +union t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> + | shorter m1 m2 = union1
> + | shorter m2 m1 = union2
> + | p1 == p2 = Bin p1 m1 (union l1 l2) (union r1 r2)
> + | otherwise = join p1 t1 p2 t2
> + where
> + union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
> + | zero p2 m1 = Bin p1 m1 (union l1 t2) r1
> + | otherwise = Bin p1 m1 l1 (union r1 t2)
> +
> + union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
> + | zero p1 m2 = Bin p2 m2 (union t1 l2) r2
> + | otherwise = Bin p2 m2 l2 (union t1 r2)
> +
> +union (Tip k x) t = insert k x t
> +union t (Tip k x) = insertWith (\_ y -> y) k x t -- right bias
> +union Nil t = t
> +union t Nil = t
> +
> +-- | /O(n+m)/. The union with a combining function.
> +--
> +-- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]
> +
> +unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
> +unionWith f m1 m2
> + = unionWithKey (\_ x y -> f x y) m1 m2
> +
> +-- | /O(n+m)/. The union with a combining function.
> +--
> +-- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value
> +-- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")]
> +
> +unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
> +unionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> + | shorter m1 m2 = union1
> + | shorter m2 m1 = union2
> + | p1 == p2 = Bin p1 m1 (unionWithKey f l1 l2) (unionWithKey f r1 r2)
> + | otherwise = join p1 t1 p2 t2
> + where
> + union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
> + | zero p2 m1 = Bin p1 m1 (unionWithKey f l1 t2) r1
> + | otherwise = Bin p1 m1 l1 (unionWithKey f r1 t2)
> +
> + union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
> + | zero p1 m2 = Bin p2 m2 (unionWithKey f t1 l2) r2
> + | otherwise = Bin p2 m2 l2 (unionWithKey f t1 r2)
> +
> +unionWithKey f (Tip k x) t = insertWithKey f k x t
> +unionWithKey f t (Tip k x) = insertWithKey (\k' x' y' -> f k' y' x') k x t -- right bias
> +unionWithKey _ Nil t = t
> +unionWithKey _ t Nil = t
> +
> +{--------------------------------------------------------------------
> + Difference
> +--------------------------------------------------------------------}
> +-- | /O(n+m)/. Difference between two maps (based on keys).
> +--
> +-- > difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b"
> +
> +difference :: IntMap a -> IntMap b -> IntMap a
> +difference t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> + | shorter m1 m2 = difference1
> + | shorter m2 m1 = difference2
> + | p1 == p2 = bin p1 m1 (difference l1 l2) (difference r1 r2)
> + | otherwise = t1
> + where
> + difference1 | nomatch p2 p1 m1 = t1
> + | zero p2 m1 = bin p1 m1 (difference l1 t2) r1
> + | otherwise = bin p1 m1 l1 (difference r1 t2)
> +
> + difference2 | nomatch p1 p2 m2 = t1
> + | zero p1 m2 = difference t1 l2
> + | otherwise = difference t1 r2
> +
> +difference t1@(Tip k _) t2
> + | member k t2 = Nil
> + | otherwise = t1
> +
> +difference Nil _ = Nil
> +difference t (Tip k _) = delete k t
> +difference t Nil = t
> +
> +-- | /O(n+m)/. Difference with a combining function.
> +--
> +-- > let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing
> +-- > differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")])
> +-- > == singleton 3 "b:B"
> +
> +differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
> +differenceWith f m1 m2
> + = differenceWithKey (\_ x y -> f x y) m1 m2
> +
> +-- | /O(n+m)/. Difference with a combining function. When two equal keys are
> +-- encountered, the combining function is applied to the key and both values.
> +-- If it returns 'Nothing', the element is discarded (proper set difference).
> +-- If it returns (@'Just' y@), the element is updated with a new value @y at .
> +--
> +-- > let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing
> +-- > differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")])
> +-- > == singleton 3 "3:b|B"
> +
> +differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
> +differenceWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> + | shorter m1 m2 = difference1
> + | shorter m2 m1 = difference2
> + | p1 == p2 = bin p1 m1 (differenceWithKey f l1 l2) (differenceWithKey f r1 r2)
> + | otherwise = t1
> + where
> + difference1 | nomatch p2 p1 m1 = t1
> + | zero p2 m1 = bin p1 m1 (differenceWithKey f l1 t2) r1
> + | otherwise = bin p1 m1 l1 (differenceWithKey f r1 t2)
> +
> + difference2 | nomatch p1 p2 m2 = t1
> + | zero p1 m2 = differenceWithKey f t1 l2
> + | otherwise = differenceWithKey f t1 r2
> +
> +differenceWithKey f t1@(Tip k x) t2
> + = case lookup k t2 of
> + Just y -> case f k x y of
> + Just y' -> Tip k y'
> + Nothing -> Nil
> + Nothing -> t1
> +
> +differenceWithKey _ Nil _ = Nil
> +differenceWithKey f t (Tip k y) = updateWithKey (\k' x -> f k' x y) k t
> +differenceWithKey _ t Nil = t
> +
> +
> +{--------------------------------------------------------------------
> + Intersection
> +--------------------------------------------------------------------}
> +-- | /O(n+m)/. The (left-biased) intersection of two maps (based on keys).
> +--
> +-- > intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a"
> +
> +intersection :: IntMap a -> IntMap b -> IntMap a
> +intersection t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> + | shorter m1 m2 = intersection1
> + | shorter m2 m1 = intersection2
> + | p1 == p2 = bin p1 m1 (intersection l1 l2) (intersection r1 r2)
> + | otherwise = Nil
> + where
> + intersection1 | nomatch p2 p1 m1 = Nil
> + | zero p2 m1 = intersection l1 t2
> + | otherwise = intersection r1 t2
> +
> + intersection2 | nomatch p1 p2 m2 = Nil
> + | zero p1 m2 = intersection t1 l2
> + | otherwise = intersection t1 r2
> +
> +intersection t1@(Tip k _) t2
> + | member k t2 = t1
> + | otherwise = Nil
> +intersection t (Tip k _)
> + = case lookup k t of
> + Just y -> Tip k y
> + Nothing -> Nil
> +intersection Nil _ = Nil
> +intersection _ Nil = Nil
> +
> +-- | /O(n+m)/. The intersection with a combining function.
> +--
> +-- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA"
> +
> +intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
> +intersectionWith f m1 m2
> + = intersectionWithKey (\_ x y -> f x y) m1 m2
> +
> +-- | /O(n+m)/. The intersection with a combining function.
> +--
> +-- > let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar
> +-- > intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A"
> +
> +intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
> +intersectionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> + | shorter m1 m2 = intersection1
> + | shorter m2 m1 = intersection2
> + | p1 == p2 = bin p1 m1 (intersectionWithKey f l1 l2) (intersectionWithKey f r1 r2)
> + | otherwise = Nil
> + where
> + intersection1 | nomatch p2 p1 m1 = Nil
> + | zero p2 m1 = intersectionWithKey f l1 t2
> + | otherwise = intersectionWithKey f r1 t2
> +
> + intersection2 | nomatch p1 p2 m2 = Nil
> + | zero p1 m2 = intersectionWithKey f t1 l2
> + | otherwise = intersectionWithKey f t1 r2
> +
> +intersectionWithKey f (Tip k x) t2
> + = case lookup k t2 of
> + Just y -> Tip k (f k x y)
> + Nothing -> Nil
> +intersectionWithKey f t1 (Tip k y)
> + = case lookup k t1 of
> + Just x -> Tip k (f k x y)
> + Nothing -> Nil
> +intersectionWithKey _ Nil _ = Nil
> +intersectionWithKey _ _ Nil = Nil
> +
> +
> +{--------------------------------------------------------------------
> + Min\/Max
> +--------------------------------------------------------------------}
> +
> +-- | /O(log n)/. Update the value at the minimal key.
> +--
> +-- > updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")]
> +-- > updateMinWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> +
> +updateMinWithKey :: (Key -> a -> a) -> IntMap a -> IntMap a
> +updateMinWithKey f t
> + = case t of
> + Bin p m l r | m < 0 -> let t' = updateMinWithKeyUnsigned f r in Bin p m l t'
> + Bin p m l r -> let t' = updateMinWithKeyUnsigned f l in Bin p m t' r
> + Tip k y -> Tip k (f k y)
> + Nil -> error "maxView: empty map has no maximal element"
> +
> +updateMinWithKeyUnsigned :: (Key -> a -> a) -> IntMap a -> IntMap a
> +updateMinWithKeyUnsigned f t
> + = case t of
> + Bin p m l r -> let t' = updateMinWithKeyUnsigned f l in Bin p m t' r
> + Tip k y -> Tip k (f k y)
> + Nil -> error "updateMinWithKeyUnsigned Nil"
> +
> +-- | /O(log n)/. Update the value at the maximal key.
> +--
> +-- > updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")]
> +-- > updateMaxWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
> +
> +updateMaxWithKey :: (Key -> a -> a) -> IntMap a -> IntMap a
> +updateMaxWithKey f t
> + = case t of
> + Bin p m l r | m < 0 -> let t' = updateMaxWithKeyUnsigned f l in Bin p m t' r
> + Bin p m l r -> let t' = updateMaxWithKeyUnsigned f r in Bin p m l t'
> + Tip k y -> Tip k (f k y)
> + Nil -> error "maxView: empty map has no maximal element"
> +
> +updateMaxWithKeyUnsigned :: (Key -> a -> a) -> IntMap a -> IntMap a
> +updateMaxWithKeyUnsigned f t
> + = case t of
> + Bin p m l r -> let t' = updateMaxWithKeyUnsigned f r in Bin p m l t'
> + Tip k y -> Tip k (f k y)
> + Nil -> error "updateMaxWithKeyUnsigned Nil"
> +
> +
> +-- | /O(log n)/. Retrieves the maximal (key,value) pair of the map, and
> +-- the map stripped of that element, or 'Nothing' if passed an empty map.
> +--
> +-- > maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b")
> +-- > maxViewWithKey empty == Nothing
> +
> +maxViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a)
> +maxViewWithKey t
> + = case t of
> + Bin p m l r | m < 0 -> let (result, t') = maxViewUnsigned l in Just (result, bin p m t' r)
> + Bin p m l r -> let (result, t') = maxViewUnsigned r in Just (result, bin p m l t')
> + Tip k y -> Just ((k,y), Nil)
> + Nil -> Nothing
> +
> +maxViewUnsigned :: IntMap a -> ((Key, a), IntMap a)
> +maxViewUnsigned t
> + = case t of
> + Bin p m l r -> let (result,t') = maxViewUnsigned r in (result,bin p m l t')
> + Tip k y -> ((k,y), Nil)
> + Nil -> error "maxViewUnsigned Nil"
> +
> +-- | /O(log n)/. Retrieves the minimal (key,value) pair of the map, and
> +-- the map stripped of that element, or 'Nothing' if passed an empty map.
> +--
> +-- > minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a")
> +-- > minViewWithKey empty == Nothing
> +
> +minViewWithKey :: IntMap a -> Maybe ((Key, a), IntMap a)
> +minViewWithKey t
> + = case t of
> + Bin p m l r | m < 0 -> let (result, t') = minViewUnsigned r in Just (result, bin p m l t')
> + Bin p m l r -> let (result, t') = minViewUnsigned l in Just (result, bin p m t' r)
> + Tip k y -> Just ((k,y),Nil)
> + Nil -> Nothing
> +
> +minViewUnsigned :: IntMap a -> ((Key, a), IntMap a)
> +minViewUnsigned t
> + = case t of
> + Bin p m l r -> let (result,t') = minViewUnsigned l in (result,bin p m t' r)
> + Tip k y -> ((k,y),Nil)
> + Nil -> error "minViewUnsigned Nil"
> +
> +
> +-- | /O(log n)/. Update the value at the maximal key.
> +--
> +-- > updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")]
> +-- > updateMax (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
> +
> +updateMax :: (a -> a) -> IntMap a -> IntMap a
> +updateMax f = updateMaxWithKey (const f)
> +
> +-- | /O(log n)/. Update the value at the minimal key.
> +--
> +-- > updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")]
> +-- > updateMin (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> +
> +updateMin :: (a -> a) -> IntMap a -> IntMap a
> +updateMin f = updateMinWithKey (const f)
> +
> +-- Similar to the Arrow instance.
> +first :: (a -> c) -> (a, b) -> (c, b)
> +first f (x,y) = (f x,y)
> +
> +-- | /O(log n)/. Retrieves the maximal key of the map, and the map
> +-- stripped of that element, or 'Nothing' if passed an empty map.
> +maxView :: IntMap a -> Maybe (a, IntMap a)
> +maxView t = liftM (first snd) (maxViewWithKey t)
> +
> +-- | /O(log n)/. Retrieves the minimal key of the map, and the map
> +-- stripped of that element, or 'Nothing' if passed an empty map.
> +minView :: IntMap a -> Maybe (a, IntMap a)
> +minView t = liftM (first snd) (minViewWithKey t)
> +
> +-- | /O(log n)/. Delete and find the maximal element.
> +deleteFindMax :: IntMap a -> (a, IntMap a)
> +deleteFindMax = fromMaybe (error "deleteFindMax: empty map has no maximal element") . maxView
> +
> +-- | /O(log n)/. Delete and find the minimal element.
> +deleteFindMin :: IntMap a -> (a, IntMap a)
> +deleteFindMin = fromMaybe (error "deleteFindMin: empty map has no minimal element") . minView
> +
> +-- | /O(log n)/. The minimal key of the map.
> +findMin :: IntMap a -> (Key, a)
> +findMin Nil = error $ "findMin: empty map has no minimal element"
> +findMin (Tip k v) = (k,v)
> +findMin (Bin _ m l r)
> + | m < 0 = go r
> + | otherwise = go l
> + where go (Tip k v) = (k,v)
> + go (Bin _ _ l' _) = go l'
> + go Nil = error "findMax Nil"
> +
> +-- | /O(log n)/. The maximal key of the map.
> +findMax :: IntMap a -> (Key, a)
> +findMax Nil = error $ "findMax: empty map has no maximal element"
> +findMax (Tip k v) = (k,v)
> +findMax (Bin _ m l r)
> + | m < 0 = go l
> + | otherwise = go r
> + where go (Tip k v) = (k,v)
> + go (Bin _ _ _ r') = go r'
> + go Nil = error "findMax Nil"
> +
> +-- | /O(log n)/. Delete the minimal key. An error is thrown if the IntMap is already empty.
> +-- Note, this is not the same behavior Map.
> +deleteMin :: IntMap a -> IntMap a
> +deleteMin = maybe (error "deleteMin: empty map has no minimal element") snd . minView
> +
> +-- | /O(log n)/. Delete the maximal key. An error is thrown if the IntMap is already empty.
> +-- Note, this is not the same behavior Map.
> +deleteMax :: IntMap a -> IntMap a
> +deleteMax = maybe (error "deleteMax: empty map has no maximal element") snd . maxView
> +
> +
> +{--------------------------------------------------------------------
> + Submap
> +--------------------------------------------------------------------}
> +-- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
> +-- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
> +isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
> +isProperSubmapOf m1 m2
> + = isProperSubmapOfBy (==) m1 m2
> +
> +{- | /O(n+m)/. Is this a proper submap? (ie. a submap but not equal).
> + The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
> + @m1@ and @m2@ are not equal,
> + all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
> + applied to their respective values. For example, the following
> + expressions are all 'True':
> +
> + > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> + > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> +
> + But the following are all 'False':
> +
> + > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
> + > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
> + > isProperSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> +-}
> +isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
> +isProperSubmapOfBy predicate t1 t2
> + = case submapCmp predicate t1 t2 of
> + LT -> True
> + _ -> False
> +
> +submapCmp :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
> +submapCmp predicate t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
> + | shorter m1 m2 = GT
> + | shorter m2 m1 = submapCmpLt
> + | p1 == p2 = submapCmpEq
> + | otherwise = GT -- disjoint
> + where
> + submapCmpLt | nomatch p1 p2 m2 = GT
> + | zero p1 m2 = submapCmp predicate t1 l2
> + | otherwise = submapCmp predicate t1 r2
> + submapCmpEq = case (submapCmp predicate l1 l2, submapCmp predicate r1 r2) of
> + (GT,_ ) -> GT
> + (_ ,GT) -> GT
> + (EQ,EQ) -> EQ
> + _ -> LT
> +
> +submapCmp _ (Bin _ _ _ _) _ = GT
> +submapCmp predicate (Tip kx x) (Tip ky y)
> + | (kx == ky) && predicate x y = EQ
> + | otherwise = GT -- disjoint
> +submapCmp predicate (Tip k x) t
> + = case lookup k t of
> + Just y | predicate x y -> LT
> + _ -> GT -- disjoint
> +submapCmp _ Nil Nil = EQ
> +submapCmp _ Nil _ = LT
> +
> +-- | /O(n+m)/. Is this a submap?
> +-- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
> +isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
> +isSubmapOf m1 m2
> + = isSubmapOfBy (==) m1 m2
> +
> +{- | /O(n+m)/.
> + The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if
> + all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
> + applied to their respective values. For example, the following
> + expressions are all 'True':
> +
> + > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> + > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> + > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
> +
> + But the following are all 'False':
> +
> + > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
> + > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
> + > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
> +-}
> +isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
> +isSubmapOfBy predicate t1@(Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
> + | shorter m1 m2 = False
> + | shorter m2 m1 = match p1 p2 m2 && (if zero p1 m2 then isSubmapOfBy predicate t1 l2
> + else isSubmapOfBy predicate t1 r2)
> + | otherwise = (p1==p2) && isSubmapOfBy predicate l1 l2 && isSubmapOfBy predicate r1 r2
> +isSubmapOfBy _ (Bin _ _ _ _) _ = False
> +isSubmapOfBy predicate (Tip k x) t = case lookup k t of
> + Just y -> predicate x y
> + Nothing -> False
> +isSubmapOfBy _ Nil _ = True
> +
> +{--------------------------------------------------------------------
> + Mapping
> +--------------------------------------------------------------------}
> +-- | /O(n)/. Map a function over all values in the map.
> +--
> +-- > map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]
> +
> +map :: (a -> b) -> IntMap a -> IntMap b
> +map f = mapWithKey (\_ x -> f x)
> +
> +-- | /O(n)/. Map a function over all values in the map.
> +--
> +-- > let f key x = (show key) ++ ":" ++ x
> +-- > mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")]
> +
> +mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
> +mapWithKey f t
> + = case t of
> + Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r)
> + Tip k x -> Tip k (f k x)
> + Nil -> Nil
> +
> +-- | /O(n)/. The function @'mapAccum'@ threads an accumulating
> +-- argument through the map in ascending order of keys.
> +--
> +-- > let f a b = (a ++ b, b ++ "X")
> +-- > mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")])
> +
> +mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> +mapAccum f = mapAccumWithKey (\a' _ x -> f a' x)
> +
> +-- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
> +-- argument through the map in ascending order of keys.
> +--
> +-- > let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X")
> +-- > mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")])
> +
> +mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> +mapAccumWithKey f a t
> + = mapAccumL f a t
> +
> +-- | /O(n)/. The function @'mapAccumL'@ threads an accumulating
> +-- argument through the map in ascending order of keys.
> +mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> +mapAccumL f a t
> + = case t of
> + Bin p m l r -> let (a1,l') = mapAccumL f a l
> + (a2,r') = mapAccumL f a1 r
> + in (a2,Bin p m l' r')
> + Tip k x -> let (a',x') = f a k x in (a',Tip k x')
> + Nil -> (a,Nil)
> +
> +-- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
> +-- argument through the map in descending order of keys.
> +mapAccumRWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> +mapAccumRWithKey f a t
> + = case t of
> + Bin p m l r -> let (a1,r') = mapAccumRWithKey f a r
> + (a2,l') = mapAccumRWithKey f a1 l
> + in (a2,Bin p m l' r')
> + Tip k x -> let (a',x') = f a k x in (a',Tip k x')
> + Nil -> (a,Nil)
> +
> +{--------------------------------------------------------------------
> + Filter
> +--------------------------------------------------------------------}
> +-- | /O(n)/. Filter all values that satisfy some predicate.
> +--
> +-- > filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
> +-- > filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty
> +-- > filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty
> +
> +filter :: (a -> Bool) -> IntMap a -> IntMap a
> +filter p m
> + = filterWithKey (\_ x -> p x) m
> +
> +-- | /O(n)/. Filter all keys\/values that satisfy some predicate.
> +--
> +-- > filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> +
> +filterWithKey :: (Key -> a -> Bool) -> IntMap a -> IntMap a
> +filterWithKey predicate t
> + = case t of
> + Bin p m l r
> + -> bin p m (filterWithKey predicate l) (filterWithKey predicate r)
> + Tip k x
> + | predicate k x -> t
> + | otherwise -> Nil
> + Nil -> Nil
> +
> +-- | /O(n)/. Partition the map according to some predicate. The first
> +-- map contains all elements that satisfy the predicate, the second all
> +-- elements that fail the predicate. See also 'split'.
> +--
> +-- > partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
> +-- > partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
> +-- > partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])
> +
> +partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
> +partition p m
> + = partitionWithKey (\_ x -> p x) m
> +
> +-- | /O(n)/. Partition the map according to some predicate. The first
> +-- map contains all elements that satisfy the predicate, the second all
> +-- elements that fail the predicate. See also 'split'.
> +--
> +-- > partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b")
> +-- > partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
> +-- > partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])
> +
> +partitionWithKey :: (Key -> a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
> +partitionWithKey predicate t
> + = case t of
> + Bin p m l r
> + -> let (l1,l2) = partitionWithKey predicate l
> + (r1,r2) = partitionWithKey predicate r
> + in (bin p m l1 r1, bin p m l2 r2)
> + Tip k x
> + | predicate k x -> (t,Nil)
> + | otherwise -> (Nil,t)
> + Nil -> (Nil,Nil)
> +
> +-- | /O(n)/. Map values and collect the 'Just' results.
> +--
> +-- > let f x = if x == "a" then Just "new a" else Nothing
> +-- > mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a"
> +
> +mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b
> +mapMaybe f = mapMaybeWithKey (\_ x -> f x)
> +
> +-- | /O(n)/. Map keys\/values and collect the 'Just' results.
> +--
> +-- > let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing
> +-- > mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3"
> +
> +mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b
> +mapMaybeWithKey f (Bin p m l r)
> + = bin p m (mapMaybeWithKey f l) (mapMaybeWithKey f r)
> +mapMaybeWithKey f (Tip k x) = case f k x of
> + Just y -> Tip k y
> + Nothing -> Nil
> +mapMaybeWithKey _ Nil = Nil
> +
> +-- | /O(n)/. Map values and separate the 'Left' and 'Right' results.
> +--
> +-- > let f a = if a < "c" then Left a else Right a
> +-- > mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> +-- > == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")])
> +-- >
> +-- > mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> +-- > == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> +
> +mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
> +mapEither f m
> + = mapEitherWithKey (\_ x -> f x) m
> +
> +-- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results.
> +--
> +-- > let f k a = if k < 5 then Left (k * 2) else Right (a ++ a)
> +-- > mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> +-- > == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")])
> +-- >
> +-- > mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> +-- > == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")])
> +
> +mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
> +mapEitherWithKey f (Bin p m l r)
> + = (bin p m l1 r1, bin p m l2 r2)
> + where
> + (l1,l2) = mapEitherWithKey f l
> + (r1,r2) = mapEitherWithKey f r
> +mapEitherWithKey f (Tip k x) = case f k x of
> + Left y -> (Tip k y, Nil)
> + Right z -> (Nil, Tip k z)
> +mapEitherWithKey _ Nil = (Nil, Nil)
> +
> +-- | /O(log n)/. The expression (@'split' k map@) is a pair @(map1,map2)@
> +-- where all keys in @map1@ are lower than @k@ and all keys in
> +-- @map2@ larger than @k at . Any key equal to @k@ is found in neither @map1@ nor @map2 at .
> +--
> +-- > split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")])
> +-- > split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a")
> +-- > split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
> +-- > split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty)
> +-- > split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty)
> +
> +split :: Key -> IntMap a -> (IntMap a,IntMap a)
> +split k t
> + = case t of
> + Bin _ m l r
> + | m < 0 -> (if k >= 0 -- handle negative numbers.
> + then let (lt,gt) = split' k l in (union r lt, gt)
> + else let (lt,gt) = split' k r in (lt, union gt l))
> + | otherwise -> split' k t
> + Tip ky _
> + | k>ky -> (t,Nil)
> + | k<ky -> (Nil,t)
> + | otherwise -> (Nil,Nil)
> + Nil -> (Nil,Nil)
> +
> +split' :: Key -> IntMap a -> (IntMap a,IntMap a)
> +split' k t
> + = case t of
> + Bin p m l r
> + | nomatch k p m -> if k>p then (t,Nil) else (Nil,t)
> + | zero k m -> let (lt,gt) = split k l in (lt,union gt r)
> + | otherwise -> let (lt,gt) = split k r in (union l lt,gt)
> + Tip ky _
> + | k>ky -> (t,Nil)
> + | k<ky -> (Nil,t)
> + | otherwise -> (Nil,Nil)
> + Nil -> (Nil,Nil)
> +
> +-- | /O(log n)/. Performs a 'split' but also returns whether the pivot
> +-- key was found in the original map.
> +--
> +-- > splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")])
> +-- > splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a")
> +-- > splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a")
> +-- > splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty)
> +-- > splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty)
> +
> +splitLookup :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
> +splitLookup k t
> + = case t of
> + Bin _ m l r
> + | m < 0 -> (if k >= 0 -- handle negative numbers.
> + then let (lt,found,gt) = splitLookup' k l in (union r lt,found, gt)
> + else let (lt,found,gt) = splitLookup' k r in (lt,found, union gt l))
> + | otherwise -> splitLookup' k t
> + Tip ky y
> + | k>ky -> (t,Nothing,Nil)
> + | k<ky -> (Nil,Nothing,t)
> + | otherwise -> (Nil,Just y,Nil)
> + Nil -> (Nil,Nothing,Nil)
> +
> +splitLookup' :: Key -> IntMap a -> (IntMap a,Maybe a,IntMap a)
> +splitLookup' k t
> + = case t of
> + Bin p m l r
> + | nomatch k p m -> if k>p then (t,Nothing,Nil) else (Nil,Nothing,t)
> + | zero k m -> let (lt,found,gt) = splitLookup k l in (lt,found,union gt r)
> + | otherwise -> let (lt,found,gt) = splitLookup k r in (union l lt,found,gt)
> + Tip ky y
> + | k>ky -> (t,Nothing,Nil)
> + | k<ky -> (Nil,Nothing,t)
> + | otherwise -> (Nil,Just y,Nil)
> + Nil -> (Nil,Nothing,Nil)
> +
> +{--------------------------------------------------------------------
> + Fold
> +--------------------------------------------------------------------}
> +-- | /O(n)/. Fold the values in the map using the given right-associative
> +-- binary operator, such that @'foldr' f z == 'Prelude.foldr' f z . 'elems'@.
> +--
> +-- For example,
> +--
> +-- > elems map = foldr (:) [] map
> +--
> +-- > let f a len = len + (length a)
> +-- > foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
> +foldr :: (a -> b -> b) -> b -> IntMap a -> b
> +foldr f z t =
> + case t of Bin 0 m l r | m < 0 -> go (go z l) r -- put negative numbers before
> + _ -> go z t
> + where
> + go z' Nil = z'
> + go z' (Tip _ x) = f x z'
> + go z' (Bin _ _ l r) = go (go z' r) l
> +{-# INLINE foldr #-}
> +
> +-- | /O(n)/. A strict version of 'foldr'. Each application of the operator is
> +-- evaluated before using the result in the next application. This
> +-- function is strict in the starting value.
> +foldr' :: (a -> b -> b) -> b -> IntMap a -> b
> +foldr' f z t =
> + case t of Bin 0 m l r | m < 0 -> go (go z l) r -- put negative numbers before
> + _ -> go z t
> + where
> + STRICT_1_OF_2(go)
> + go z' Nil = z'
> + go z' (Tip _ x) = f x z'
> + go z' (Bin _ _ l r) = go (go z' r) l
> +{-# INLINE foldr' #-}
> +
> +-- | /O(n)/. Fold the values in the map using the given left-associative
> +-- binary operator, such that @'foldl' f z == 'Prelude.foldl' f z . 'elems'@.
> +--
> +-- For example,
> +--
> +-- > elems = reverse . foldl (flip (:)) []
> +--
> +-- > let f len a = len + (length a)
> +-- > foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
> +foldl :: (a -> b -> a) -> a -> IntMap b -> a
> +foldl f z t =
> + case t of Bin 0 m l r | m < 0 -> go (go z r) l -- put negative numbers before
> + _ -> go z t
> + where
> + go z' Nil = z'
> + go z' (Tip _ x) = f z' x
> + go z' (Bin _ _ l r) = go (go z' l) r
> +{-# INLINE foldl #-}
> +
> +-- | /O(n)/. A strict version of 'foldl'. Each application of the operator is
> +-- evaluated before using the result in the next application. This
> +-- function is strict in the starting value.
> +foldl' :: (a -> b -> a) -> a -> IntMap b -> a
> +foldl' f z t =
> + case t of Bin 0 m l r | m < 0 -> go (go z r) l -- put negative numbers before
> + _ -> go z t
> + where
> + STRICT_1_OF_2(go)
> + go z' Nil = z'
> + go z' (Tip _ x) = f z' x
> + go z' (Bin _ _ l r) = go (go z' l) r
> +{-# INLINE foldl' #-}
> +
> +-- | /O(n)/. Fold the keys and values in the map using the given right-associative
> +-- binary operator, such that
> +-- @'foldrWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
> +--
> +-- For example,
> +--
> +-- > keys map = foldrWithKey (\k x ks -> k:ks) [] map
> +--
> +-- > let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
> +-- > foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"
> +foldrWithKey :: (Int -> a -> b -> b) -> b -> IntMap a -> b
> +foldrWithKey f z t =
> + case t of Bin 0 m l r | m < 0 -> go (go z l) r -- put negative numbers before
> + _ -> go z t
> + where
> + go z' Nil = z'
> + go z' (Tip kx x) = f kx x z'
> + go z' (Bin _ _ l r) = go (go z' r) l
> +{-# INLINE foldrWithKey #-}
> +
> +-- | /O(n)/. A strict version of 'foldrWithKey'. Each application of the operator is
> +-- evaluated before using the result in the next application. This
> +-- function is strict in the starting value.
> +foldrWithKey' :: (Int -> a -> b -> b) -> b -> IntMap a -> b
> +foldrWithKey' f z t =
> + case t of Bin 0 m l r | m < 0 -> go (go z l) r -- put negative numbers before
> + _ -> go z t
> + where
> + STRICT_1_OF_2(go)
> + go z' Nil = z'
> + go z' (Tip kx x) = f kx x z'
> + go z' (Bin _ _ l r) = go (go z' r) l
> +{-# INLINE foldrWithKey' #-}
> +
> +-- | /O(n)/. Fold the keys and values in the map using the given left-associative
> +-- binary operator, such that
> +-- @'foldlWithKey' f z == 'Prelude.foldl' (\\z' (kx, x) -> f z' kx x) z . 'toAscList'@.
> +--
> +-- For example,
> +--
> +-- > keys = reverse . foldlWithKey (\ks k x -> k:ks) []
> +--
> +-- > let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
> +-- > foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)"
> +foldlWithKey :: (a -> Int -> b -> a) -> a -> IntMap b -> a
> +foldlWithKey f z t =
> + case t of Bin 0 m l r | m < 0 -> go (go z r) l -- put negative numbers before
> + _ -> go z t
> + where
> + go z' Nil = z'
> + go z' (Tip kx x) = f z' kx x
> + go z' (Bin _ _ l r) = go (go z' l) r
> +{-# INLINE foldlWithKey #-}
> +
> +-- | /O(n)/. A strict version of 'foldlWithKey'. Each application of the operator is
> +-- evaluated before using the result in the next application. This
> +-- function is strict in the starting value.
> +foldlWithKey' :: (a -> Int -> b -> a) -> a -> IntMap b -> a
> +foldlWithKey' f z t =
> + case t of Bin 0 m l r | m < 0 -> go (go z r) l -- put negative numbers before
> + _ -> go z t
> + where
> + STRICT_1_OF_2(go)
> + go z' Nil = z'
> + go z' (Tip kx x) = f z' kx x
> + go z' (Bin _ _ l r) = go (go z' l) r
> +{-# INLINE foldlWithKey' #-}
> +
> +{--------------------------------------------------------------------
> + List variations
> +--------------------------------------------------------------------}
> +-- | /O(n)/.
> +-- Return all elements of the map in the ascending order of their keys.
> +--
> +-- > elems (fromList [(5,"a"), (3,"b")]) == ["b","a"]
> +-- > elems empty == []
> +
> +elems :: IntMap a -> [a]
> +elems
> + = foldr (:) []
> +
> +-- | /O(n)/. Return all keys of the map in ascending order.
> +--
> +-- > keys (fromList [(5,"a"), (3,"b")]) == [3,5]
> +-- > keys empty == []
> +
> +keys :: IntMap a -> [Key]
> +keys
> + = foldrWithKey (\k _ ks -> k:ks) []
> +
> +-- | /O(n*min(n,W))/. The set of all keys of the map.
> +--
> +-- > keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5]
> +-- > keysSet empty == Data.IntSet.empty
> +
> +keysSet :: IntMap a -> IntSet.IntSet
> +keysSet m = IntSet.fromDistinctAscList (keys m)
> +
> +
> +-- | /O(n)/. Return all key\/value pairs in the map in ascending key order.
> +--
> +-- > assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
> +-- > assocs empty == []
> +
> +assocs :: IntMap a -> [(Key,a)]
> +assocs m
> + = toList m
> +
> +
> +{--------------------------------------------------------------------
> + Lists
> +--------------------------------------------------------------------}
> +-- | /O(n)/. Convert the map to a list of key\/value pairs.
> +--
> +-- > toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
> +-- > toList empty == []
> +
> +toList :: IntMap a -> [(Key,a)]
> +toList
> + = foldrWithKey (\k x xs -> (k,x):xs) []
> +
> +-- | /O(n)/. Convert the map to a list of key\/value pairs where the
> +-- keys are in ascending order.
> +--
> +-- > toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
> +
> +toAscList :: IntMap a -> [(Key,a)]
> +toAscList t
> + = -- NOTE: the following algorithm only works for big-endian trees
> + let (pos,neg) = span (\(k,_) -> k >=0) (foldrWithKey (\k x xs -> (k,x):xs) [] t) in neg ++ pos
> +
> +-- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs.
> +--
> +-- > fromList [] == empty
> +-- > fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")]
> +-- > fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")]
> +
> +fromList :: [(Key,a)] -> IntMap a
> +fromList xs
> + = foldlStrict ins empty xs
> + where
> + ins t (k,x) = insert k x t
> +
> +-- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
> +--
> +-- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")]
> +-- > fromListWith (++) [] == empty
> +
> +fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
> +fromListWith f xs
> + = fromListWithKey (\_ x y -> f x y) xs
> +
> +-- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
> +--
> +-- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")]
> +-- > fromListWith (++) [] == empty
> +
> +fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
> +fromListWithKey f xs
> + = foldlStrict ins empty xs
> + where
> + ins t (k,x) = insertWithKey f k x t
> +
> +-- | /O(n)/. Build a map from a list of key\/value pairs where
> +-- the keys are in ascending order.
> +--
> +-- > fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
> +-- > fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")]
> +
> +fromAscList :: [(Key,a)] -> IntMap a
> +fromAscList xs
> + = fromAscListWithKey (\_ x _ -> x) xs
> +
> +-- | /O(n)/. Build a map from a list of key\/value pairs where
> +-- the keys are in ascending order, with a combining function on equal keys.
> +-- /The precondition (input list is ascending) is not checked./
> +--
> +-- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]
> +
> +fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
> +fromAscListWith f xs
> + = fromAscListWithKey (\_ x y -> f x y) xs
> +
> +-- | /O(n)/. Build a map from a list of key\/value pairs where
> +-- the keys are in ascending order, with a combining function on equal keys.
> +-- /The precondition (input list is ascending) is not checked./
> +--
> +-- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]
> +
> +fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
> +fromAscListWithKey _ [] = Nil
> +fromAscListWithKey f (x0 : xs0) = fromDistinctAscList (combineEq x0 xs0)
> + where
> + -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs]
> + combineEq z [] = [z]
> + combineEq z@(kz,zz) (x@(kx,xx):xs)
> + | kx==kz = let yy = f kx xx zz in combineEq (kx,yy) xs
> + | otherwise = z:combineEq x xs
> +
> +-- | /O(n)/. Build a map from a list of key\/value pairs where
> +-- the keys are in ascending order and all distinct.
> +-- /The precondition (input list is strictly ascending) is not checked./
> +--
> +-- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
> +
> +#ifdef __GLASGOW_HASKELL__
> +fromDistinctAscList :: forall a. [(Key,a)] -> IntMap a
> +#else
> +fromDistinctAscList :: [(Key,a)] -> IntMap a
> +#endif
> +fromDistinctAscList [] = Nil
> +fromDistinctAscList (z0 : zs0) = work z0 zs0 Nada
> + where
> + work (kx,vx) [] stk = finish kx (Tip kx vx) stk
> + work (kx,vx) (z@(kz,_):zs) stk = reduce z zs (branchMask kx kz) kx (Tip kx vx) stk
> +
> +#ifdef __GLASGOW_HASKELL__
> + reduce :: (Key,a) -> [(Key,a)] -> Mask -> Prefix -> IntMap a -> Stack a -> IntMap a
> +#endif
> + reduce z zs _ px tx Nada = work z zs (Push px tx Nada)
> + reduce z zs m px tx stk@(Push py ty stk') =
> + let mxy = branchMask px py
> + pxy = mask px mxy
> + in if shorter m mxy
> + then reduce z zs m pxy (Bin pxy mxy ty tx) stk'
> + else work z zs (Push px tx stk)
> +
> + finish _ t Nada = t
> + finish px tx (Push py ty stk) = finish p (join py ty px tx) stk
> + where m = branchMask px py
> + p = mask px m
> +
> +data Stack a = Push {-# UNPACK #-} !Prefix !(IntMap a) !(Stack a) | Nada
> +
> +
> +{--------------------------------------------------------------------
> + Eq
> +--------------------------------------------------------------------}
> +instance Eq a => Eq (IntMap a) where
> + t1 == t2 = equal t1 t2
> + t1 /= t2 = nequal t1 t2
> +
> +equal :: Eq a => IntMap a -> IntMap a -> Bool
> +equal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
> + = (m1 == m2) && (p1 == p2) && (equal l1 l2) && (equal r1 r2)
> +equal (Tip kx x) (Tip ky y)
> + = (kx == ky) && (x==y)
> +equal Nil Nil = True
> +equal _ _ = False
> +
> +nequal :: Eq a => IntMap a -> IntMap a -> Bool
> +nequal (Bin p1 m1 l1 r1) (Bin p2 m2 l2 r2)
> + = (m1 /= m2) || (p1 /= p2) || (nequal l1 l2) || (nequal r1 r2)
> +nequal (Tip kx x) (Tip ky y)
> + = (kx /= ky) || (x/=y)
> +nequal Nil Nil = False
> +nequal _ _ = True
> +
> +{--------------------------------------------------------------------
> + Ord
> +--------------------------------------------------------------------}
> +
> +instance Ord a => Ord (IntMap a) where
> + compare m1 m2 = compare (toList m1) (toList m2)
> +
> +{--------------------------------------------------------------------
> + Functor
> +--------------------------------------------------------------------}
> +
> +instance Functor IntMap where
> + fmap = map
> +
> +{--------------------------------------------------------------------
> + Show
> +--------------------------------------------------------------------}
> +
> +instance Show a => Show (IntMap a) where
> + showsPrec d m = showParen (d > 10) $
> + showString "fromList " . shows (toList m)
> +
> +{-
> +XXX unused code
> +
> +showMap :: (Show a) => [(Key,a)] -> ShowS
> +showMap []
> + = showString "{}"
> +showMap (x:xs)
> + = showChar '{' . showElem x . showTail xs
> + where
> + showTail [] = showChar '}'
> + showTail (x':xs') = showChar ',' . showElem x' . showTail xs'
> +
> + showElem (k,v) = shows k . showString ":=" . shows v
> +-}
> +
> +{--------------------------------------------------------------------
> + Read
> +--------------------------------------------------------------------}
> +instance (Read e) => Read (IntMap e) where
> +#ifdef __GLASGOW_HASKELL__
> + readPrec = parens $ prec 10 $ do
> + Ident "fromList" <- lexP
> + xs <- readPrec
> + return (fromList xs)
> +
> + readListPrec = readListPrecDefault
> +#else
> + readsPrec p = readParen (p > 10) $ \ r -> do
> + ("fromList",s) <- lex r
> + (xs,t) <- reads s
> + return (fromList xs,t)
> +#endif
> +
> +{--------------------------------------------------------------------
> + Typeable
> +--------------------------------------------------------------------}
> +
> +#include "Typeable.h"
> +INSTANCE_TYPEABLE1(IntMap,intMapTc,"IntMap")
> +
> +{--------------------------------------------------------------------
> + Debugging
> +--------------------------------------------------------------------}
> +-- | /O(n)/. Show the tree that implements the map. The tree is shown
> +-- in a compressed, hanging format.
> +showTree :: Show a => IntMap a -> String
> +showTree s
> + = showTreeWith True False s
> +
> +
> +{- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
> + the tree that implements the map. If @hang@ is
> + 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
> + @wide@ is 'True', an extra wide version is shown.
> +-}
> +showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
> +showTreeWith hang wide t
> + | hang = (showsTreeHang wide [] t) ""
> + | otherwise = (showsTree wide [] [] t) ""
> +
> +showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS
> +showsTree wide lbars rbars t
> + = case t of
> + Bin p m l r
> + -> showsTree wide (withBar rbars) (withEmpty rbars) r .
> + showWide wide rbars .
> + showsBars lbars . showString (showBin p m) . showString "\n" .
> + showWide wide lbars .
> + showsTree wide (withEmpty lbars) (withBar lbars) l
> + Tip k x
> + -> showsBars lbars . showString " " . shows k . showString ":=" . shows x . showString "\n"
> + Nil -> showsBars lbars . showString "|\n"
> +
> +showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS
> +showsTreeHang wide bars t
> + = case t of
> + Bin p m l r
> + -> showsBars bars . showString (showBin p m) . showString "\n" .
> + showWide wide bars .
> + showsTreeHang wide (withBar bars) l .
> + showWide wide bars .
> + showsTreeHang wide (withEmpty bars) r
> + Tip k x
> + -> showsBars bars . showString " " . shows k . showString ":=" . shows x . showString "\n"
> + Nil -> showsBars bars . showString "|\n"
> +
> +showBin :: Prefix -> Mask -> String
> +showBin _ _
> + = "*" -- ++ show (p,m)
> +
> +showWide :: Bool -> [String] -> String -> String
> +showWide wide bars
> + | wide = showString (concat (reverse bars)) . showString "|\n"
> + | otherwise = id
> +
> +showsBars :: [String] -> ShowS
> +showsBars bars
> + = case bars of
> + [] -> id
> + _ -> showString (concat (reverse (tail bars))) . showString node
> +
> +node :: String
> +node = "+--"
> +
> +withBar, withEmpty :: [String] -> [String]
> +withBar bars = "| ":bars
> +withEmpty bars = " ":bars
> diff --git a/Data/IntMap/Strict.hs b/Data/IntMap/Strict.hs
> new file mode 100644
> index 0000000..4946319
> --- /dev/null
> +++ b/Data/IntMap/Strict.hs
> @@ -0,0 +1,883 @@
> +{-# LANGUAGE CPP, NoBangPatterns, MagicHash, ScopedTypeVariables #-}
> +-----------------------------------------------------------------------------
> +-- |
> +-- Module : Data.IntMap.Strict
> +-- Copyright : (c) Daan Leijen 2002
> +-- (c) Andriy Palamarchuk 2008
> +-- License : BSD-style
> +-- Maintainer : libraries at haskell.org
> +-- Stability : provisional
> +-- Portability : portable
> +--
> +-- An efficient implementation of maps from integer keys to strict
> +-- values.
> +--
> +-- Since many function names (but not the type name) clash with
> +-- "Prelude" names, this module is usually imported @qualified@, e.g.
> +--
> +-- > import Data.IntMap (IntMap)
> +-- > import qualified Data.IntMap as IntMap
> +--
> +-- The implementation is based on /big-endian patricia trees/. This data
> +-- structure performs especially well on binary operations like 'union'
> +-- and 'intersection'. However, my benchmarks show that it is also
> +-- (much) faster on insertions and deletions when compared to a generic
> +-- size-balanced map implementation (see "Data.Map").
> +--
> +-- * Chris Okasaki and Andy Gill, \"/Fast Mergeable Integer Maps/\",
> +-- Workshop on ML, September 1998, pages 77-86,
> +-- <http://citeseer.ist.psu.edu/okasaki98fast.html>
> +--
> +-- * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve
> +-- Information Coded In Alphanumeric/\", Journal of the ACM, 15(4),
> +-- October 1968, pages 514-534.
> +--
> +-- Operation comments contain the operation time complexity in
> +-- the Big-O notation <http://en.wikipedia.org/wiki/Big_O_notation>.
> +-- Many operations have a worst-case complexity of /O(min(n,W))/.
> +-- This means that the operation can become linear in the number of
> +-- elements with a maximum of /W/ -- the number of bits in an 'Int'
> +-- (32 or 64).
> +--
> +-- Valid instances that work properly on strict maps are 'Foldable',
> +-- 'Monoid', 'Data', 'Eq', 'Ord', 'Show', 'Read' and 'Typeable'.
> +-- Notably, you cannot define strict versions of 'Functor' and
> +-- 'Traversable', so if they are used on strict maps, the resulting
> +-- maps will be lazy.
> +-----------------------------------------------------------------------------
> +
> +module Data.IntMap.Strict (
> + -- * Map type
> +#if !defined(TESTING)
> + IntMap, Key -- instance Eq,Show
> +#else
> + IntMap(..), Key -- instance Eq,Show
> +#endif
> +
> + -- * Operators
> + , (!), (\\)
> +
> + -- * Query
> + , null
> + , size
> + , member
> + , notMember
> + , lookup
> + , findWithDefault
> +
> + -- * Construction
> + , empty
> + , singleton
> +
> + -- ** Insertion
> + , insert
> + , insertWith
> + , insertWithKey
> + , insertLookupWithKey
> +
> + -- ** Delete\/Update
> + , delete
> + , adjust
> + , adjustWithKey
> + , update
> + , updateWithKey
> + , updateLookupWithKey
> + , alter
> +
> + -- * Combine
> +
> + -- ** Union
> + , union
> + , unionWith
> + , unionWithKey
> + , unions
> + , unionsWith
> +
> + -- ** Difference
> + , difference
> + , differenceWith
> + , differenceWithKey
> +
> + -- ** Intersection
> + , intersection
> + , intersectionWith
> + , intersectionWithKey
> +
> + -- * Traversal
> + -- ** Map
> + , map
> + , mapWithKey
> + , mapAccum
> + , mapAccumWithKey
> + , mapAccumRWithKey
> +
> + -- * Folds
> + , foldr
> + , foldl
> + , foldrWithKey
> + , foldlWithKey
> + -- ** Strict folds
> + , foldr'
> + , foldl'
> + , foldrWithKey'
> + , foldlWithKey'
> +
> + -- * Conversion
> + , elems
> + , keys
> + , keysSet
> + , assocs
> +
> + -- ** Lists
> + , toList
> + , fromList
> + , fromListWith
> + , fromListWithKey
> +
> + -- ** Ordered lists
> + , toAscList
> + , fromAscList
> + , fromAscListWith
> + , fromAscListWithKey
> + , fromDistinctAscList
> +
> + -- * Filter
> + , filter
> + , filterWithKey
> + , partition
> + , partitionWithKey
> +
> + , mapMaybe
> + , mapMaybeWithKey
> + , mapEither
> + , mapEitherWithKey
> +
> + , split
> + , splitLookup
> +
> + -- * Submap
> + , isSubmapOf, isSubmapOfBy
> + , isProperSubmapOf, isProperSubmapOfBy
> +
> + -- * Min\/Max
> + , findMin
> + , findMax
> + , deleteMin
> + , deleteMax
> + , deleteFindMin
> + , deleteFindMax
> + , updateMin
> + , updateMax
> + , updateMinWithKey
> + , updateMaxWithKey
> + , minView
> + , maxView
> + , minViewWithKey
> + , maxViewWithKey
> +
> + -- * Debugging
> + , showTree
> + , showTreeWith
> + ) where
> +
> +import Prelude hiding (lookup,map,filter,foldr,foldl,null)
> +
> +import Data.IntMap.Common
> +import Data.IntMap.Lazy hiding
> + ( singleton
> + , insert
> + , insertWith
> + , insertWithKey
> + , insertLookupWithKey
> + , adjust
> + , adjustWithKey
> + , update
> + , updateWithKey
> + , updateLookupWithKey
> + , alter
> + , unionsWith
> + , unionWith
> + , unionWithKey
> + , differenceWith
> + , differenceWithKey
> + , intersectionWith
> + , intersectionWithKey
> + , updateMinWithKey
> + , updateMaxWithKey
> + , updateMax
> + , updateMin
> + , map
> + , mapWithKey
> + , mapAccum
> + , mapAccumWithKey
> + , mapAccumRWithKey
> + , mapMaybe
> + , mapMaybeWithKey
> + , mapEither
> + , mapEitherWithKey
> + , fromList
> + , fromListWith
> + , fromListWithKey
> + , fromAscList
> + , fromAscListWith
> + , fromAscListWithKey
> + , fromDistinctAscList
> + )
> +
> +
> +{--------------------------------------------------------------------
> + Construction
> +--------------------------------------------------------------------}
> +-- | /O(1)/. A map of one element.
> +--
> +-- > singleton 1 'a' == fromList [(1, 'a')]
> +-- > size (singleton 1 'a') == 1
> +
> +singleton :: Key -> a -> IntMap a
> +singleton k x
> + = x `seq` Tip k x
> +
> +{--------------------------------------------------------------------
> + Insert
> +--------------------------------------------------------------------}
> +-- | /O(min(n,W))/. Insert a new key\/value pair in the map.
> +-- If the key is already present in the map, the associated value is
> +-- replaced with the supplied value, i.e. 'insert' is equivalent to
> +-- @'insertWith' 'const'@.
> +--
> +-- > insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')]
> +-- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')]
> +-- > insert 5 'x' empty == singleton 5 'x'
> +
> +insert :: Key -> a -> IntMap a -> IntMap a
> +insert k x t = k `seq` x `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> join k (Tip k x) p t
> + | zero k m -> Bin p m (insert k x l) r
> + | otherwise -> Bin p m l (insert k x r)
> + Tip ky _
> + | k==ky -> Tip k x
> + | otherwise -> join k (Tip k x) ky t
> + Nil -> Tip k x
> +
> +-- right-biased insertion, used by 'union'
> +-- | /O(min(n,W))/. Insert with a combining function.
> +-- @'insertWith' f key value mp@
> +-- will insert the pair (key, value) into @mp@ if key does
> +-- not exist in the map. If the key does exist, the function will
> +-- insert @f new_value old_value at .
> +--
> +-- > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")]
> +-- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
> +-- > insertWith (++) 5 "xxx" empty == singleton 5 "xxx"
> +
> +insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
> +insertWith f k x t
> + = insertWithKey (\_ x' y' -> f x' y') k x t
> +
> +-- | /O(min(n,W))/. Insert with a combining function.
> +-- @'insertWithKey' f key value mp@
> +-- will insert the pair (key, value) into @mp@ if key does
> +-- not exist in the map. If the key does exist, the function will
> +-- insert @f key new_value old_value at .
> +--
> +-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
> +-- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")]
> +-- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
> +-- > insertWithKey f 5 "xxx" empty == singleton 5 "xxx"
> +--
> +-- If the key exists in the map, this function is lazy in @x@ but strict
> +-- in the result of @f at .
> +
> +insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
> +insertWithKey f k x t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> x `seq` join k (Tip k x) p t
> + | zero k m -> Bin p m (insertWithKey f k x l) r
> + | otherwise -> Bin p m l (insertWithKey f k x r)
> + Tip ky y
> + | k==ky -> Tip k $! f k x y
> + | otherwise -> x `seq` join k (Tip k x) ky t
> + Nil -> x `seq` Tip k x
> +
> +-- | /O(min(n,W))/. The expression (@'insertLookupWithKey' f k x map@)
> +-- is a pair where the first element is equal to (@'lookup' k map@)
> +-- and the second element equal to (@'insertWithKey' f k x map@).
> +--
> +-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
> +-- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
> +-- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "xxx")])
> +-- > insertLookupWithKey f 5 "xxx" empty == (Nothing, singleton 5 "xxx")
> +--
> +-- This is how to define @insertLookup@ using @insertLookupWithKey@:
> +--
> +-- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t
> +-- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")])
> +-- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a"), (7, "x")])
> +
> +insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
> +insertLookupWithKey f k x t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> x `seq` (Nothing `strictPair` join k (Tip k x) p t)
> + | zero k m -> let (found,l') = insertLookupWithKey f k x l in (found `strictPair` Bin p m l' r)
> + | otherwise -> let (found,r') = insertLookupWithKey f k x r in (found `strictPair` Bin p m l r')
> + Tip ky y
> + | k==ky -> (Just y `strictPair` (Tip k $! f k x y))
> + | otherwise -> x `seq` (Nothing `strictPair` join k (Tip k x) ky t)
> + Nil -> x `seq` (Nothing `strictPair` Tip k x)
> +
> +
> +{--------------------------------------------------------------------
> + Deletion
> + [delete] is the inlined version of [deleteWith (\k x -> Nothing)]
> +--------------------------------------------------------------------}
> +-- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
> +-- a member of the map, the original map is returned.
> +--
> +-- > adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
> +-- > adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> +-- > adjust ("new " ++) 7 empty == empty
> +
> +adjust :: (a -> a) -> Key -> IntMap a -> IntMap a
> +adjust f k m
> + = adjustWithKey (\_ x -> f x) k m
> +
> +-- | /O(min(n,W))/. Adjust a value at a specific key. When the key is not
> +-- a member of the map, the original map is returned.
> +--
> +-- > let f key x = (show key) ++ ":new " ++ x
> +-- > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
> +-- > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> +-- > adjustWithKey f 7 empty == empty
> +
> +adjustWithKey :: (Key -> a -> a) -> Key -> IntMap a -> IntMap a
> +adjustWithKey f
> + = updateWithKey (\k' x -> Just (f k' x))
> +
> +-- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
> +-- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
> +-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y at .
> +--
> +-- > let f x = if x == "a" then Just "new a" else Nothing
> +-- > update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
> +-- > update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> +-- > update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> +
> +update :: (a -> Maybe a) -> Key -> IntMap a -> IntMap a
> +update f
> + = updateWithKey (\_ x -> f x)
> +
> +-- | /O(min(n,W))/. The expression (@'update' f k map@) updates the value @x@
> +-- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is
> +-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y at .
> +--
> +-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
> +-- > updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
> +-- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
> +-- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> +
> +updateWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
> +updateWithKey f k t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> t
> + | zero k m -> bin p m (updateWithKey f k l) r
> + | otherwise -> bin p m l (updateWithKey f k r)
> + Tip ky y
> + | k==ky -> case (f k y) of
> + Just y' -> y' `seq` Tip ky y'
> + Nothing -> Nil
> + | otherwise -> t
> + Nil -> Nil
> +
> +-- | /O(min(n,W))/. Lookup and update.
> +-- The function returns original value, if it is updated.
> +-- This is different behavior than 'Data.Map.updateLookupWithKey'.
> +-- Returns the original key value if the map entry is deleted.
> +--
> +-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
> +-- > updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:new a")])
> +-- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing, fromList [(3, "b"), (5, "a")])
> +-- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a")
> +
> +updateLookupWithKey :: (Key -> a -> Maybe a) -> Key -> IntMap a -> (Maybe a,IntMap a)
> +updateLookupWithKey f k t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> (Nothing, t)
> + | zero k m -> let (found,l') = updateLookupWithKey f k l in (found `strictPair` bin p m l' r)
> + | otherwise -> let (found,r') = updateLookupWithKey f k r in (found `strictPair` bin p m l r')
> + Tip ky y
> + | k==ky -> case (f k y) of
> + Just y' -> y' `seq` (Just y `strictPair` Tip ky y')
> + Nothing -> (Just y, Nil)
> + | otherwise -> (Nothing,t)
> + Nil -> (Nothing,Nil)
> +
> +
> +
> +-- | /O(log n)/. The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof.
> +-- 'alter' can be used to insert, delete, or update a value in an 'IntMap'.
> +-- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@.
> +alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap a
> +alter f k t = k `seq`
> + case t of
> + Bin p m l r
> + | nomatch k p m -> case f Nothing of
> + Nothing -> t
> + Just x -> x `seq` join k (Tip k x) p t
> + | zero k m -> bin p m (alter f k l) r
> + | otherwise -> bin p m l (alter f k r)
> + Tip ky y
> + | k==ky -> case f (Just y) of
> + Just x -> x `seq` Tip ky x
> + Nothing -> Nil
> + | otherwise -> case f Nothing of
> + Just x -> x `seq` join k (Tip k x) ky t
> + Nothing -> t
> + Nil -> case f Nothing of
> + Just x -> x `seq` Tip k x
> + Nothing -> Nil
> +
> +
> +{--------------------------------------------------------------------
> + Union
> +--------------------------------------------------------------------}
> +-- | The union of a list of maps, with a combining operation.
> +--
> +-- > unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
> +-- > == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")]
> +
> +unionsWith :: (a->a->a) -> [IntMap a] -> IntMap a
> +unionsWith f ts
> + = foldlStrict (unionWith f) empty ts
> +
> +-- | /O(n+m)/. The union with a combining function.
> +--
> +-- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]
> +
> +unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
> +unionWith f m1 m2
> + = unionWithKey (\_ x y -> f x y) m1 m2
> +
> +-- | /O(n+m)/. The union with a combining function.
> +--
> +-- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value
> +-- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")]
> +
> +unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
> +unionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> + | shorter m1 m2 = union1
> + | shorter m2 m1 = union2
> + | p1 == p2 = Bin p1 m1 (unionWithKey f l1 l2) (unionWithKey f r1 r2)
> + | otherwise = join p1 t1 p2 t2
> + where
> + union1 | nomatch p2 p1 m1 = join p1 t1 p2 t2
> + | zero p2 m1 = Bin p1 m1 (unionWithKey f l1 t2) r1
> + | otherwise = Bin p1 m1 l1 (unionWithKey f r1 t2)
> +
> + union2 | nomatch p1 p2 m2 = join p1 t1 p2 t2
> + | zero p1 m2 = Bin p2 m2 (unionWithKey f t1 l2) r2
> + | otherwise = Bin p2 m2 l2 (unionWithKey f t1 r2)
> +
> +unionWithKey f (Tip k x) t = insertWithKey f k x t
> +unionWithKey f t (Tip k x) = insertWithKey (\k' x' y' -> f k' y' x') k x t -- right bias
> +unionWithKey _ Nil t = t
> +unionWithKey _ t Nil = t
> +
> +{--------------------------------------------------------------------
> + Difference
> +--------------------------------------------------------------------}
> +
> +-- | /O(n+m)/. Difference with a combining function.
> +--
> +-- > let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing
> +-- > differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")])
> +-- > == singleton 3 "b:B"
> +
> +differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
> +differenceWith f m1 m2
> + = differenceWithKey (\_ x y -> f x y) m1 m2
> +
> +-- | /O(n+m)/. Difference with a combining function. When two equal keys are
> +-- encountered, the combining function is applied to the key and both values.
> +-- If it returns 'Nothing', the element is discarded (proper set difference).
> +-- If it returns (@'Just' y@), the element is updated with a new value @y at .
> +--
> +-- > let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing
> +-- > differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")])
> +-- > == singleton 3 "3:b|B"
> +
> +differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
> +differenceWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> + | shorter m1 m2 = difference1
> + | shorter m2 m1 = difference2
> + | p1 == p2 = bin p1 m1 (differenceWithKey f l1 l2) (differenceWithKey f r1 r2)
> + | otherwise = t1
> + where
> + difference1 | nomatch p2 p1 m1 = t1
> + | zero p2 m1 = bin p1 m1 (differenceWithKey f l1 t2) r1
> + | otherwise = bin p1 m1 l1 (differenceWithKey f r1 t2)
> +
> + difference2 | nomatch p1 p2 m2 = t1
> + | zero p1 m2 = differenceWithKey f t1 l2
> + | otherwise = differenceWithKey f t1 r2
> +
> +differenceWithKey f t1@(Tip k x) t2
> + = case lookup k t2 of
> + Just y -> case f k x y of
> + Just y' -> y' `seq` Tip k y'
> + Nothing -> Nil
> + Nothing -> t1
> +
> +differenceWithKey _ Nil _ = Nil
> +differenceWithKey f t (Tip k y) = updateWithKey (\k' x -> f k' x y) k t
> +differenceWithKey _ t Nil = t
> +
> +
> +{--------------------------------------------------------------------
> + Intersection
> +--------------------------------------------------------------------}
> +
> +-- | /O(n+m)/. The intersection with a combining function.
> +--
> +-- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA"
> +
> +intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
> +intersectionWith f m1 m2
> + = intersectionWithKey (\_ x y -> f x y) m1 m2
> +
> +-- | /O(n+m)/. The intersection with a combining function.
> +--
> +-- > let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar
> +-- > intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A"
> +
> +intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
> +intersectionWithKey f t1@(Bin p1 m1 l1 r1) t2@(Bin p2 m2 l2 r2)
> + | shorter m1 m2 = intersection1
> + | shorter m2 m1 = intersection2
> + | p1 == p2 = bin p1 m1 (intersectionWithKey f l1 l2) (intersectionWithKey f r1 r2)
> + | otherwise = Nil
> + where
> + intersection1 | nomatch p2 p1 m1 = Nil
> + | zero p2 m1 = intersectionWithKey f l1 t2
> + | otherwise = intersectionWithKey f r1 t2
> +
> + intersection2 | nomatch p1 p2 m2 = Nil
> + | zero p1 m2 = intersectionWithKey f t1 l2
> + | otherwise = intersectionWithKey f t1 r2
> +
> +intersectionWithKey f (Tip k x) t2
> + = case lookup k t2 of
> + Just y -> Tip k $! f k x y
> + Nothing -> Nil
> +intersectionWithKey f t1 (Tip k y)
> + = case lookup k t1 of
> + Just x -> Tip k $! f k x y
> + Nothing -> Nil
> +intersectionWithKey _ Nil _ = Nil
> +intersectionWithKey _ _ Nil = Nil
> +
> +
> +{--------------------------------------------------------------------
> + Min\/Max
> +--------------------------------------------------------------------}
> +
> +-- | /O(log n)/. Update the value at the minimal key.
> +--
> +-- > updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")]
> +-- > updateMinWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> +
> +updateMinWithKey :: (Key -> a -> a) -> IntMap a -> IntMap a
> +updateMinWithKey f t
> + = case t of
> + Bin p m l r | m < 0 -> let t' = updateMinWithKeyUnsigned f r in Bin p m l t'
> + Bin p m l r -> let t' = updateMinWithKeyUnsigned f l in Bin p m t' r
> + Tip k y -> Tip k $! f k y
> + Nil -> error "maxView: empty map has no maximal element"
> +
> +updateMinWithKeyUnsigned :: (Key -> a -> a) -> IntMap a -> IntMap a
> +updateMinWithKeyUnsigned f t
> + = case t of
> + Bin p m l r -> let t' = updateMinWithKeyUnsigned f l in Bin p m t' r
> + Tip k y -> Tip k $! f k y
> + Nil -> error "updateMinWithKeyUnsigned Nil"
> +
> +-- | /O(log n)/. Update the value at the maximal key.
> +--
> +-- > updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")]
> +-- > updateMaxWithKey (\ _ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
> +
> +updateMaxWithKey :: (Key -> a -> a) -> IntMap a -> IntMap a
> +updateMaxWithKey f t
> + = case t of
> + Bin p m l r | m < 0 -> let t' = updateMaxWithKeyUnsigned f l in Bin p m t' r
> + Bin p m l r -> let t' = updateMaxWithKeyUnsigned f r in Bin p m l t'
> + Tip k y -> Tip k $! f k y
> + Nil -> error "maxView: empty map has no maximal element"
> +
> +updateMaxWithKeyUnsigned :: (Key -> a -> a) -> IntMap a -> IntMap a
> +updateMaxWithKeyUnsigned f t
> + = case t of
> + Bin p m l r -> let t' = updateMaxWithKeyUnsigned f r in Bin p m l t'
> + Tip k y -> Tip k $! f k y
> + Nil -> error "updateMaxWithKeyUnsigned Nil"
> +
> +
> +-- | /O(log n)/. Update the value at the maximal key.
> +--
> +-- > updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")]
> +-- > updateMax (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
> +
> +updateMax :: (a -> a) -> IntMap a -> IntMap a
> +updateMax f = updateMaxWithKey (const f)
> +
> +-- | /O(log n)/. Update the value at the minimal key.
> +--
> +-- > updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")]
> +-- > updateMin (\ _ -> Nothing) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
> +
> +updateMin :: (a -> a) -> IntMap a -> IntMap a
> +updateMin f = updateMinWithKey (const f)
> +
> +
> +{--------------------------------------------------------------------
> + Mapping
> +--------------------------------------------------------------------}
> +-- | /O(n)/. Map a function over all values in the map.
> +--
> +-- > map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]
> +
> +map :: (a -> b) -> IntMap a -> IntMap b
> +map f = mapWithKey (\_ x -> f x)
> +
> +-- | /O(n)/. Map a function over all values in the map.
> +--
> +-- > let f key x = (show key) ++ ":" ++ x
> +-- > mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")]
> +
> +mapWithKey :: (Key -> a -> b) -> IntMap a -> IntMap b
> +mapWithKey f t
> + = case t of
> + Bin p m l r -> Bin p m (mapWithKey f l) (mapWithKey f r)
> + Tip k x -> Tip k $! f k x
> + Nil -> Nil
> +
> +-- | /O(n)/. The function @'mapAccum'@ threads an accumulating
> +-- argument through the map in ascending order of keys.
> +--
> +-- > let f a b = (a ++ b, b ++ "X")
> +-- > mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")])
> +
> +mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> +mapAccum f = mapAccumWithKey (\a' _ x -> f a' x)
> +
> +-- | /O(n)/. The function @'mapAccumWithKey'@ threads an accumulating
> +-- argument through the map in ascending order of keys.
> +--
> +-- > let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X")
> +-- > mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")])
> +
> +mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> +mapAccumWithKey f a t
> + = mapAccumL f a t
> +
> +-- | /O(n)/. The function @'mapAccumL'@ threads an accumulating
> +-- argument through the map in ascending order of keys. Strict in
> +-- the accumulating argument and the both elements of the
> +-- result of the function.
> +mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> +mapAccumL f a t
> + = case t of
> + Bin p m l r -> let (a1,l') = mapAccumL f a l
> + (a2,r') = mapAccumL f a1 r
> + in (a2 `strictPair` Bin p m l' r')
> + Tip k x -> let (a',x') = f a k x in x' `seq` (a' `strictPair` Tip k x')
> + Nil -> (a `strictPair` Nil)
> +
> +-- | /O(n)/. The function @'mapAccumR'@ threads an accumulating
> +-- argument through the map in descending order of keys.
> +mapAccumRWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
> +mapAccumRWithKey f a t
> + = case t of
> + Bin p m l r -> let (a1,r') = mapAccumRWithKey f a r
> + (a2,l') = mapAccumRWithKey f a1 l
> + in (a2 `strictPair` Bin p m l' r')
> + Tip k x -> let (a',x') = f a k x in x' `seq` (a' `strictPair` Tip k x')
> + Nil -> (a `strictPair` Nil)
> +
> +{--------------------------------------------------------------------
> + Filter
> +--------------------------------------------------------------------}
> +-- | /O(n)/. Map values and collect the 'Just' results.
> +--
> +-- > let f x = if x == "a" then Just "new a" else Nothing
> +-- > mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a"
> +
> +mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b
> +mapMaybe f = mapMaybeWithKey (\_ x -> f x)
> +
> +-- | /O(n)/. Map keys\/values and collect the 'Just' results.
> +--
> +-- > let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing
> +-- > mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3"
> +
> +mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b
> +mapMaybeWithKey f (Bin p m l r)
> + = bin p m (mapMaybeWithKey f l) (mapMaybeWithKey f r)
> +mapMaybeWithKey f (Tip k x) = case f k x of
> + Just y -> y `seq` Tip k y
> + Nothing -> Nil
> +mapMaybeWithKey _ Nil = Nil
> +
> +-- | /O(n)/. Map values and separate the 'Left' and 'Right' results.
> +--
> +-- > let f a = if a < "c" then Left a else Right a
> +-- > mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> +-- > == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")])
> +-- >
> +-- > mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> +-- > == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> +
> +mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
> +mapEither f m
> + = mapEitherWithKey (\_ x -> f x) m
> +
> +-- | /O(n)/. Map keys\/values and separate the 'Left' and 'Right' results.
> +--
> +-- > let f k a = if k < 5 then Left (k * 2) else Right (a ++ a)
> +-- > mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> +-- > == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")])
> +-- >
> +-- > mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
> +-- > == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")])
> +
> +mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
> +mapEitherWithKey f (Bin p m l r)
> + = (bin p m l1 r1, bin p m l2 r2)
> + where
> + (l1,l2) = mapEitherWithKey f l
> + (r1,r2) = mapEitherWithKey f r
> +mapEitherWithKey f (Tip k x) = case f k x of
> + Left y -> y `seq` (Tip k y, Nil)
> + Right z -> z `seq` (Nil, Tip k z)
> +mapEitherWithKey _ Nil = (Nil, Nil)
> +
> +
> +{--------------------------------------------------------------------
> + Lists
> +--------------------------------------------------------------------}
> +-- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs.
> +--
> +-- > fromList [] == empty
> +-- > fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")]
> +-- > fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")]
> +
> +fromList :: [(Key,a)] -> IntMap a
> +fromList xs
> + = foldlStrict ins empty xs
> + where
> + ins t (k,x) = insert k x t
> +
> +-- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
> +--
> +-- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")]
> +-- > fromListWith (++) [] == empty
> +
> +fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
> +fromListWith f xs
> + = fromListWithKey (\_ x y -> f x y) xs
> +
> +-- | /O(n*min(n,W))/. Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
> +--
> +-- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"a")] == fromList [(3, "ab"), (5, "aba")]
> +-- > fromListWith (++) [] == empty
> +
> +fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
> +fromListWithKey f xs
> + = foldlStrict ins empty xs
> + where
> + ins t (k,x) = insertWithKey f k x t
> +
> +-- | /O(n)/. Build a map from a list of key\/value pairs where
> +-- the keys are in ascending order.
> +--
> +-- > fromAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
> +-- > fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")]
> +
> +fromAscList :: [(Key,a)] -> IntMap a
> +fromAscList xs
> + = fromAscListWithKey (\_ x _ -> x) xs
> +
> +-- | /O(n)/. Build a map from a list of key\/value pairs where
> +-- the keys are in ascending order, with a combining function on equal keys.
> +-- /The precondition (input list is ascending) is not checked./
> +--
> +-- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]
> +
> +fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
> +fromAscListWith f xs
> + = fromAscListWithKey (\_ x y -> f x y) xs
> +
> +-- | /O(n)/. Build a map from a list of key\/value pairs where
> +-- the keys are in ascending order, with a combining function on equal keys.
> +-- /The precondition (input list is ascending) is not checked./
> +--
> +-- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]
> +
> +fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
> +fromAscListWithKey _ [] = Nil
> +fromAscListWithKey f (x0 : xs0) = fromDistinctAscList (combineEq x0 xs0)
> + where
> + -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs]
> + combineEq z [] = [z]
> + combineEq z@(kz,zz) (x@(kx,xx):xs)
> + | kx==kz = let yy = f kx xx zz in yy `seq` combineEq (kx,yy) xs
> + | otherwise = z:combineEq x xs
> +
> +-- | /O(n)/. Build a map from a list of key\/value pairs where
> +-- the keys are in ascending order and all distinct.
> +-- /The precondition (input list is strictly ascending) is not checked./
> +--
> +-- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
> +
> +#ifdef __GLASGOW_HASKELL__
> +fromDistinctAscList :: forall a. [(Key,a)] -> IntMap a
> +#else
> +fromDistinctAscList :: [(Key,a)] -> IntMap a
> +#endif
> +fromDistinctAscList [] = Nil
> +fromDistinctAscList (z0 : zs0) = work z0 zs0 Nada
> + where
> + work (kx,vx) [] stk = vx `seq` finish kx (Tip kx vx) stk
> + work (kx,vx) (z@(kz,_):zs) stk = vx `seq` reduce z zs (branchMask kx kz) kx (Tip kx vx) stk
> +
> +#ifdef __GLASGOW_HASKELL__
> + reduce :: (Key,a) -> [(Key,a)] -> Mask -> Prefix -> IntMap a -> Stack a -> IntMap a
> +#endif
> + reduce z zs _ px tx Nada = work z zs (Push px tx Nada)
> + reduce z zs m px tx stk@(Push py ty stk') =
> + let mxy = branchMask px py
> + pxy = mask px mxy
> + in if shorter m mxy
> + then reduce z zs m pxy (Bin pxy mxy ty tx) stk'
> + else work z zs (Push px tx stk)
> +
> + finish _ t Nada = t
> + finish px tx (Push py ty stk) = finish p (join py ty px tx) stk
> + where m = branchMask px py
> + p = mask px m
> +
> +data Stack a = Push {-# UNPACK #-} !Prefix !(IntMap a) !(Stack a) | Nada
> +
> +
> +{--------------------------------------------------------------------
> + Utility
> +--------------------------------------------------------------------}
> +
> +strictPair :: a -> b -> (a, b)
> +strictPair x y = x `seq` y `seq` (x, y)
> +{-# INLINE strictPair #-}
> diff --git a/containers.cabal b/containers.cabal
> index ed339ba..a8a1cb7 100644
> --- a/containers.cabal
> +++ b/containers.cabal
> @@ -24,8 +24,12 @@ Library {
> ghc-options: -O2
> if impl(ghc>6.10)
> Ghc-Options: -fregs-graph
> + other-modules:
> + Data.IntMap.Common
> exposed-modules:
> Data.IntMap
> + Data.IntMap.Strict
> + Data.IntMap.Lazy
> Data.IntSet
> Data.Map
> Data.Set
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