    {-# LANGUAGE CPP #-}
    {-# LANGUAGE BangPatterns #-}
    {-# LANGUAGE PatternGuards #-}
    #ifdef __GLASGOW_HASKELL__
    {-# LANGUAGE DeriveLift #-}
    {-# LANGUAGE MagicHash #-}
    {-# LANGUAGE ScopedTypeVariables #-}
    {-# LANGUAGE StandaloneDeriving #-}
    {-# LANGUAGE TypeFamilies #-}
    #endif
    #if !defined(TESTING) && defined(__GLASGOW_HASKELL__)
    {-# LANGUAGE Trustworthy #-}
    #endif

    {-# OPTIONS_HADDOCK not-home #-}
    {-# OPTIONS_GHC -fno-warn-incomplete-uni-patterns #-}

    #include "containers.h"

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.IntMap.Internal
    -- Copyright   :  (c) Daan Leijen 2002
    --                (c) Andriy Palamarchuk 2008
    --                (c) wren romano 2016
    -- License     :  BSD-style
    -- Maintainer  :  libraries@haskell.org
    -- Portability :  portable
    --
    -- = WARNING
    --
    -- This module is considered __internal__.
    --
    -- The Package Versioning Policy __does not apply__.
    --
    -- The contents of this module may change __in any way whatsoever__
    -- and __without any warning__ between minor versions of this package.
    --
    -- Authors importing this module are expected to track development
    -- closely.
    --
    -- = Description
    --
    -- This defines the data structures and core (hidden) manipulations
    -- on representations.
    --
    -- @since 0.5.9
    -----------------------------------------------------------------------------

    -- [Note: INLINE bit fiddling]
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~
    -- 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.

    -- [Note: Local 'go' functions and capturing]
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    -- Care must be taken when using 'go' function which captures an argument.
    -- Sometimes (for example when the argument is passed to a data constructor,
    -- as in insert), GHC heap-allocates more than necessary. Therefore C-- code
    -- must be checked for increased allocation when creating and modifying such
    -- functions.

    -- [Note: Order of constructors]
    -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    -- 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 benchmark by circa 10%.
    --

    module Data.IntMap.Internal (
        -- * Map type
          IntMap(..), Key          -- instance Eq,Show

        -- * Operators
        , (!), (!?), (\\)

        -- * Query
        , null
        , size
        , member
        , notMember
        , lookup
        , findWithDefault
        , lookupLT
        , lookupGT
        , lookupLE
        , lookupGE
        , disjoint

        -- * Construction
        , empty
        , singleton

        -- ** Insertion
        , insert
        , insertWith
        , insertWithKey
        , insertLookupWithKey

        -- ** Delete\/Update
        , delete
        , adjust
        , adjustWithKey
        , update
        , updateWithKey
        , updateLookupWithKey
        , alter
        , alterF

        -- * Combine

        -- ** Union
        , union
        , unionWith
        , unionWithKey
        , unions
        , unionsWith

        -- ** Difference
        , difference
        , differenceWith
        , differenceWithKey

        -- ** Intersection
        , intersection
        , intersectionWith
        , intersectionWithKey

        -- ** Compose
        , compose

        -- ** General combining function
        , SimpleWhenMissing
        , SimpleWhenMatched
        , runWhenMatched
        , runWhenMissing
        , merge
        -- *** @WhenMatched@ tactics
        , zipWithMaybeMatched
        , zipWithMatched
        -- *** @WhenMissing@ tactics
        , mapMaybeMissing
        , dropMissing
        , preserveMissing
        , mapMissing
        , filterMissing

        -- ** Applicative general combining function
        , WhenMissing (..)
        , WhenMatched (..)
        , mergeA
        -- *** @WhenMatched@ tactics
        -- | The tactics described for 'merge' work for
        -- 'mergeA' as well. Furthermore, the following
        -- are available.
        , zipWithMaybeAMatched
        , zipWithAMatched
        -- *** @WhenMissing@ tactics
        -- | The tactics described for 'merge' work for
        -- 'mergeA' as well. Furthermore, the following
        -- are available.
        , traverseMaybeMissing
        , traverseMissing
        , filterAMissing

        -- ** Deprecated general combining function
        , mergeWithKey
        , mergeWithKey'

        -- * Traversal
        -- ** Map
        , map
        , mapWithKey
        , traverseWithKey
        , traverseMaybeWithKey
        , mapAccum
        , mapAccumWithKey
        , mapAccumRWithKey
        , mapKeys
        , mapKeysWith
        , mapKeysMonotonic

        -- * Folds
        , foldr
        , foldl
        , foldrWithKey
        , foldlWithKey
        , foldMapWithKey

        -- ** Strict folds
        , foldr'
        , foldl'
        , foldrWithKey'
        , foldlWithKey'

        -- * Conversion
        , elems
        , keys
        , assocs
        , keysSet
        , fromSet

        -- ** Lists
        , toList
        , fromList
        , fromListWith
        , fromListWithKey

        -- ** Ordered lists
        , toAscList
        , toDescList
        , fromAscList
        , fromAscListWith
        , fromAscListWithKey
        , fromDistinctAscList

        -- * Filter
        , filter
        , filterWithKey
        , restrictKeys
        , withoutKeys
        , partition
        , partitionWithKey

        , takeWhileAntitone
        , dropWhileAntitone
        , spanAntitone

        , mapMaybe
        , mapMaybeWithKey
        , mapEither
        , mapEitherWithKey

        , split
        , splitLookup
        , splitRoot

        -- * Submap
        , isSubmapOf, isSubmapOfBy
        , isProperSubmapOf, isProperSubmapOfBy

        -- * Min\/Max
        , lookupMin
        , lookupMax
        , findMin
        , findMax
        , deleteMin
        , deleteMax
        , deleteFindMin
        , deleteFindMax
        , updateMin
        , updateMax
        , updateMinWithKey
        , updateMaxWithKey
        , minView
        , maxView
        , minViewWithKey
        , maxViewWithKey

        -- * Debugging
        , showTree
        , showTreeWith

        -- * Internal types
        , Mask, Prefix, Nat

        -- * Utility
        , natFromInt
        , intFromNat
        , link
        , linkWithMask
        , bin
        , binCheckLeft
        , binCheckRight
        , zero
        , nomatch
        , match
        , mask
        , maskW
        , shorter
        , branchMask
        , highestBitMask

        -- * Used by "IntMap.Merge.Lazy" and "IntMap.Merge.Strict"
        , mapWhenMissing
        , mapWhenMatched
        , lmapWhenMissing
        , contramapFirstWhenMatched
        , contramapSecondWhenMatched
        , mapGentlyWhenMissing
        , mapGentlyWhenMatched
        ) where

    import Data.Functor.Identity (Identity (..))
    import Data.Semigroup (Semigroup(stimes))
    #if !(MIN_VERSION_base(4,11,0))
    import Data.Semigroup (Semigroup((<>)))
    #endif
    import Data.Semigroup (stimesIdempotentMonoid)
    import Data.Functor.Classes

    import Control.DeepSeq (NFData(rnf))
    import Data.Bits
    import qualified Data.Foldable as Foldable
    import Data.Maybe (fromMaybe)
    import Utils.Containers.Internal.Prelude hiding
      (lookup, map, filter, foldr, foldl, foldl', null)
    import Prelude ()

    import Data.IntSet.Internal (Key)
    import qualified Data.IntSet.Internal as IntSet
    import Utils.Containers.Internal.BitUtil
    import Utils.Containers.Internal.StrictPair

    #ifdef __GLASGOW_HASKELL__
    import Data.Coerce
    import Data.Data (Data(..), Constr, mkConstr, constrIndex, Fixity(Prefix),
                      DataType, mkDataType, gcast1)
    import GHC.Exts (build)
    import qualified GHC.Exts as GHCExts
    import Text.Read
    import Language.Haskell.TH.Syntax (Lift)
    -- See Note [ Template Haskell Dependencies ]
    import Language.Haskell.TH ()
    #endif
    import qualified Control.Category as Category

    -- A "Nat" is a natural machine word (an unsigned Int)
    type Nat = Word

    natFromInt :: Key -> Nat
    natFromInt :: Int -> Nat
    natFromInt = Int -> Nat
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral
    {-# INLINE natFromInt #-}

    intFromNat :: Nat -> Key
    intFromNat :: Nat -> Int
    intFromNat = Nat -> Int
    forall a b. (Integral a, Num b) => a -> b
    fromIntegral
    {-# INLINE intFromNat #-}

    {--------------------------------------------------------------------
      Types
    --------------------------------------------------------------------}

    -- | A map of integers to values @a@.

    -- See Note: Order of constructors
    data IntMap a = Bin {-# UNPACK #-} !Prefix
                        {-# UNPACK #-} !Mask
                        !(IntMap a)
                        !(IntMap a)
    -- Fields:
    --   prefix: The most significant bits shared by all keys in this Bin.
    --   mask: The switching bit to determine if a key should follow the left
    --         or right subtree of a 'Bin'.
    -- Invariant: Nil is never found as a child of Bin.
    -- Invariant: The Mask is a power of 2. It is the largest bit position at which
    --            two keys of the map differ.
    -- Invariant: Prefix is the common high-order bits that all elements share to
    --            the left of the Mask bit.
    -- Invariant: In (Bin prefix mask left right), left consists of the elements that
    --            don't have the mask bit set; right is all the elements that do.
                  | Tip {-# UNPACK #-} !Key a
                  | Nil

    type Prefix = Int
    type Mask   = Int

    -- Some stuff from "Data.IntSet.Internal", for 'restrictKeys' and
    -- 'withoutKeys' to use.
    type IntSetPrefix = Int
    type IntSetBitMap = Word

    -- | @since 0.6.6
    deriving instance Lift a => Lift (IntMap a)

    bitmapOf :: Int -> IntSetBitMap
    bitmapOf :: Int -> Nat
    bitmapOf Int
    x = Nat -> Int -> Nat
    shiftLL Nat
    1 (Int
    x Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.suffixBitMask)
    {-# INLINE bitmapOf #-}

    {--------------------------------------------------------------------
      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
    ! :: forall a. IntMap a -> Int -> a
    (!) IntMap a
    m Int
    k = Int -> IntMap a -> a
    forall a. Int -> IntMap a -> a
    find Int
    k IntMap a
    m

    -- | \(O(\min(n,W))\). Find the value at a key.
    -- Returns 'Nothing' when the element can not be found.
    --
    -- > fromList [(5,'a'), (3,'b')] !? 1 == Nothing
    -- > fromList [(5,'a'), (3,'b')] !? 5 == Just 'a'
    --
    -- @since 0.5.11

    (!?) :: IntMap a -> Key -> Maybe a
    !? :: forall a. IntMap a -> Int -> Maybe a
    (!?) IntMap a
    m Int
    k = Int -> IntMap a -> Maybe a
    forall a. Int -> IntMap a -> Maybe a
    lookup Int
    k IntMap a
    m

    -- | Same as 'difference'.
    (\\) :: IntMap a -> IntMap b -> IntMap a
    IntMap a
    m1 \\ :: forall a b. IntMap a -> IntMap b -> IntMap a
    \\ IntMap b
    m2 = IntMap a -> IntMap b -> IntMap a
    forall a b. IntMap a -> IntMap b -> IntMap a
    difference IntMap a
    m1 IntMap b
    m2

    infixl 9 !?,\\{-This comment teaches CPP correct behaviour -}

    {--------------------------------------------------------------------
      Types
    --------------------------------------------------------------------}

    instance Monoid (IntMap a) where
        mempty :: IntMap a
    mempty  = IntMap a
    forall a. IntMap a
    empty
        mconcat :: [IntMap a] -> IntMap a
    mconcat = [IntMap a] -> IntMap a
    forall (f :: * -> *) a. Foldable f => f (IntMap a) -> IntMap a
    unions
        mappend :: IntMap a -> IntMap a -> IntMap a
    mappend = IntMap a -> IntMap a -> IntMap a
    forall a. Semigroup a => a -> a -> a
    (<>)

    -- | @since 0.5.7
    instance Semigroup (IntMap a) where
        <> :: IntMap a -> IntMap a -> IntMap a
    (<>)    = IntMap a -> IntMap a -> IntMap a
    forall a. IntMap a -> IntMap a -> IntMap a
    union
        stimes :: forall b. Integral b => b -> IntMap a -> IntMap a
    stimes  = b -> IntMap a -> IntMap a
    forall b a. (Integral b, Monoid a) => b -> a -> a
    stimesIdempotentMonoid

    -- | Folds in order of increasing key.
    instance Foldable.Foldable IntMap where
      fold :: forall m. Monoid m => IntMap m -> m
    fold = IntMap m -> m
    forall m. Monoid m => IntMap m -> m
    go
        where go :: IntMap t -> t
    go IntMap t
    Nil = t
    forall a. Monoid a => a
    mempty
              go (Tip Int
    _ t
    v) = t
    v
              go (Bin Int
    _ Int
    m IntMap t
    l IntMap t
    r)
                | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = IntMap t -> t
    go IntMap t
    r t -> t -> t
    forall a. Monoid a => a -> a -> a
    `mappend` IntMap t -> t
    go IntMap t
    l
                | Bool
    otherwise = IntMap t -> t
    go IntMap t
    l t -> t -> t
    forall a. Monoid a => a -> a -> a
    `mappend` IntMap t -> t
    go IntMap t
    r
      {-# INLINABLE fold #-}
      foldr :: forall a b. (a -> b -> b) -> b -> IntMap a -> b
    foldr = (a -> b -> b) -> b -> IntMap a -> b
    forall a b. (a -> b -> b) -> b -> IntMap a -> b
    foldr
      {-# INLINE foldr #-}
      foldl :: forall b a. (b -> a -> b) -> b -> IntMap a -> b
    foldl = (b -> a -> b) -> b -> IntMap a -> b
    forall b a. (b -> a -> b) -> b -> IntMap a -> b
    foldl
      {-# INLINE foldl #-}
      foldMap :: forall m a. Monoid m => (a -> m) -> IntMap a -> m
    foldMap a -> m
    f IntMap a
    t = IntMap a -> m
    go IntMap a
    t
        where go :: IntMap a -> m
    go IntMap a
    Nil = m
    forall a. Monoid a => a
    mempty
              go (Tip Int
    _ a
    v) = a -> m
    f a
    v
              go (Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r)
                | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = IntMap a -> m
    go IntMap a
    r m -> m -> m
    forall a. Monoid a => a -> a -> a
    `mappend` IntMap a -> m
    go IntMap a
    l
                | Bool
    otherwise = IntMap a -> m
    go IntMap a
    l m -> m -> m
    forall a. Monoid a => a -> a -> a
    `mappend` IntMap a -> m
    go IntMap a
    r
      {-# INLINE foldMap #-}
      foldl' :: forall b a. (b -> a -> b) -> b -> IntMap a -> b
    foldl' = (b -> a -> b) -> b -> IntMap a -> b
    forall b a. (b -> a -> b) -> b -> IntMap a -> b
    foldl'
      {-# INLINE foldl' #-}
      foldr' :: forall a b. (a -> b -> b) -> b -> IntMap a -> b
    foldr' = (a -> b -> b) -> b -> IntMap a -> b
    forall a b. (a -> b -> b) -> b -> IntMap a -> b
    foldr'
      {-# INLINE foldr' #-}
      length :: forall a. IntMap a -> Int
    length = IntMap a -> Int
    forall a. IntMap a -> Int
    size
      {-# INLINE length #-}
      null :: forall a. IntMap a -> Bool
    null   = IntMap a -> Bool
    forall a. IntMap a -> Bool
    null
      {-# INLINE null #-}
      toList :: forall a. IntMap a -> [a]
    toList = IntMap a -> [a]
    forall a. IntMap a -> [a]
    elems -- NB: Foldable.toList /= IntMap.toList
      {-# INLINE toList #-}
      elem :: forall a. Eq a => a -> IntMap a -> Bool
    elem = a -> IntMap a -> Bool
    forall a. Eq a => a -> IntMap a -> Bool
    go
        where go :: t -> IntMap t -> Bool
    go !t
    _ IntMap t
    Nil = Bool
    False
              go t
    x (Tip Int
    _ t
    y) = t
    x t -> t -> Bool
    forall a. Eq a => a -> a -> Bool
    == t
    y
              go t
    x (Bin Int
    _ Int
    _ IntMap t
    l IntMap t
    r) = t -> IntMap t -> Bool
    go t
    x IntMap t
    l Bool -> Bool -> Bool
    || t -> IntMap t -> Bool
    go t
    x IntMap t
    r
      {-# INLINABLE elem #-}
      maximum :: forall a. Ord a => IntMap a -> a
    maximum = IntMap a -> a
    forall a. Ord a => IntMap a -> a
    start
        where start :: IntMap t -> t
    start IntMap t
    Nil = [Char] -> t
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "Data.Foldable.maximum (for Data.IntMap): empty map"
              start (Tip Int
    _ t
    y) = t
    y
              start (Bin Int
    _ Int
    m IntMap t
    l IntMap t
    r)
                | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = t -> IntMap t -> t
    forall {t}. Ord t => t -> IntMap t -> t
    go (IntMap t -> t
    start IntMap t
    r) IntMap t
    l
                | Bool
    otherwise = t -> IntMap t -> t
    forall {t}. Ord t => t -> IntMap t -> t
    go (IntMap t -> t
    start IntMap t
    l) IntMap t
    r

              go :: t -> IntMap t -> t
    go !t
    m IntMap t
    Nil = t
    m
              go t
    m (Tip Int
    _ t
    y) = t -> t -> t
    forall a. Ord a => a -> a -> a
    max t
    m t
    y
              go t
    m (Bin Int
    _ Int
    _ IntMap t
    l IntMap t
    r) = t -> IntMap t -> t
    go (t -> IntMap t -> t
    go t
    m IntMap t
    l) IntMap t
    r
      {-# INLINABLE maximum #-}
      minimum :: forall a. Ord a => IntMap a -> a
    minimum = IntMap a -> a
    forall a. Ord a => IntMap a -> a
    start
        where start :: IntMap t -> t
    start IntMap t
    Nil = [Char] -> t
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "Data.Foldable.minimum (for Data.IntMap): empty map"
              start (Tip Int
    _ t
    y) = t
    y
              start (Bin Int
    _ Int
    m IntMap t
    l IntMap t
    r)
                | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = t -> IntMap t -> t
    forall {t}. Ord t => t -> IntMap t -> t
    go (IntMap t -> t
    start IntMap t
    r) IntMap t
    l
                | Bool
    otherwise = t -> IntMap t -> t
    forall {t}. Ord t => t -> IntMap t -> t
    go (IntMap t -> t
    start IntMap t
    l) IntMap t
    r

              go :: t -> IntMap t -> t
    go !t
    m IntMap t
    Nil = t
    m
              go t
    m (Tip Int
    _ t
    y) = t -> t -> t
    forall a. Ord a => a -> a -> a
    min t
    m t
    y
              go t
    m (Bin Int
    _ Int
    _ IntMap t
    l IntMap t
    r) = t -> IntMap t -> t
    go (t -> IntMap t -> t
    go t
    m IntMap t
    l) IntMap t
    r
      {-# INLINABLE minimum #-}
      sum :: forall a. Num a => IntMap a -> a
    sum = (a -> a -> a) -> a -> IntMap a -> a
    forall b a. (b -> a -> b) -> b -> IntMap a -> b
    foldl' a -> a -> a
    forall a. Num a => a -> a -> a
    (+) a
    0
      {-# INLINABLE sum #-}
      product :: forall a. Num a => IntMap a -> a
    product = (a -> a -> a) -> a -> IntMap a -> a
    forall b a. (b -> a -> b) -> b -> IntMap a -> b
    foldl' a -> a -> a
    forall a. Num a => a -> a -> a
    (*) a
    1
      {-# INLINABLE product #-}

    -- | Traverses in order of increasing key.
    instance Traversable IntMap where
        traverse :: forall (f :: * -> *) a b.
    Applicative f =>
    (a -> f b) -> IntMap a -> f (IntMap b)
    traverse a -> f b
    f = (Int -> a -> f b) -> IntMap a -> f (IntMap b)
    forall (t :: * -> *) a b.
    Applicative t =>
    (Int -> a -> t b) -> IntMap a -> t (IntMap b)
    traverseWithKey (\Int
    _ -> a -> f b
    f)
        {-# INLINE traverse #-}

    instance NFData a => NFData (IntMap a) where
        rnf :: IntMap a -> ()
    rnf IntMap a
    Nil = ()
        rnf (Tip Int
    _ a
    v) = a -> ()
    forall a. NFData a => a -> ()
    rnf a
    v
        rnf (Bin Int
    _ Int
    _ IntMap a
    l IntMap a
    r) = IntMap a -> ()
    forall a. NFData a => a -> ()
    rnf IntMap a
    l () -> () -> ()
    forall a b. a -> b -> b
    `seq` IntMap a -> ()
    forall a. NFData a => a -> ()
    rnf IntMap a
    r

    #if __GLASGOW_HASKELL__

    {--------------------------------------------------------------------
      A Data instance
    --------------------------------------------------------------------}

    -- This instance preserves data abstraction at the cost of inefficiency.
    -- We provide limited reflection services for the sake of data abstraction.

    instance Data a => Data (IntMap a) where
      gfoldl :: forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> IntMap a -> c (IntMap a)
    gfoldl forall d b. Data d => c (d -> b) -> d -> c b
    f forall g. g -> c g
    z IntMap a
    im = ([(Int, a)] -> IntMap a) -> c ([(Int, a)] -> IntMap a)
    forall g. g -> c g
    z [(Int, a)] -> IntMap a
    forall a. [(Int, a)] -> IntMap a
    fromList c ([(Int, a)] -> IntMap a) -> [(Int, a)] -> c (IntMap a)
    forall d b. Data d => c (d -> b) -> d -> c b
    `f` (IntMap a -> [(Int, a)]
    forall a. IntMap a -> [(Int, a)]
    toList IntMap a
    im)
      toConstr :: IntMap a -> Constr
    toConstr IntMap a
    _     = Constr
    fromListConstr
      gunfold :: forall (c :: * -> *).
    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (IntMap a)
    gunfold forall b r. Data b => c (b -> r) -> c r
    k forall r. r -> c r
    z Constr
    c  = case Constr -> Int
    constrIndex Constr
    c of
        Int
    1 -> c ([(Int, a)] -> IntMap a) -> c (IntMap a)
    forall b r. Data b => c (b -> r) -> c r
    k (([(Int, a)] -> IntMap a) -> c ([(Int, a)] -> IntMap a)
    forall r. r -> c r
    z [(Int, a)] -> IntMap a
    forall a. [(Int, a)] -> IntMap a
    fromList)
        Int
    _ -> [Char] -> c (IntMap a)
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "gunfold"
      dataTypeOf :: IntMap a -> DataType
    dataTypeOf IntMap a
    _   = DataType
    intMapDataType
      dataCast1 :: forall (t :: * -> *) (c :: * -> *).
    Typeable t =>
    (forall d. Data d => c (t d)) -> Maybe (c (IntMap a))
    dataCast1 forall d. Data d => c (t d)
    f    = c (t a) -> Maybe (c (IntMap a))
    forall {k1} {k2} (c :: k1 -> *) (t :: k2 -> k1) (t' :: k2 -> k1)
           (a :: k2).
    (Typeable t, Typeable t') =>
    c (t a) -> Maybe (c (t' a))
    gcast1 c (t a)
    forall d. Data d => c (t d)
    f

    fromListConstr :: Constr
    fromListConstr :: Constr
    fromListConstr = DataType -> [Char] -> [[Char]] -> Fixity -> Constr
    mkConstr DataType
    intMapDataType [Char]
    "fromList" [] Fixity
    Prefix

    intMapDataType :: DataType
    intMapDataType :: DataType
    intMapDataType = [Char] -> [Constr] -> DataType
    mkDataType [Char]
    "Data.IntMap.Internal.IntMap" [Constr
    fromListConstr]

    #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 :: forall a. IntMap a -> Bool
    null IntMap a
    Nil = Bool
    True
    null IntMap a
    _   = Bool
    False
    {-# INLINE null #-}

    -- | \(O(n)\). 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 :: forall a. IntMap a -> Int
    size = Int -> IntMap a -> Int
    forall {t} {a}. Num t => t -> IntMap a -> t
    go Int
    0
      where
        go :: t -> IntMap a -> t
    go !t
    acc (Bin Int
    _ Int
    _ IntMap a
    l IntMap a
    r) = t -> IntMap a -> t
    go (t -> IntMap a -> t
    go t
    acc IntMap a
    l) IntMap a
    r
        go t
    acc (Tip Int
    _ a
    _) = t
    1 t -> t -> t
    forall a. Num a => a -> a -> a
    + t
    acc
        go t
    acc IntMap a
    Nil = t
    acc

    -- | \(O(\min(n,W))\). Is the key a member of the map?
    --
    -- > member 5 (fromList [(5,'a'), (3,'b')]) == True
    -- > member 1 (fromList [(5,'a'), (3,'b')]) == False

    -- See Note: Local 'go' functions and capturing]
    member :: Key -> IntMap a -> Bool
    member :: forall a. Int -> IntMap a -> Bool
    member !Int
    k = IntMap a -> Bool
    go
      where
        go :: IntMap a -> Bool
    go (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r) | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = Bool
    False
                         | Int -> Int -> Bool
    zero Int
    k Int
    m  = IntMap a -> Bool
    go IntMap a
    l
                         | Bool
    otherwise = IntMap a -> Bool
    go IntMap a
    r
        go (Tip Int
    kx a
    _) = Int
    k Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    kx
        go IntMap a
    Nil = Bool
    False

    -- | \(O(\min(n,W))\). 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 :: forall a. Int -> IntMap a -> Bool
    notMember Int
    k IntMap a
    m = Bool -> Bool
    not (Bool -> Bool) -> Bool -> Bool
    forall a b. (a -> b) -> a -> b
    $ Int -> IntMap a -> Bool
    forall a. Int -> IntMap a -> Bool
    member Int
    k IntMap a
    m

    -- | \(O(\min(n,W))\). Lookup the value at a key in the map. See also 'Data.Map.lookup'.

    -- See Note: Local 'go' functions and capturing
    lookup :: Key -> IntMap a -> Maybe a
    lookup :: forall a. Int -> IntMap a -> Maybe a
    lookup !Int
    k = IntMap a -> Maybe a
    go
      where
        go :: IntMap a -> Maybe a
    go (Bin Int
    _p Int
    m IntMap a
    l IntMap a
    r) | Int -> Int -> Bool
    zero Int
    k Int
    m  = IntMap a -> Maybe a
    go IntMap a
    l
                          | Bool
    otherwise = IntMap a -> Maybe a
    go IntMap a
    r
        go (Tip Int
    kx a
    x) | Int
    k Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    kx   = a -> Maybe a
    forall a. a -> Maybe a
    Just a
    x
                      | Bool
    otherwise = Maybe a
    forall a. Maybe a
    Nothing
        go IntMap a
    Nil = Maybe a
    forall a. Maybe a
    Nothing

    -- See Note: Local 'go' functions and capturing]
    find :: Key -> IntMap a -> a
    find :: forall a. Int -> IntMap a -> a
    find !Int
    k = IntMap a -> a
    go
      where
        go :: IntMap a -> a
    go (Bin Int
    _p Int
    m IntMap a
    l IntMap a
    r) | Int -> Int -> Bool
    zero Int
    k Int
    m  = IntMap a -> a
    go IntMap a
    l
                          | Bool
    otherwise = IntMap a -> a
    go IntMap a
    r
        go (Tip Int
    kx a
    x) | Int
    k Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    kx   = a
    x
                      | Bool
    otherwise = a
    not_found
        go IntMap a
    Nil = a
    not_found

        not_found :: a
    not_found = [Char] -> a
    forall a. HasCallStack => [Char] -> a
    error ([Char]
    "IntMap.!: key " [Char] -> [Char] -> [Char]
    forall a. [a] -> [a] -> [a]
    ++ Int -> [Char]
    forall a. Show a => a -> [Char]
    show Int
    k [Char] -> [Char] -> [Char]
    forall a. [a] -> [a] -> [a]
    ++ [Char]
    " is not an element of the map")

    -- | \(O(\min(n,W))\). 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'

    -- See Note: Local 'go' functions and capturing]
    findWithDefault :: a -> Key -> IntMap a -> a
    findWithDefault :: forall a. a -> Int -> IntMap a -> a
    findWithDefault a
    def !Int
    k = IntMap a -> a
    go
      where
        go :: IntMap a -> a
    go (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r) | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = a
    def
                         | Int -> Int -> Bool
    zero Int
    k Int
    m  = IntMap a -> a
    go IntMap a
    l
                         | Bool
    otherwise = IntMap a -> a
    go IntMap a
    r
        go (Tip Int
    kx a
    x) | Int
    k Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    kx   = a
    x
                      | Bool
    otherwise = a
    def
        go IntMap a
    Nil = a
    def

    -- | \(O(\min(n,W))\). Find largest key smaller than the given one and return the
    -- corresponding (key, value) pair.
    --
    -- > lookupLT 3 (fromList [(3,'a'), (5,'b')]) == Nothing
    -- > lookupLT 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')

    -- See Note: Local 'go' functions and capturing.
    lookupLT :: Key -> IntMap a -> Maybe (Key, a)
    lookupLT :: forall a. Int -> IntMap a -> Maybe (Int, a)
    lookupLT !Int
    k IntMap a
    t = case IntMap a
    t of
        Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> if Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    >= Int
    0 then IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    r IntMap a
    l else IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    forall a. IntMap a
    Nil IntMap a
    r
        IntMap a
    _ -> IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    forall a. IntMap a
    Nil IntMap a
    t
      where
        go :: IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    def (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = if Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    p then IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMax IntMap a
    def else IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMax IntMap a
    r
          | Int -> Int -> Bool
    zero Int
    k Int
    m  = IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    def IntMap a
    l
          | Bool
    otherwise = IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    l IntMap a
    r
        go IntMap a
    def (Tip Int
    ky a
    y)
          | Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    <= Int
    ky   = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMax IntMap a
    def
          | Bool
    otherwise = (Int, a) -> Maybe (Int, a)
    forall a. a -> Maybe a
    Just (Int
    ky, a
    y)
        go IntMap a
    def IntMap a
    Nil = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMax IntMap a
    def

    -- | \(O(\min(n,W))\). Find smallest key greater than the given one and return the
    -- corresponding (key, value) pair.
    --
    -- > lookupGT 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')
    -- > lookupGT 5 (fromList [(3,'a'), (5,'b')]) == Nothing

    -- See Note: Local 'go' functions and capturing.
    lookupGT :: Key -> IntMap a -> Maybe (Key, a)
    lookupGT :: forall a. Int -> IntMap a -> Maybe (Int, a)
    lookupGT !Int
    k IntMap a
    t = case IntMap a
    t of
        Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> if Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    >= Int
    0 then IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    forall a. IntMap a
    Nil IntMap a
    l else IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    l IntMap a
    r
        IntMap a
    _ -> IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    forall a. IntMap a
    Nil IntMap a
    t
      where
        go :: IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    def (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = if Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    p then IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMin IntMap a
    l else IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMin IntMap a
    def
          | Int -> Int -> Bool
    zero Int
    k Int
    m  = IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    r IntMap a
    l
          | Bool
    otherwise = IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    def IntMap a
    r
        go IntMap a
    def (Tip Int
    ky a
    y)
          | Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    >= Int
    ky   = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMin IntMap a
    def
          | Bool
    otherwise = (Int, a) -> Maybe (Int, a)
    forall a. a -> Maybe a
    Just (Int
    ky, a
    y)
        go IntMap a
    def IntMap a
    Nil = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMin IntMap a
    def

    -- | \(O(\min(n,W))\). Find largest key smaller or equal to the given one and return
    -- the corresponding (key, value) pair.
    --
    -- > lookupLE 2 (fromList [(3,'a'), (5,'b')]) == Nothing
    -- > lookupLE 4 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')
    -- > lookupLE 5 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')

    -- See Note: Local 'go' functions and capturing.
    lookupLE :: Key -> IntMap a -> Maybe (Key, a)
    lookupLE :: forall a. Int -> IntMap a -> Maybe (Int, a)
    lookupLE !Int
    k IntMap a
    t = case IntMap a
    t of
        Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> if Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    >= Int
    0 then IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    r IntMap a
    l else IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    forall a. IntMap a
    Nil IntMap a
    r
        IntMap a
    _ -> IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    forall a. IntMap a
    Nil IntMap a
    t
      where
        go :: IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    def (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = if Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    p then IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMax IntMap a
    def else IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMax IntMap a
    r
          | Int -> Int -> Bool
    zero Int
    k Int
    m  = IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    def IntMap a
    l
          | Bool
    otherwise = IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    l IntMap a
    r
        go IntMap a
    def (Tip Int
    ky a
    y)
          | Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    ky    = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMax IntMap a
    def
          | Bool
    otherwise = (Int, a) -> Maybe (Int, a)
    forall a. a -> Maybe a
    Just (Int
    ky, a
    y)
        go IntMap a
    def IntMap a
    Nil = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMax IntMap a
    def

    -- | \(O(\min(n,W))\). Find smallest key greater or equal to the given one and return
    -- the corresponding (key, value) pair.
    --
    -- > lookupGE 3 (fromList [(3,'a'), (5,'b')]) == Just (3, 'a')
    -- > lookupGE 4 (fromList [(3,'a'), (5,'b')]) == Just (5, 'b')
    -- > lookupGE 6 (fromList [(3,'a'), (5,'b')]) == Nothing

    -- See Note: Local 'go' functions and capturing.
    lookupGE :: Key -> IntMap a -> Maybe (Key, a)
    lookupGE :: forall a. Int -> IntMap a -> Maybe (Int, a)
    lookupGE !Int
    k IntMap a
    t = case IntMap a
    t of
        Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> if Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    >= Int
    0 then IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    forall a. IntMap a
    Nil IntMap a
    l else IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    l IntMap a
    r
        IntMap a
    _ -> IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    forall a. IntMap a
    Nil IntMap a
    t
      where
        go :: IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    def (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = if Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    p then IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMin IntMap a
    l else IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMin IntMap a
    def
          | Int -> Int -> Bool
    zero Int
    k Int
    m  = IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    r IntMap a
    l
          | Bool
    otherwise = IntMap a -> IntMap a -> Maybe (Int, a)
    go IntMap a
    def IntMap a
    r
        go IntMap a
    def (Tip Int
    ky a
    y)
          | Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > Int
    ky    = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMin IntMap a
    def
          | Bool
    otherwise = (Int, a) -> Maybe (Int, a)
    forall a. a -> Maybe a
    Just (Int
    ky, a
    y)
        go IntMap a
    def IntMap a
    Nil = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMin IntMap a
    def

    -- Helper function for lookupGE and lookupGT. It assumes that if a Bin node is
    -- given, it has m > 0.
    unsafeFindMin :: IntMap a -> Maybe (Key, a)
    unsafeFindMin :: forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMin IntMap a
    Nil = Maybe (Int, a)
    forall a. Maybe a
    Nothing
    unsafeFindMin (Tip Int
    ky a
    y) = (Int, a) -> Maybe (Int, a)
    forall a. a -> Maybe a
    Just (Int
    ky, a
    y)
    unsafeFindMin (Bin Int
    _ Int
    _ IntMap a
    l IntMap a
    _) = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMin IntMap a
    l

    -- Helper function for lookupLE and lookupLT. It assumes that if a Bin node is
    -- given, it has m > 0.
    unsafeFindMax :: IntMap a -> Maybe (Key, a)
    unsafeFindMax :: forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMax IntMap a
    Nil = Maybe (Int, a)
    forall a. Maybe a
    Nothing
    unsafeFindMax (Tip Int
    ky a
    y) = (Int, a) -> Maybe (Int, a)
    forall a. a -> Maybe a
    Just (Int
    ky, a
    y)
    unsafeFindMax (Bin Int
    _ Int
    _ IntMap a
    _ IntMap a
    r) = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    unsafeFindMax IntMap a
    r

    {--------------------------------------------------------------------
      Disjoint
    --------------------------------------------------------------------}
    -- | \(O(n+m)\). Check whether the key sets of two maps are disjoint
    -- (i.e. their 'intersection' is empty).
    --
    -- > disjoint (fromList [(2,'a')]) (fromList [(1,()), (3,())])   == True
    -- > disjoint (fromList [(2,'a')]) (fromList [(1,'a'), (2,'b')]) == False
    -- > disjoint (fromList [])        (fromList [])                 == True
    --
    -- > disjoint a b == null (intersection a b)
    --
    -- @since 0.6.2.1
    disjoint :: IntMap a -> IntMap b -> Bool
    disjoint :: forall a b. IntMap a -> IntMap b -> Bool
    disjoint IntMap a
    Nil IntMap b
    _ = Bool
    True
    disjoint IntMap a
    _ IntMap b
    Nil = Bool
    True
    disjoint (Tip Int
    kx a
    _) IntMap b
    ys = Int -> IntMap b -> Bool
    forall a. Int -> IntMap a -> Bool
    notMember Int
    kx IntMap b
    ys
    disjoint IntMap a
    xs (Tip Int
    ky b
    _) = Int -> IntMap a -> Bool
    forall a. Int -> IntMap a -> Bool
    notMember Int
    ky IntMap a
    xs
    disjoint t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1) t2 :: IntMap b
    t2@(Bin Int
    p2 Int
    m2 IntMap b
    l2 IntMap b
    r2)
      | Int -> Int -> Bool
    shorter Int
    m1 Int
    m2 = Bool
    disjoint1
      | Int -> Int -> Bool
    shorter Int
    m2 Int
    m1 = Bool
    disjoint2
      | Int
    p1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    p2      = IntMap a -> IntMap b -> Bool
    forall a b. IntMap a -> IntMap b -> Bool
    disjoint IntMap a
    l1 IntMap b
    l2 Bool -> Bool -> Bool
    && IntMap a -> IntMap b -> Bool
    forall a b. IntMap a -> IntMap b -> Bool
    disjoint IntMap a
    r1 IntMap b
    r2
      | Bool
    otherwise     = Bool
    True
      where
        disjoint1 :: Bool
    disjoint1 | Int -> Int -> Int -> Bool
    nomatch Int
    p2 Int
    p1 Int
    m1 = Bool
    True
                  | Int -> Int -> Bool
    zero Int
    p2 Int
    m1       = IntMap a -> IntMap b -> Bool
    forall a b. IntMap a -> IntMap b -> Bool
    disjoint IntMap a
    l1 IntMap b
    t2
                  | Bool
    otherwise        = IntMap a -> IntMap b -> Bool
    forall a b. IntMap a -> IntMap b -> Bool
    disjoint IntMap a
    r1 IntMap b
    t2
        disjoint2 :: Bool
    disjoint2 | Int -> Int -> Int -> Bool
    nomatch Int
    p1 Int
    p2 Int
    m2 = Bool
    True
                  | Int -> Int -> Bool
    zero Int
    p1 Int
    m2       = IntMap a -> IntMap b -> Bool
    forall a b. IntMap a -> IntMap b -> Bool
    disjoint IntMap a
    t1 IntMap b
    l2
                  | Bool
    otherwise        = IntMap a -> IntMap b -> Bool
    forall a b. IntMap a -> IntMap b -> Bool
    disjoint IntMap a
    t1 IntMap b
    r2

    {--------------------------------------------------------------------
      Compose
    --------------------------------------------------------------------}
    -- | Relate the keys of one map to the values of
    -- the other, by using the values of the former as keys for lookups
    -- in the latter.
    --
    -- Complexity: \( O(n * \min(m,W)) \), where \(m\) is the size of the first argument
    --
    -- > compose (fromList [('a', "A"), ('b', "B")]) (fromList [(1,'a'),(2,'b'),(3,'z')]) = fromList [(1,"A"),(2,"B")]
    --
    -- @
    -- ('compose' bc ab '!?') = (bc '!?') <=< (ab '!?')
    -- @
    --
    -- __Note:__ Prior to v0.6.4, "Data.IntMap.Strict" exposed a version of
    -- 'compose' that forced the values of the output 'IntMap'. This version does
    -- not force these values.
    --
    -- @since 0.6.3.1
    compose :: IntMap c -> IntMap Int -> IntMap c
    compose :: forall c. IntMap c -> IntMap Int -> IntMap c
    compose IntMap c
    bc !IntMap Int
    ab
      | IntMap c -> Bool
    forall a. IntMap a -> Bool
    null IntMap c
    bc = IntMap c
    forall a. IntMap a
    empty
      | Bool
    otherwise = (Int -> Maybe c) -> IntMap Int -> IntMap c
    forall a b. (a -> Maybe b) -> IntMap a -> IntMap b
    mapMaybe (IntMap c
    bc IntMap c -> Int -> Maybe c
    forall a. IntMap a -> Int -> Maybe a
    !?) IntMap Int
    ab

    {--------------------------------------------------------------------
      Construction
    --------------------------------------------------------------------}
    -- | \(O(1)\). The empty map.
    --
    -- > empty      == fromList []
    -- > size empty == 0

    empty :: IntMap a
    empty :: forall a. IntMap a
    empty
      = IntMap a
    forall a. IntMap a
    Nil
    {-# INLINE empty #-}

    -- | \(O(1)\). A map of one element.
    --
    -- > singleton 1 'a'        == fromList [(1, 'a')]
    -- > size (singleton 1 'a') == 1

    singleton :: Key -> a -> IntMap a
    singleton :: forall a. Int -> a -> IntMap a
    singleton Int
    k a
    x
      = Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x
    {-# INLINE singleton #-}

    {--------------------------------------------------------------------
      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 :: forall a. Int -> a -> IntMap a -> IntMap a
    insert !Int
    k a
    x t :: IntMap a
    t@(Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = Int -> IntMap a -> Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    k (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x) Int
    p IntMap a
    t
      | Int -> Int -> Bool
    zero Int
    k Int
    m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m (Int -> a -> IntMap a -> IntMap a
    forall a. Int -> a -> IntMap a -> IntMap a
    insert Int
    k a
    x IntMap a
    l) IntMap a
    r
      | Bool
    otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap a
    l (Int -> a -> IntMap a -> IntMap a
    forall a. Int -> a -> IntMap a -> IntMap a
    insert Int
    k a
    x IntMap a
    r)
    insert Int
    k a
    x t :: IntMap a
    t@(Tip Int
    ky a
    _)
      | Int
    kInt -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    ==Int
    ky         = Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x
      | Bool
    otherwise     = Int -> IntMap a -> Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    k (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x) Int
    ky IntMap a
    t
    insert Int
    k a
    x IntMap a
    Nil = Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    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@.
    --
    -- > 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"
    --
    -- Also see the performance note on 'fromListWith'.

    insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
    insertWith :: forall a. (a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
    insertWith a -> a -> a
    f Int
    k a
    x IntMap a
    t
      = (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
    forall a. (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
    insertWithKey (\Int
    _ a
    x' a
    y' -> a -> a -> a
    f a
    x' a
    y') Int
    k a
    x IntMap a
    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@.
    --
    -- > 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"
    --
    -- Also see the performance note on 'fromListWith'.

    insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
    insertWithKey :: forall a. (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
    insertWithKey Int -> a -> a -> a
    f !Int
    k a
    x t :: IntMap a
    t@(Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = Int -> IntMap a -> Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    k (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x) Int
    p IntMap a
    t
      | Int -> Int -> Bool
    zero Int
    k Int
    m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m ((Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
    forall a. (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
    insertWithKey Int -> a -> a -> a
    f Int
    k a
    x IntMap a
    l) IntMap a
    r
      | Bool
    otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap a
    l ((Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
    forall a. (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
    insertWithKey Int -> a -> a -> a
    f Int
    k a
    x IntMap a
    r)
    insertWithKey Int -> a -> a -> a
    f Int
    k a
    x t :: IntMap a
    t@(Tip Int
    ky a
    y)
      | Int
    k Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    ky       = Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k (Int -> a -> a -> a
    f Int
    k a
    x a
    y)
      | Bool
    otherwise     = Int -> IntMap a -> Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    k (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x) Int
    ky IntMap a
    t
    insertWithKey Int -> a -> a -> a
    _ Int
    k a
    x IntMap a
    Nil = Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    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")])
    --
    -- Also see the performance note on 'fromListWith'.

    insertLookupWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> (Maybe a, IntMap a)
    insertLookupWithKey :: forall a.
    (Int -> a -> a -> a) -> Int -> a -> IntMap a -> (Maybe a, IntMap a)
    insertLookupWithKey Int -> a -> a -> a
    f !Int
    k a
    x t :: IntMap a
    t@(Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = (Maybe a
    forall a. Maybe a
    Nothing,Int -> IntMap a -> Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    k (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x) Int
    p IntMap a
    t)
      | Int -> Int -> Bool
    zero Int
    k Int
    m      = let (Maybe a
    found,IntMap a
    l') = (Int -> a -> a -> a) -> Int -> a -> IntMap a -> (Maybe a, IntMap a)
    forall a.
    (Int -> a -> a -> a) -> Int -> a -> IntMap a -> (Maybe a, IntMap a)
    insertLookupWithKey Int -> a -> a -> a
    f Int
    k a
    x IntMap a
    l
                        in (Maybe a
    found,Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap a
    l' IntMap a
    r)
      | Bool
    otherwise     = let (Maybe a
    found,IntMap a
    r') = (Int -> a -> a -> a) -> Int -> a -> IntMap a -> (Maybe a, IntMap a)
    forall a.
    (Int -> a -> a -> a) -> Int -> a -> IntMap a -> (Maybe a, IntMap a)
    insertLookupWithKey Int -> a -> a -> a
    f Int
    k a
    x IntMap a
    r
                        in (Maybe a
    found,Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap a
    l IntMap a
    r')
    insertLookupWithKey Int -> a -> a -> a
    f Int
    k a
    x t :: IntMap a
    t@(Tip Int
    ky a
    y)
      | Int
    k Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    ky       = (a -> Maybe a
    forall a. a -> Maybe a
    Just a
    y,Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k (Int -> a -> a -> a
    f Int
    k a
    x a
    y))
      | Bool
    otherwise     = (Maybe a
    forall a. Maybe a
    Nothing,Int -> IntMap a -> Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    k (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x) Int
    ky IntMap a
    t)
    insertLookupWithKey Int -> a -> a -> a
    _ Int
    k a
    x IntMap a
    Nil = (Maybe a
    forall a. Maybe a
    Nothing,Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x)

    {--------------------------------------------------------------------
      Deletion
    --------------------------------------------------------------------}
    -- | \(O(\min(n,W))\). 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 :: forall a. Int -> IntMap a -> IntMap a
    delete !Int
    k t :: IntMap a
    t@(Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = IntMap a
    t
      | Int -> Int -> Bool
    zero Int
    k Int
    m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    p Int
    m (Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> IntMap a
    delete Int
    k IntMap a
    l) IntMap a
    r
      | Bool
    otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    p Int
    m IntMap a
    l (Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> IntMap a
    delete Int
    k IntMap a
    r)
    delete Int
    k t :: IntMap a
    t@(Tip Int
    ky a
    _)
      | Int
    k Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    ky       = IntMap a
    forall a. IntMap a
    Nil
      | Bool
    otherwise     = IntMap a
    t
    delete Int
    _k IntMap a
    Nil = IntMap a
    forall a. IntMap a
    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 :: forall a. (a -> a) -> Int -> IntMap a -> IntMap a
    adjust a -> a
    f Int
    k IntMap a
    m
      = (Int -> a -> a) -> Int -> IntMap a -> IntMap a
    forall a. (Int -> a -> a) -> Int -> IntMap a -> IntMap a
    adjustWithKey (\Int
    _ a
    x -> a -> a
    f a
    x) Int
    k IntMap a
    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 :: forall a. (Int -> a -> a) -> Int -> IntMap a -> IntMap a
    adjustWithKey Int -> a -> a
    f !Int
    k (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      | Int -> Int -> Bool
    zero Int
    k Int
    m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m ((Int -> a -> a) -> Int -> IntMap a -> IntMap a
    forall a. (Int -> a -> a) -> Int -> IntMap a -> IntMap a
    adjustWithKey Int -> a -> a
    f Int
    k IntMap a
    l) IntMap a
    r
      | Bool
    otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap a
    l ((Int -> a -> a) -> Int -> IntMap a -> IntMap a
    forall a. (Int -> a -> a) -> Int -> IntMap a -> IntMap a
    adjustWithKey Int -> a -> a
    f Int
    k IntMap a
    r)
    adjustWithKey Int -> a -> a
    f Int
    k t :: IntMap a
    t@(Tip Int
    ky a
    y)
      | Int
    k Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    ky       = Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    ky (Int -> a -> a
    f Int
    k a
    y)
      | Bool
    otherwise     = IntMap a
    t
    adjustWithKey Int -> a -> a
    _ Int
    _ IntMap a
    Nil = IntMap a
    forall a. IntMap a
    Nil

    -- | \(O(\min(n,W))\). 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@.
    --
    -- > 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 :: forall a. (a -> Maybe a) -> Int -> IntMap a -> IntMap a
    update a -> Maybe a
    f
      = (Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
    forall a. (Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
    updateWithKey (\Int
    _ a
    x -> a -> Maybe a
    f a
    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@.
    --
    -- > 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 :: forall a. (Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
    updateWithKey Int -> a -> Maybe a
    f !Int
    k (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      | Int -> Int -> Bool
    zero Int
    k Int
    m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    p Int
    m ((Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
    forall a. (Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
    updateWithKey Int -> a -> Maybe a
    f Int
    k IntMap a
    l) IntMap a
    r
      | Bool
    otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    p Int
    m IntMap a
    l ((Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
    forall a. (Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
    updateWithKey Int -> a -> Maybe a
    f Int
    k IntMap a
    r)
    updateWithKey Int -> a -> Maybe a
    f Int
    k t :: IntMap a
    t@(Tip Int
    ky a
    y)
      | Int
    k Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    ky       = case (Int -> a -> Maybe a
    f Int
    k a
    y) of
                          Just a
    y' -> Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    ky a
    y'
                          Maybe a
    Nothing -> IntMap a
    forall a. IntMap a
    Nil
      | Bool
    otherwise     = IntMap a
    t
    updateWithKey Int -> a -> Maybe a
    _ Int
    _ IntMap a
    Nil = IntMap a
    forall a. IntMap a
    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 :: forall a.
    (Int -> a -> Maybe a) -> Int -> IntMap a -> (Maybe a, IntMap a)
    updateLookupWithKey Int -> a -> Maybe a
    f !Int
    k (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      | Int -> Int -> Bool
    zero Int
    k Int
    m      = let !(Maybe a
    found,IntMap a
    l') = (Int -> a -> Maybe a) -> Int -> IntMap a -> (Maybe a, IntMap a)
    forall a.
    (Int -> a -> Maybe a) -> Int -> IntMap a -> (Maybe a, IntMap a)
    updateLookupWithKey Int -> a -> Maybe a
    f Int
    k IntMap a
    l
                        in (Maybe a
    found,Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    p Int
    m IntMap a
    l' IntMap a
    r)
      | Bool
    otherwise     = let !(Maybe a
    found,IntMap a
    r') = (Int -> a -> Maybe a) -> Int -> IntMap a -> (Maybe a, IntMap a)
    forall a.
    (Int -> a -> Maybe a) -> Int -> IntMap a -> (Maybe a, IntMap a)
    updateLookupWithKey Int -> a -> Maybe a
    f Int
    k IntMap a
    r
                        in (Maybe a
    found,Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    p Int
    m IntMap a
    l IntMap a
    r')
    updateLookupWithKey Int -> a -> Maybe a
    f Int
    k t :: IntMap a
    t@(Tip Int
    ky a
    y)
      | Int
    kInt -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    ==Int
    ky         = case (Int -> a -> Maybe a
    f Int
    k a
    y) of
                          Just a
    y' -> (a -> Maybe a
    forall a. a -> Maybe a
    Just a
    y,Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    ky a
    y')
                          Maybe a
    Nothing -> (a -> Maybe a
    forall a. a -> Maybe a
    Just a
    y,IntMap a
    forall a. IntMap a
    Nil)
      | Bool
    otherwise     = (Maybe a
    forall a. Maybe a
    Nothing,IntMap a
    t)
    updateLookupWithKey Int -> a -> Maybe a
    _ Int
    _ IntMap a
    Nil = (Maybe a
    forall a. Maybe a
    Nothing,IntMap a
    forall a. IntMap a
    Nil)

    -- | \(O(\min(n,W))\). 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 :: forall a. (Maybe a -> Maybe a) -> Int -> IntMap a -> IntMap a
    alter Maybe a -> Maybe a
    f !Int
    k t :: IntMap a
    t@(Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      | Int -> Int -> Int -> Bool
    nomatch Int
    k Int
    p Int
    m = case Maybe a -> Maybe a
    f Maybe a
    forall a. Maybe a
    Nothing of
                          Maybe a
    Nothing -> IntMap a
    t
                          Just a
    x -> Int -> IntMap a -> Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    k (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x) Int
    p IntMap a
    t
      | Int -> Int -> Bool
    zero Int
    k Int
    m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    p Int
    m ((Maybe a -> Maybe a) -> Int -> IntMap a -> IntMap a
    forall a. (Maybe a -> Maybe a) -> Int -> IntMap a -> IntMap a
    alter Maybe a -> Maybe a
    f Int
    k IntMap a
    l) IntMap a
    r
      | Bool
    otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    p Int
    m IntMap a
    l ((Maybe a -> Maybe a) -> Int -> IntMap a -> IntMap a
    forall a. (Maybe a -> Maybe a) -> Int -> IntMap a -> IntMap a
    alter Maybe a -> Maybe a
    f Int
    k IntMap a
    r)
    alter Maybe a -> Maybe a
    f Int
    k t :: IntMap a
    t@(Tip Int
    ky a
    y)
      | Int
    kInt -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    ==Int
    ky         = case Maybe a -> Maybe a
    f (a -> Maybe a
    forall a. a -> Maybe a
    Just a
    y) of
                          Just a
    x -> Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    ky a
    x
                          Maybe a
    Nothing -> IntMap a
    forall a. IntMap a
    Nil
      | Bool
    otherwise     = case Maybe a -> Maybe a
    f Maybe a
    forall a. Maybe a
    Nothing of
                          Just a
    x -> Int -> IntMap a -> Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    k (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x) Int
    ky IntMap a
    t
                          Maybe a
    Nothing -> Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    ky a
    y
    alter Maybe a -> Maybe a
    f Int
    k IntMap a
    Nil     = case Maybe a -> Maybe a
    f Maybe a
    forall a. Maybe a
    Nothing of
                          Just a
    x -> Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    x
                          Maybe a
    Nothing -> IntMap a
    forall a. IntMap a
    Nil

    -- | \(O(\min(n,W))\). The expression (@'alterF' f k map@) alters the value @x@ at
    -- @k@, or absence thereof.  'alterF' can be used to inspect, insert, delete,
    -- or update a value in an 'IntMap'.  In short : @'lookup' k <$> 'alterF' f k m = f
    -- ('lookup' k m)@.
    --
    -- Example:
    --
    -- @
    -- interactiveAlter :: Int -> IntMap String -> IO (IntMap String)
    -- interactiveAlter k m = alterF f k m where
    --   f Nothing = do
    --      putStrLn $ show k ++
    --          " was not found in the map. Would you like to add it?"
    --      getUserResponse1 :: IO (Maybe String)
    --   f (Just old) = do
    --      putStrLn $ "The key is currently bound to " ++ show old ++
    --          ". Would you like to change or delete it?"
    --      getUserResponse2 :: IO (Maybe String)
    -- @
    --
    -- 'alterF' is the most general operation for working with an individual
    -- key that may or may not be in a given map.
    --
    -- Note: 'alterF' is a flipped version of the @at@ combinator from
    -- @Control.Lens.At@.
    --
    -- @since 0.5.8

    alterF :: Functor f
           => (Maybe a -> f (Maybe a)) -> Key -> IntMap a -> f (IntMap a)
    -- This implementation was stolen from 'Control.Lens.At'.
    alterF :: forall (f :: * -> *) a.
    Functor f =>
    (Maybe a -> f (Maybe a)) -> Int -> IntMap a -> f (IntMap a)
    alterF Maybe a -> f (Maybe a)
    f Int
    k IntMap a
    m = ((Maybe a -> IntMap a) -> f (Maybe a) -> f (IntMap a)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Maybe a -> f (Maybe a)
    f Maybe a
    mv) ((Maybe a -> IntMap a) -> f (IntMap a))
    -> (Maybe a -> IntMap a) -> f (IntMap a)
    forall a b. (a -> b) -> a -> b
    $ \Maybe a
    fres ->
      case Maybe a
    fres of
        Maybe a
    Nothing -> IntMap a -> (a -> IntMap a) -> Maybe a -> IntMap a
    forall b a. b -> (a -> b) -> Maybe a -> b
    maybe IntMap a
    m (IntMap a -> a -> IntMap a
    forall a b. a -> b -> a
    const (Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> IntMap a
    delete Int
    k IntMap a
    m)) Maybe a
    mv
        Just a
    v' -> Int -> a -> IntMap a -> IntMap a
    forall a. Int -> a -> IntMap a -> IntMap a
    insert Int
    k a
    v' IntMap a
    m
      where mv :: Maybe a
    mv = Int -> IntMap a -> Maybe a
    forall a. Int -> IntMap a -> Maybe a
    lookup Int
    k IntMap a
    m

    {--------------------------------------------------------------------
      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 :: Foldable f => f (IntMap a) -> IntMap a
    unions :: forall (f :: * -> *) a. Foldable f => f (IntMap a) -> IntMap a
    unions f (IntMap a)
    xs
      = (IntMap a -> IntMap a -> IntMap a)
    -> IntMap a -> f (IntMap a) -> IntMap a
    forall b a. (b -> a -> b) -> b -> f a -> b
    forall (t :: * -> *) b a.
    Foldable t =>
    (b -> a -> b) -> b -> t a -> b
    Foldable.foldl' IntMap a -> IntMap a -> IntMap a
    forall a. IntMap a -> IntMap a -> IntMap a
    union IntMap a
    forall a. IntMap a
    empty f (IntMap a)
    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 :: Foldable f => (a->a->a) -> f (IntMap a) -> IntMap a
    unionsWith :: forall (f :: * -> *) a.
    Foldable f =>
    (a -> a -> a) -> f (IntMap a) -> IntMap a
    unionsWith a -> a -> a
    f f (IntMap a)
    ts
      = (IntMap a -> IntMap a -> IntMap a)
    -> IntMap a -> f (IntMap a) -> IntMap a
    forall b a. (b -> a -> b) -> b -> f a -> b
    forall (t :: * -> *) b a.
    Foldable t =>
    (b -> a -> b) -> b -> t a -> b
    Foldable.foldl' ((a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
    forall a. (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
    unionWith a -> a -> a
    f) IntMap a
    forall a. IntMap a
    empty f (IntMap a)
    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 :: forall a. IntMap a -> IntMap a -> IntMap a
    union IntMap a
    m1 IntMap a
    m2
      = (Int -> Int -> IntMap a -> IntMap a -> IntMap a)
    -> (IntMap a -> IntMap a -> IntMap a)
    -> (IntMap a -> IntMap a)
    -> (IntMap a -> IntMap a)
    -> IntMap a
    -> IntMap a
    -> IntMap a
    forall c a b.
    (Int -> Int -> IntMap c -> IntMap c -> IntMap c)
    -> (IntMap a -> IntMap b -> IntMap c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    mergeWithKey' Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin IntMap a -> IntMap a -> IntMap a
    forall a b. a -> b -> a
    const IntMap a -> IntMap a
    forall a. a -> a
    id IntMap a -> IntMap a
    forall a. a -> a
    id IntMap a
    m1 IntMap a
    m2

    -- | \(O(n+m)\). The union with a combining function.
    --
    -- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]
    --
    -- Also see the performance note on 'fromListWith'.

    unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
    unionWith :: forall a. (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
    unionWith a -> a -> a
    f IntMap a
    m1 IntMap a
    m2
      = (Int -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
    forall a. (Int -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
    unionWithKey (\Int
    _ a
    x a
    y -> a -> a -> a
    f a
    x a
    y) IntMap a
    m1 IntMap a
    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")]
    --
    -- Also see the performance note on 'fromListWith'.

    unionWithKey :: (Key -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
    unionWithKey :: forall a. (Int -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
    unionWithKey Int -> a -> a -> a
    f IntMap a
    m1 IntMap a
    m2
      = (Int -> Int -> IntMap a -> IntMap a -> IntMap a)
    -> (IntMap a -> IntMap a -> IntMap a)
    -> (IntMap a -> IntMap a)
    -> (IntMap a -> IntMap a)
    -> IntMap a
    -> IntMap a
    -> IntMap a
    forall c a b.
    (Int -> Int -> IntMap c -> IntMap c -> IntMap c)
    -> (IntMap a -> IntMap b -> IntMap c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    mergeWithKey' Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin (\(Tip Int
    k1 a
    x1) (Tip Int
    _k2 a
    x2) -> Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k1 (Int -> a -> a -> a
    f Int
    k1 a
    x1 a
    x2)) IntMap a -> IntMap a
    forall a. a -> a
    id IntMap a -> IntMap a
    forall a. a -> a
    id IntMap a
    m1 IntMap a
    m2

    {--------------------------------------------------------------------
      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 :: forall a b. IntMap a -> IntMap b -> IntMap a
    difference IntMap a
    m1 IntMap b
    m2
      = (Int -> a -> b -> Maybe a)
    -> (IntMap a -> IntMap a)
    -> (IntMap b -> IntMap a)
    -> IntMap a
    -> IntMap b
    -> IntMap a
    forall a b c.
    (Int -> a -> b -> Maybe c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    mergeWithKey (\Int
    _ a
    _ b
    _ -> Maybe a
    forall a. Maybe a
    Nothing) IntMap a -> IntMap a
    forall a. a -> a
    id (IntMap a -> IntMap b -> IntMap a
    forall a b. a -> b -> a
    const IntMap a
    forall a. IntMap a
    Nil) IntMap a
    m1 IntMap b
    m2

    -- | \(O(n+m)\). 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 :: forall a b. (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
    differenceWith a -> b -> Maybe a
    f IntMap a
    m1 IntMap b
    m2
      = (Int -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
    forall a b.
    (Int -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
    differenceWithKey (\Int
    _ a
    x b
    y -> a -> b -> Maybe a
    f a
    x b
    y) IntMap a
    m1 IntMap b
    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@.
    --
    -- > 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 :: forall a b.
    (Int -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
    differenceWithKey Int -> a -> b -> Maybe a
    f IntMap a
    m1 IntMap b
    m2
      = (Int -> a -> b -> Maybe a)
    -> (IntMap a -> IntMap a)
    -> (IntMap b -> IntMap a)
    -> IntMap a
    -> IntMap b
    -> IntMap a
    forall a b c.
    (Int -> a -> b -> Maybe c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    mergeWithKey Int -> a -> b -> Maybe a
    f IntMap a -> IntMap a
    forall a. a -> a
    id (IntMap a -> IntMap b -> IntMap a
    forall a b. a -> b -> a
    const IntMap a
    forall a. IntMap a
    Nil) IntMap a
    m1 IntMap b
    m2

    -- TODO(wrengr): re-verify that asymptotic bound
    -- | \(O(n+m)\). Remove all the keys in a given set from a map.
    --
    -- @
    -- m \`withoutKeys\` s = 'filterWithKey' (\\k _ -> k ``IntSet.notMember`` s) m
    -- @
    --
    -- @since 0.5.8
    withoutKeys :: IntMap a -> IntSet.IntSet -> IntMap a
    withoutKeys :: forall a. IntMap a -> IntSet -> IntMap a
    withoutKeys t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1) t2 :: IntSet
    t2@(IntSet.Bin Int
    p2 Int
    m2 IntSet
    l2 IntSet
    r2)
        | Int -> Int -> Bool
    shorter Int
    m1 Int
    m2  = IntMap a
    difference1
        | Int -> Int -> Bool
    shorter Int
    m2 Int
    m1  = IntMap a
    difference2
        | Int
    p1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    p2       = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p1 Int
    m1 (IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    withoutKeys IntMap a
    l1 IntSet
    l2) (IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    withoutKeys IntMap a
    r1 IntSet
    r2)
        | Bool
    otherwise      = IntMap a
    t1
        where
        difference1 :: IntMap a
    difference1
            | Int -> Int -> Int -> Bool
    nomatch Int
    p2 Int
    p1 Int
    m1  = IntMap a
    t1
            | Int -> Int -> Bool
    zero Int
    p2 Int
    m1        = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    p1 Int
    m1 (IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    withoutKeys IntMap a
    l1 IntSet
    t2) IntMap a
    r1
            | Bool
    otherwise         = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    p1 Int
    m1 IntMap a
    l1 (IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    withoutKeys IntMap a
    r1 IntSet
    t2)
        difference2 :: IntMap a
    difference2
            | Int -> Int -> Int -> Bool
    nomatch Int
    p1 Int
    p2 Int
    m2  = IntMap a
    t1
            | Int -> Int -> Bool
    zero Int
    p1 Int
    m2        = IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    withoutKeys IntMap a
    t1 IntSet
    l2
            | Bool
    otherwise         = IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    withoutKeys IntMap a
    t1 IntSet
    r2
    withoutKeys t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    _ IntMap a
    _) (IntSet.Tip Int
    p2 Nat
    bm2) =
        let minbit :: Nat
    minbit = Int -> Nat
    bitmapOf Int
    p1
            lt_minbit :: Nat
    lt_minbit = Nat
    minbit Nat -> Nat -> Nat
    forall a. Num a => a -> a -> a
    - Nat
    1
            maxbit :: Nat
    maxbit = Int -> Nat
    bitmapOf (Int
    p1 Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. (Int
    m1 Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. (Int
    m1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    1)))
            gt_maxbit :: Nat
    gt_maxbit = (-Nat
    maxbit) Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    `xor` Nat
    maxbit
        -- TODO(wrengr): should we manually inline/unroll 'updatePrefix'
        -- and 'withoutBM' here, in order to avoid redundant case analyses?
        in Int -> IntMap a -> (IntMap a -> IntMap a) -> IntMap a
    forall a. Int -> IntMap a -> (IntMap a -> IntMap a) -> IntMap a
    updatePrefix Int
    p2 IntMap a
    t1 ((IntMap a -> IntMap a) -> IntMap a)
    -> (IntMap a -> IntMap a) -> IntMap a
    forall a b. (a -> b) -> a -> b
    $ Nat -> IntMap a -> IntMap a
    forall a. Nat -> IntMap a -> IntMap a
    withoutBM (Nat
    bm2 Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .|. Nat
    lt_minbit Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .|. Nat
    gt_maxbit)
    withoutKeys t1 :: IntMap a
    t1@(Bin Int
    _ Int
    _ IntMap a
    _ IntMap a
    _) IntSet
    IntSet.Nil = IntMap a
    t1
    withoutKeys t1 :: IntMap a
    t1@(Tip Int
    k1 a
    _) IntSet
    t2
        | Int
    k1 Int -> IntSet -> Bool
    `IntSet.member` IntSet
    t2 = IntMap a
    forall a. IntMap a
    Nil
        | Bool
    otherwise = IntMap a
    t1
    withoutKeys IntMap a
    Nil IntSet
    _ = IntMap a
    forall a. IntMap a
    Nil

    updatePrefix
        :: IntSetPrefix -> IntMap a -> (IntMap a -> IntMap a) -> IntMap a
    updatePrefix :: forall a. Int -> IntMap a -> (IntMap a -> IntMap a) -> IntMap a
    updatePrefix !Int
    kp t :: IntMap a
    t@(Bin Int
    p Int
    m IntMap a
    l IntMap a
    r) IntMap a -> IntMap a
    f
        | Int
    m Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.suffixBitMask Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    /= Int
    0 =
            if Int
    p Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.prefixBitMask Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    kp then IntMap a -> IntMap a
    f IntMap a
    t else IntMap a
    t
        | Int -> Int -> Int -> Bool
    nomatch Int
    kp Int
    p Int
    m = IntMap a
    t
        | Int -> Int -> Bool
    zero Int
    kp Int
    m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    p Int
    m (Int -> IntMap a -> (IntMap a -> IntMap a) -> IntMap a
    forall a. Int -> IntMap a -> (IntMap a -> IntMap a) -> IntMap a
    updatePrefix Int
    kp IntMap a
    l IntMap a -> IntMap a
    f) IntMap a
    r
        | Bool
    otherwise      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    p Int
    m IntMap a
    l (Int -> IntMap a -> (IntMap a -> IntMap a) -> IntMap a
    forall a. Int -> IntMap a -> (IntMap a -> IntMap a) -> IntMap a
    updatePrefix Int
    kp IntMap a
    r IntMap a -> IntMap a
    f)
    updatePrefix Int
    kp t :: IntMap a
    t@(Tip Int
    kx a
    _) IntMap a -> IntMap a
    f
        | Int
    kx Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.prefixBitMask Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    kp = IntMap a -> IntMap a
    f IntMap a
    t
        | Bool
    otherwise = IntMap a
    t
    updatePrefix Int
    _ IntMap a
    Nil IntMap a -> IntMap a
    _ = IntMap a
    forall a. IntMap a
    Nil

    withoutBM :: IntSetBitMap -> IntMap a -> IntMap a
    withoutBM :: forall a. Nat -> IntMap a -> IntMap a
    withoutBM Nat
    0 IntMap a
    t = IntMap a
    t
    withoutBM Nat
    bm (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r) =
        let leftBits :: Nat
    leftBits = Int -> Nat
    bitmapOf (Int
    p Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    m) Nat -> Nat -> Nat
    forall a. Num a => a -> a -> a
    - Nat
    1
            bmL :: Nat
    bmL = Nat
    bm Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .&. Nat
    leftBits
            bmR :: Nat
    bmR = Nat
    bm Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    `xor` Nat
    bmL -- = (bm .&. complement leftBits)
        in  Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m (Nat -> IntMap a -> IntMap a
    forall a. Nat -> IntMap a -> IntMap a
    withoutBM Nat
    bmL IntMap a
    l) (Nat -> IntMap a -> IntMap a
    forall a. Nat -> IntMap a -> IntMap a
    withoutBM Nat
    bmR IntMap a
    r)
    withoutBM Nat
    bm t :: IntMap a
    t@(Tip Int
    k a
    _)
        -- TODO(wrengr): need we manually inline 'IntSet.Member' here?
        | Int
    k Int -> IntSet -> Bool
    `IntSet.member` Int -> Nat -> IntSet
    IntSet.Tip (Int
    k Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.prefixBitMask) Nat
    bm = IntMap a
    forall a. IntMap a
    Nil
        | Bool
    otherwise = IntMap a
    t
    withoutBM Nat
    _ IntMap a
    Nil = IntMap a
    forall a. IntMap a
    Nil

    {--------------------------------------------------------------------
      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 :: forall a b. IntMap a -> IntMap b -> IntMap a
    intersection IntMap a
    m1 IntMap b
    m2
      = (Int -> Int -> IntMap a -> IntMap a -> IntMap a)
    -> (IntMap a -> IntMap b -> IntMap a)
    -> (IntMap a -> IntMap a)
    -> (IntMap b -> IntMap a)
    -> IntMap a
    -> IntMap b
    -> IntMap a
    forall c a b.
    (Int -> Int -> IntMap c -> IntMap c -> IntMap c)
    -> (IntMap a -> IntMap b -> IntMap c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    mergeWithKey' Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin IntMap a -> IntMap b -> IntMap a
    forall a b. a -> b -> a
    const (IntMap a -> IntMap a -> IntMap a
    forall a b. a -> b -> a
    const IntMap a
    forall a. IntMap a
    Nil) (IntMap a -> IntMap b -> IntMap a
    forall a b. a -> b -> a
    const IntMap a
    forall a. IntMap a
    Nil) IntMap a
    m1 IntMap b
    m2

    -- TODO(wrengr): re-verify that asymptotic bound
    -- | \(O(n+m)\). The restriction of a map to the keys in a set.
    --
    -- @
    -- m \`restrictKeys\` s = 'filterWithKey' (\\k _ -> k ``IntSet.member`` s) m
    -- @
    --
    -- @since 0.5.8
    restrictKeys :: IntMap a -> IntSet.IntSet -> IntMap a
    restrictKeys :: forall a. IntMap a -> IntSet -> IntMap a
    restrictKeys t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1) t2 :: IntSet
    t2@(IntSet.Bin Int
    p2 Int
    m2 IntSet
    l2 IntSet
    r2)
        | Int -> Int -> Bool
    shorter Int
    m1 Int
    m2  = IntMap a
    intersection1
        | Int -> Int -> Bool
    shorter Int
    m2 Int
    m1  = IntMap a
    intersection2
        | Int
    p1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    p2       = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p1 Int
    m1 (IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    restrictKeys IntMap a
    l1 IntSet
    l2) (IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    restrictKeys IntMap a
    r1 IntSet
    r2)
        | Bool
    otherwise      = IntMap a
    forall a. IntMap a
    Nil
        where
        intersection1 :: IntMap a
    intersection1
            | Int -> Int -> Int -> Bool
    nomatch Int
    p2 Int
    p1 Int
    m1  = IntMap a
    forall a. IntMap a
    Nil
            | Int -> Int -> Bool
    zero Int
    p2 Int
    m1        = IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    restrictKeys IntMap a
    l1 IntSet
    t2
            | Bool
    otherwise         = IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    restrictKeys IntMap a
    r1 IntSet
    t2
        intersection2 :: IntMap a
    intersection2
            | Int -> Int -> Int -> Bool
    nomatch Int
    p1 Int
    p2 Int
    m2  = IntMap a
    forall a. IntMap a
    Nil
            | Int -> Int -> Bool
    zero Int
    p1 Int
    m2        = IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    restrictKeys IntMap a
    t1 IntSet
    l2
            | Bool
    otherwise         = IntMap a -> IntSet -> IntMap a
    forall a. IntMap a -> IntSet -> IntMap a
    restrictKeys IntMap a
    t1 IntSet
    r2
    restrictKeys t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    _ IntMap a
    _) (IntSet.Tip Int
    p2 Nat
    bm2) =
        let minbit :: Nat
    minbit = Int -> Nat
    bitmapOf Int
    p1
            ge_minbit :: Nat
    ge_minbit = Nat -> Nat
    forall a. Bits a => a -> a
    complement (Nat
    minbit Nat -> Nat -> Nat
    forall a. Num a => a -> a -> a
    - Nat
    1)
            maxbit :: Nat
    maxbit = Int -> Nat
    bitmapOf (Int
    p1 Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. (Int
    m1 Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. (Int
    m1 Int -> Int -> Int
    forall a. Num a => a -> a -> a
    - Int
    1)))
            le_maxbit :: Nat
    le_maxbit = Nat
    maxbit Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .|. (Nat
    maxbit Nat -> Nat -> Nat
    forall a. Num a => a -> a -> a
    - Nat
    1)
        -- TODO(wrengr): should we manually inline/unroll 'lookupPrefix'
        -- and 'restrictBM' here, in order to avoid redundant case analyses?
        in Nat -> IntMap a -> IntMap a
    forall a. Nat -> IntMap a -> IntMap a
    restrictBM (Nat
    bm2 Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .&. Nat
    ge_minbit Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .&. Nat
    le_maxbit) (Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> IntMap a
    lookupPrefix Int
    p2 IntMap a
    t1)
    restrictKeys (Bin Int
    _ Int
    _ IntMap a
    _ IntMap a
    _) IntSet
    IntSet.Nil = IntMap a
    forall a. IntMap a
    Nil
    restrictKeys t1 :: IntMap a
    t1@(Tip Int
    k1 a
    _) IntSet
    t2
        | Int
    k1 Int -> IntSet -> Bool
    `IntSet.member` IntSet
    t2 = IntMap a
    t1
        | Bool
    otherwise = IntMap a
    forall a. IntMap a
    Nil
    restrictKeys IntMap a
    Nil IntSet
    _ = IntMap a
    forall a. IntMap a
    Nil

    -- | \(O(\min(n,W))\). Restrict to the sub-map with all keys matching
    -- a key prefix.
    lookupPrefix :: IntSetPrefix -> IntMap a -> IntMap a
    lookupPrefix :: forall a. Int -> IntMap a -> IntMap a
    lookupPrefix !Int
    kp t :: IntMap a
    t@(Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
        | Int
    m Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.suffixBitMask Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    /= Int
    0 =
            if Int
    p Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.prefixBitMask Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    kp then IntMap a
    t else IntMap a
    forall a. IntMap a
    Nil
        | Int -> Int -> Int -> Bool
    nomatch Int
    kp Int
    p Int
    m = IntMap a
    forall a. IntMap a
    Nil
        | Int -> Int -> Bool
    zero Int
    kp Int
    m      = Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> IntMap a
    lookupPrefix Int
    kp IntMap a
    l
        | Bool
    otherwise      = Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> IntMap a
    lookupPrefix Int
    kp IntMap a
    r
    lookupPrefix Int
    kp t :: IntMap a
    t@(Tip Int
    kx a
    _)
        | (Int
    kx Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.prefixBitMask) Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    kp = IntMap a
    t
        | Bool
    otherwise = IntMap a
    forall a. IntMap a
    Nil
    lookupPrefix Int
    _ IntMap a
    Nil = IntMap a
    forall a. IntMap a
    Nil

    restrictBM :: IntSetBitMap -> IntMap a -> IntMap a
    restrictBM :: forall a. Nat -> IntMap a -> IntMap a
    restrictBM Nat
    0 IntMap a
    _ = IntMap a
    forall a. IntMap a
    Nil
    restrictBM Nat
    bm (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r) =
        let leftBits :: Nat
    leftBits = Int -> Nat
    bitmapOf (Int
    p Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .|. Int
    m) Nat -> Nat -> Nat
    forall a. Num a => a -> a -> a
    - Nat
    1
            bmL :: Nat
    bmL = Nat
    bm Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .&. Nat
    leftBits
            bmR :: Nat
    bmR = Nat
    bm Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    `xor` Nat
    bmL -- = (bm .&. complement leftBits)
        in  Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m (Nat -> IntMap a -> IntMap a
    forall a. Nat -> IntMap a -> IntMap a
    restrictBM Nat
    bmL IntMap a
    l) (Nat -> IntMap a -> IntMap a
    forall a. Nat -> IntMap a -> IntMap a
    restrictBM Nat
    bmR IntMap a
    r)
    restrictBM Nat
    bm t :: IntMap a
    t@(Tip Int
    k a
    _)
        -- TODO(wrengr): need we manually inline 'IntSet.Member' here?
        | Int
    k Int -> IntSet -> Bool
    `IntSet.member` Int -> Nat -> IntSet
    IntSet.Tip (Int
    k Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.prefixBitMask) Nat
    bm = IntMap a
    t
        | Bool
    otherwise = IntMap a
    forall a. IntMap a
    Nil
    restrictBM Nat
    _ IntMap a
    Nil = IntMap a
    forall a. IntMap a
    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 :: forall a b c. (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
    intersectionWith a -> b -> c
    f IntMap a
    m1 IntMap b
    m2
      = (Int -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
    forall a b c.
    (Int -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
    intersectionWithKey (\Int
    _ a
    x b
    y -> a -> b -> c
    f a
    x b
    y) IntMap a
    m1 IntMap b
    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 :: forall a b c.
    (Int -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
    intersectionWithKey Int -> a -> b -> c
    f IntMap a
    m1 IntMap b
    m2
      = (Int -> Int -> IntMap c -> IntMap c -> IntMap c)
    -> (IntMap a -> IntMap b -> IntMap c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    forall c a b.
    (Int -> Int -> IntMap c -> IntMap c -> IntMap c)
    -> (IntMap a -> IntMap b -> IntMap c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    mergeWithKey' Int -> Int -> IntMap c -> IntMap c -> IntMap c
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin (\(Tip Int
    k1 a
    x1) (Tip Int
    _k2 b
    x2) -> Int -> c -> IntMap c
    forall a. Int -> a -> IntMap a
    Tip Int
    k1 (Int -> a -> b -> c
    f Int
    k1 a
    x1 b
    x2)) (IntMap c -> IntMap a -> IntMap c
    forall a b. a -> b -> a
    const IntMap c
    forall a. IntMap a
    Nil) (IntMap c -> IntMap b -> IntMap c
    forall a b. a -> b -> a
    const IntMap c
    forall a. IntMap a
    Nil) IntMap a
    m1 IntMap b
    m2

    {--------------------------------------------------------------------
      MergeWithKey
    --------------------------------------------------------------------}

    -- | \(O(n+m)\). A high-performance universal combining function. Using
    -- 'mergeWithKey', all combining functions can be defined without any loss of
    -- efficiency (with exception of 'union', 'difference' and 'intersection',
    -- where sharing of some nodes is lost with 'mergeWithKey').
    --
    -- Please make sure you know what is going on when using 'mergeWithKey',
    -- otherwise you can be surprised by unexpected code growth or even
    -- corruption of the data structure.
    --
    -- When 'mergeWithKey' is given three arguments, it is inlined to the call
    -- site. You should therefore use 'mergeWithKey' only to define your custom
    -- combining functions. For example, you could define 'unionWithKey',
    -- 'differenceWithKey' and 'intersectionWithKey' as
    --
    -- > myUnionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) id id m1 m2
    -- > myDifferenceWithKey f m1 m2 = mergeWithKey f id (const empty) m1 m2
    -- > myIntersectionWithKey f m1 m2 = mergeWithKey (\k x1 x2 -> Just (f k x1 x2)) (const empty) (const empty) m1 m2
    --
    -- When calling @'mergeWithKey' combine only1 only2@, a function combining two
    -- 'IntMap's is created, such that
    --
    -- * if a key is present in both maps, it is passed with both corresponding
    --   values to the @combine@ function. Depending on the result, the key is either
    --   present in the result with specified value, or is left out;
    --
    -- * a nonempty subtree present only in the first map is passed to @only1@ and
    --   the output is added to the result;
    --
    -- * a nonempty subtree present only in the second map is passed to @only2@ and
    --   the output is added to the result.
    --
    -- The @only1@ and @only2@ methods /must return a map with a subset (possibly empty) of the keys of the given map/.
    -- The values can be modified arbitrarily. Most common variants of @only1@ and
    -- @only2@ are 'id' and @'const' 'empty'@, but for example @'map' f@ or
    -- @'filterWithKey' f@ could be used for any @f@.

    mergeWithKey :: (Key -> a -> b -> Maybe c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c)
                 -> IntMap a -> IntMap b -> IntMap c
    mergeWithKey :: forall a b c.
    (Int -> a -> b -> Maybe c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    mergeWithKey Int -> a -> b -> Maybe c
    f IntMap a -> IntMap c
    g1 IntMap b -> IntMap c
    g2 = (Int -> Int -> IntMap c -> IntMap c -> IntMap c)
    -> (IntMap a -> IntMap b -> IntMap c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    forall c a b.
    (Int -> Int -> IntMap c -> IntMap c -> IntMap c)
    -> (IntMap a -> IntMap b -> IntMap c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    mergeWithKey' Int -> Int -> IntMap c -> IntMap c -> IntMap c
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin IntMap a -> IntMap b -> IntMap c
    combine IntMap a -> IntMap c
    g1 IntMap b -> IntMap c
    g2
      where -- We use the lambda form to avoid non-exhaustive pattern matches warning.
            combine :: IntMap a -> IntMap b -> IntMap c
    combine = \(Tip Int
    k1 a
    x1) (Tip Int
    _k2 b
    x2) ->
              case Int -> a -> b -> Maybe c
    f Int
    k1 a
    x1 b
    x2 of
                Maybe c
    Nothing -> IntMap c
    forall a. IntMap a
    Nil
                Just c
    x -> Int -> c -> IntMap c
    forall a. Int -> a -> IntMap a
    Tip Int
    k1 c
    x
            {-# INLINE combine #-}
    {-# INLINE mergeWithKey #-}

    -- Slightly more general version of mergeWithKey. It differs in the following:
    --
    -- * the combining function operates on maps instead of keys and values. The
    --   reason is to enable sharing in union, difference and intersection.
    --
    -- * mergeWithKey' is given an equivalent of bin. The reason is that in union*,
    --   Bin constructor can be used, because we know both subtrees are nonempty.

    mergeWithKey' :: (Prefix -> Mask -> IntMap c -> IntMap c -> IntMap c)
                  -> (IntMap a -> IntMap b -> IntMap c) -> (IntMap a -> IntMap c) -> (IntMap b -> IntMap c)
                  -> IntMap a -> IntMap b -> IntMap c
    mergeWithKey' :: forall c a b.
    (Int -> Int -> IntMap c -> IntMap c -> IntMap c)
    -> (IntMap a -> IntMap b -> IntMap c)
    -> (IntMap a -> IntMap c)
    -> (IntMap b -> IntMap c)
    -> IntMap a
    -> IntMap b
    -> IntMap c
    mergeWithKey' Int -> Int -> IntMap c -> IntMap c -> IntMap c
    bin' IntMap a -> IntMap b -> IntMap c
    f IntMap a -> IntMap c
    g1 IntMap b -> IntMap c
    g2 = IntMap a -> IntMap b -> IntMap c
    go
      where
        go :: IntMap a -> IntMap b -> IntMap c
    go t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1) t2 :: IntMap b
    t2@(Bin Int
    p2 Int
    m2 IntMap b
    l2 IntMap b
    r2)
          | Int -> Int -> Bool
    shorter Int
    m1 Int
    m2  = IntMap c
    merge1
          | Int -> Int -> Bool
    shorter Int
    m2 Int
    m1  = IntMap c
    merge2
          | Int
    p1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    p2       = Int -> Int -> IntMap c -> IntMap c -> IntMap c
    bin' Int
    p1 Int
    m1 (IntMap a -> IntMap b -> IntMap c
    go IntMap a
    l1 IntMap b
    l2) (IntMap a -> IntMap b -> IntMap c
    go IntMap a
    r1 IntMap b
    r2)
          | Bool
    otherwise      = Int -> IntMap c -> Int -> IntMap c -> IntMap c
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    maybe_link Int
    p1 (IntMap a -> IntMap c
    g1 IntMap a
    t1) Int
    p2 (IntMap b -> IntMap c
    g2 IntMap b
    t2)
          where
            merge1 :: IntMap c
    merge1 | Int -> Int -> Int -> Bool
    nomatch Int
    p2 Int
    p1 Int
    m1  = Int -> IntMap c -> Int -> IntMap c -> IntMap c
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    maybe_link Int
    p1 (IntMap a -> IntMap c
    g1 IntMap a
    t1) Int
    p2 (IntMap b -> IntMap c
    g2 IntMap b
    t2)
                   | Int -> Int -> Bool
    zero Int
    p2 Int
    m1        = Int -> Int -> IntMap c -> IntMap c -> IntMap c
    bin' Int
    p1 Int
    m1 (IntMap a -> IntMap b -> IntMap c
    go IntMap a
    l1 IntMap b
    t2) (IntMap a -> IntMap c
    g1 IntMap a
    r1)
                   | Bool
    otherwise         = Int -> Int -> IntMap c -> IntMap c -> IntMap c
    bin' Int
    p1 Int
    m1 (IntMap a -> IntMap c
    g1 IntMap a
    l1) (IntMap a -> IntMap b -> IntMap c
    go IntMap a
    r1 IntMap b
    t2)
            merge2 :: IntMap c
    merge2 | Int -> Int -> Int -> Bool
    nomatch Int
    p1 Int
    p2 Int
    m2  = Int -> IntMap c -> Int -> IntMap c -> IntMap c
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    maybe_link Int
    p1 (IntMap a -> IntMap c
    g1 IntMap a
    t1) Int
    p2 (IntMap b -> IntMap c
    g2 IntMap b
    t2)
                   | Int -> Int -> Bool
    zero Int
    p1 Int
    m2        = Int -> Int -> IntMap c -> IntMap c -> IntMap c
    bin' Int
    p2 Int
    m2 (IntMap a -> IntMap b -> IntMap c
    go IntMap a
    t1 IntMap b
    l2) (IntMap b -> IntMap c
    g2 IntMap b
    r2)
                   | Bool
    otherwise         = Int -> Int -> IntMap c -> IntMap c -> IntMap c
    bin' Int
    p2 Int
    m2 (IntMap b -> IntMap c
    g2 IntMap b
    l2) (IntMap a -> IntMap b -> IntMap c
    go IntMap a
    t1 IntMap b
    r2)

        go t1' :: IntMap a
    t1'@(Bin Int
    _ Int
    _ IntMap a
    _ IntMap a
    _) t2' :: IntMap b
    t2'@(Tip Int
    k2' b
    _) = IntMap b -> Int -> IntMap a -> IntMap c
    merge0 IntMap b
    t2' Int
    k2' IntMap a
    t1'
          where
            merge0 :: IntMap b -> Int -> IntMap a -> IntMap c
    merge0 IntMap b
    t2 Int
    k2 t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1)
              | Int -> Int -> Int -> Bool
    nomatch Int
    k2 Int
    p1 Int
    m1 = Int -> IntMap c -> Int -> IntMap c -> IntMap c
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    maybe_link Int
    p1 (IntMap a -> IntMap c
    g1 IntMap a
    t1) Int
    k2 (IntMap b -> IntMap c
    g2 IntMap b
    t2)
              | Int -> Int -> Bool
    zero Int
    k2 Int
    m1 = Int -> Int -> IntMap c -> IntMap c -> IntMap c
    bin' Int
    p1 Int
    m1 (IntMap b -> Int -> IntMap a -> IntMap c
    merge0 IntMap b
    t2 Int
    k2 IntMap a
    l1) (IntMap a -> IntMap c
    g1 IntMap a
    r1)
              | Bool
    otherwise  = Int -> Int -> IntMap c -> IntMap c -> IntMap c
    bin' Int
    p1 Int
    m1 (IntMap a -> IntMap c
    g1 IntMap a
    l1) (IntMap b -> Int -> IntMap a -> IntMap c
    merge0 IntMap b
    t2 Int
    k2 IntMap a
    r1)
            merge0 IntMap b
    t2 Int
    k2 t1 :: IntMap a
    t1@(Tip Int
    k1 a
    _)
              | Int
    k1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    k2 = IntMap a -> IntMap b -> IntMap c
    f IntMap a
    t1 IntMap b
    t2
              | Bool
    otherwise = Int -> IntMap c -> Int -> IntMap c -> IntMap c
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    maybe_link Int
    k1 (IntMap a -> IntMap c
    g1 IntMap a
    t1) Int
    k2 (IntMap b -> IntMap c
    g2 IntMap b
    t2)
            merge0 IntMap b
    t2 Int
    _  IntMap a
    Nil = IntMap b -> IntMap c
    g2 IntMap b
    t2

        go t1 :: IntMap a
    t1@(Bin Int
    _ Int
    _ IntMap a
    _ IntMap a
    _) IntMap b
    Nil = IntMap a -> IntMap c
    g1 IntMap a
    t1

        go t1' :: IntMap a
    t1'@(Tip Int
    k1' a
    _) IntMap b
    t2' = IntMap a -> Int -> IntMap b -> IntMap c
    merge0 IntMap a
    t1' Int
    k1' IntMap b
    t2'
          where
            merge0 :: IntMap a -> Int -> IntMap b -> IntMap c
    merge0 IntMap a
    t1 Int
    k1 t2 :: IntMap b
    t2@(Bin Int
    p2 Int
    m2 IntMap b
    l2 IntMap b
    r2)
              | Int -> Int -> Int -> Bool
    nomatch Int
    k1 Int
    p2 Int
    m2 = Int -> IntMap c -> Int -> IntMap c -> IntMap c
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    maybe_link Int
    k1 (IntMap a -> IntMap c
    g1 IntMap a
    t1) Int
    p2 (IntMap b -> IntMap c
    g2 IntMap b
    t2)
              | Int -> Int -> Bool
    zero Int
    k1 Int
    m2 = Int -> Int -> IntMap c -> IntMap c -> IntMap c
    bin' Int
    p2 Int
    m2 (IntMap a -> Int -> IntMap b -> IntMap c
    merge0 IntMap a
    t1 Int
    k1 IntMap b
    l2) (IntMap b -> IntMap c
    g2 IntMap b
    r2)
              | Bool
    otherwise  = Int -> Int -> IntMap c -> IntMap c -> IntMap c
    bin' Int
    p2 Int
    m2 (IntMap b -> IntMap c
    g2 IntMap b
    l2) (IntMap a -> Int -> IntMap b -> IntMap c
    merge0 IntMap a
    t1 Int
    k1 IntMap b
    r2)
            merge0 IntMap a
    t1 Int
    k1 t2 :: IntMap b
    t2@(Tip Int
    k2 b
    _)
              | Int
    k1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    k2 = IntMap a -> IntMap b -> IntMap c
    f IntMap a
    t1 IntMap b
    t2
              | Bool
    otherwise = Int -> IntMap c -> Int -> IntMap c -> IntMap c
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    maybe_link Int
    k1 (IntMap a -> IntMap c
    g1 IntMap a
    t1) Int
    k2 (IntMap b -> IntMap c
    g2 IntMap b
    t2)
            merge0 IntMap a
    t1 Int
    _  IntMap b
    Nil = IntMap a -> IntMap c
    g1 IntMap a
    t1

        go IntMap a
    Nil IntMap b
    t2 = IntMap b -> IntMap c
    g2 IntMap b
    t2

        maybe_link :: Int -> IntMap a -> Int -> IntMap a -> IntMap a
    maybe_link Int
    _ IntMap a
    Nil Int
    _ IntMap a
    t2 = IntMap a
    t2
        maybe_link Int
    _ IntMap a
    t1 Int
    _ IntMap a
    Nil = IntMap a
    t1
        maybe_link Int
    p1 IntMap a
    t1 Int
    p2 IntMap a
    t2 = Int -> IntMap a -> Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    p1 IntMap a
    t1 Int
    p2 IntMap a
    t2
        {-# INLINE maybe_link #-}
    {-# INLINE mergeWithKey' #-}

    {--------------------------------------------------------------------
      mergeA
    --------------------------------------------------------------------}

    -- | A tactic for dealing with keys present in one map but not the
    -- other in 'merge' or 'mergeA'.
    --
    -- A tactic of type @WhenMissing f k x z@ is an abstract representation
    -- of a function of type @Key -> x -> f (Maybe z)@.
    --
    -- @since 0.5.9

    data WhenMissing f x y = WhenMissing
      { forall (f :: * -> *) x y.
    WhenMissing f x y -> IntMap x -> f (IntMap y)
    missingSubtree :: IntMap x -> f (IntMap y)
      , forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey :: Key -> x -> f (Maybe y)}

    -- | @since 0.5.9
    instance (Applicative f, Monad f) => Functor (WhenMissing f x) where
      fmap :: forall a b. (a -> b) -> WhenMissing f x a -> WhenMissing f x b
    fmap = (a -> b) -> WhenMissing f x a -> WhenMissing f x b
    forall (f :: * -> *) a b x.
    (Applicative f, Monad f) =>
    (a -> b) -> WhenMissing f x a -> WhenMissing f x b
    mapWhenMissing
      {-# INLINE fmap #-}

    -- | @since 0.5.9
    instance (Applicative f, Monad f) => Category.Category (WhenMissing f)
      where
        id :: forall a. WhenMissing f a a
    id = WhenMissing f a a
    forall (f :: * -> *) x. Applicative f => WhenMissing f x x
    preserveMissing
        WhenMissing f b c
    f . :: forall b c a.
    WhenMissing f b c -> WhenMissing f a b -> WhenMissing f a c
    . WhenMissing f a b
    g =
          (Int -> a -> f (Maybe c)) -> WhenMissing f a c
    forall (f :: * -> *) x y.
    Applicative f =>
    (Int -> x -> f (Maybe y)) -> WhenMissing f x y
    traverseMaybeMissing ((Int -> a -> f (Maybe c)) -> WhenMissing f a c)
    -> (Int -> a -> f (Maybe c)) -> WhenMissing f a c
    forall a b. (a -> b) -> a -> b
    $ \ Int
    k a
    x -> do
            y <- WhenMissing f a b -> Int -> a -> f (Maybe b)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey WhenMissing f a b
    g Int
    k a
    x
            case y of
              Maybe b
    Nothing -> Maybe c -> f (Maybe c)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Maybe c
    forall a. Maybe a
    Nothing
              Just b
    q  -> WhenMissing f b c -> Int -> b -> f (Maybe c)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey WhenMissing f b c
    f Int
    k b
    q
        {-# INLINE id #-}
        {-# INLINE (.) #-}

    -- | Equivalent to @ReaderT k (ReaderT x (MaybeT f))@.
    --
    -- @since 0.5.9
    instance (Applicative f, Monad f) => Applicative (WhenMissing f x) where
      pure :: forall a. a -> WhenMissing f x a
    pure a
    x = (Int -> x -> a) -> WhenMissing f x a
    forall (f :: * -> *) x y.
    Applicative f =>
    (Int -> x -> y) -> WhenMissing f x y
    mapMissing (\ Int
    _ x
    _ -> a
    x)
      WhenMissing f x (a -> b)
    f <*> :: forall a b.
    WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b
    <*> WhenMissing f x a
    g =
        (Int -> x -> f (Maybe b)) -> WhenMissing f x b
    forall (f :: * -> *) x y.
    Applicative f =>
    (Int -> x -> f (Maybe y)) -> WhenMissing f x y
    traverseMaybeMissing ((Int -> x -> f (Maybe b)) -> WhenMissing f x b)
    -> (Int -> x -> f (Maybe b)) -> WhenMissing f x b
    forall a b. (a -> b) -> a -> b
    $ \Int
    k x
    x -> do
          res1 <- WhenMissing f x (a -> b) -> Int -> x -> f (Maybe (a -> b))
    forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey WhenMissing f x (a -> b)
    f Int
    k x
    x
          case res1 of
            Maybe (a -> b)
    Nothing -> Maybe b -> f (Maybe b)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Maybe b
    forall a. Maybe a
    Nothing
            Just a -> b
    r  -> (Maybe b -> f (Maybe b)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (Maybe b -> f (Maybe b)) -> Maybe b -> f (Maybe b)
    forall a b. (a -> b) -> a -> b
    $!) (Maybe b -> f (Maybe b))
    -> (Maybe a -> Maybe b) -> Maybe a -> f (Maybe b)
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a -> b) -> Maybe a -> Maybe b
    forall a b. (a -> b) -> Maybe a -> Maybe b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap a -> b
    r (Maybe a -> f (Maybe b)) -> f (Maybe a) -> f (Maybe b)
    forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
    =<< WhenMissing f x a -> Int -> x -> f (Maybe a)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey WhenMissing f x a
    g Int
    k x
    x
      {-# INLINE pure #-}
      {-# INLINE (<*>) #-}

    -- | Equivalent to @ReaderT k (ReaderT x (MaybeT f))@.
    --
    -- @since 0.5.9
    instance (Applicative f, Monad f) => Monad (WhenMissing f x) where
      WhenMissing f x a
    m >>= :: forall a b.
    WhenMissing f x a -> (a -> WhenMissing f x b) -> WhenMissing f x b
    >>= a -> WhenMissing f x b
    f =
        (Int -> x -> f (Maybe b)) -> WhenMissing f x b
    forall (f :: * -> *) x y.
    Applicative f =>
    (Int -> x -> f (Maybe y)) -> WhenMissing f x y
    traverseMaybeMissing ((Int -> x -> f (Maybe b)) -> WhenMissing f x b)
    -> (Int -> x -> f (Maybe b)) -> WhenMissing f x b
    forall a b. (a -> b) -> a -> b
    $ \Int
    k x
    x -> do
          res1 <- WhenMissing f x a -> Int -> x -> f (Maybe a)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey WhenMissing f x a
    m Int
    k x
    x
          case res1 of
            Maybe a
    Nothing -> Maybe b -> f (Maybe b)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Maybe b
    forall a. Maybe a
    Nothing
            Just a
    r  -> WhenMissing f x b -> Int -> x -> f (Maybe b)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey (a -> WhenMissing f x b
    f a
    r) Int
    k x
    x
      {-# INLINE (>>=) #-}

    -- | Map covariantly over a @'WhenMissing' f x@.
    --
    -- @since 0.5.9
    mapWhenMissing
      :: (Applicative f, Monad f)
      => (a -> b)
      -> WhenMissing f x a
      -> WhenMissing f x b
    mapWhenMissing :: forall (f :: * -> *) a b x.
    (Applicative f, Monad f) =>
    (a -> b) -> WhenMissing f x a -> WhenMissing f x b
    mapWhenMissing a -> b
    f WhenMissing f x a
    t = WhenMissing
      { missingSubtree :: IntMap x -> f (IntMap b)
    missingSubtree = \IntMap x
    m -> WhenMissing f x a -> IntMap x -> f (IntMap a)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> IntMap x -> f (IntMap y)
    missingSubtree WhenMissing f x a
    t IntMap x
    m f (IntMap a) -> (IntMap a -> f (IntMap b)) -> f (IntMap b)
    forall a b. f a -> (a -> f b) -> f b
    forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
    >>= \IntMap a
    m' -> IntMap b -> f (IntMap b)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (IntMap b -> f (IntMap b)) -> IntMap b -> f (IntMap b)
    forall a b. (a -> b) -> a -> b
    $! (a -> b) -> IntMap a -> IntMap b
    forall a b. (a -> b) -> IntMap a -> IntMap b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap a -> b
    f IntMap a
    m'
      , missingKey :: Int -> x -> f (Maybe b)
    missingKey     = \Int
    k x
    x -> WhenMissing f x a -> Int -> x -> f (Maybe a)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey WhenMissing f x a
    t Int
    k x
    x f (Maybe a) -> (Maybe a -> f (Maybe b)) -> f (Maybe b)
    forall a b. f a -> (a -> f b) -> f b
    forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
    >>= \Maybe a
    q -> (Maybe b -> f (Maybe b)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (Maybe b -> f (Maybe b)) -> Maybe b -> f (Maybe b)
    forall a b. (a -> b) -> a -> b
    $! (a -> b) -> Maybe a -> Maybe b
    forall a b. (a -> b) -> Maybe a -> Maybe b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap a -> b
    f Maybe a
    q) }
    {-# INLINE mapWhenMissing #-}

    -- | Map covariantly over a @'WhenMissing' f x@, using only a
    -- 'Functor f' constraint.
    mapGentlyWhenMissing
      :: Functor f
      => (a -> b)
      -> WhenMissing f x a
      -> WhenMissing f x b
    mapGentlyWhenMissing :: forall (f :: * -> *) a b x.
    Functor f =>
    (a -> b) -> WhenMissing f x a -> WhenMissing f x b
    mapGentlyWhenMissing a -> b
    f WhenMissing f x a
    t = WhenMissing
      { missingSubtree :: IntMap x -> f (IntMap b)
    missingSubtree = \IntMap x
    m -> (a -> b) -> IntMap a -> IntMap b
    forall a b. (a -> b) -> IntMap a -> IntMap b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap a -> b
    f (IntMap a -> IntMap b) -> f (IntMap a) -> f (IntMap b)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> WhenMissing f x a -> IntMap x -> f (IntMap a)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> IntMap x -> f (IntMap y)
    missingSubtree WhenMissing f x a
    t IntMap x
    m
      , missingKey :: Int -> x -> f (Maybe b)
    missingKey     = \Int
    k x
    x -> (a -> b) -> Maybe a -> Maybe b
    forall a b. (a -> b) -> Maybe a -> Maybe b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap a -> b
    f (Maybe a -> Maybe b) -> f (Maybe a) -> f (Maybe b)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> WhenMissing f x a -> Int -> x -> f (Maybe a)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey WhenMissing f x a
    t Int
    k x
    x }
    {-# INLINE mapGentlyWhenMissing #-}

    -- | Map covariantly over a @'WhenMatched' f k x@, using only a
    -- 'Functor f' constraint.
    mapGentlyWhenMatched
      :: Functor f
      => (a -> b)
      -> WhenMatched f x y a
      -> WhenMatched f x y b
    mapGentlyWhenMatched :: forall (f :: * -> *) a b x y.
    Functor f =>
    (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b
    mapGentlyWhenMatched a -> b
    f WhenMatched f x y a
    t =
      (Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b
    forall x y (f :: * -> *) z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    zipWithMaybeAMatched ((Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b)
    -> (Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b
    forall a b. (a -> b) -> a -> b
    $ \Int
    k x
    x y
    y -> (a -> b) -> Maybe a -> Maybe b
    forall a b. (a -> b) -> Maybe a -> Maybe b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap a -> b
    f (Maybe a -> Maybe b) -> f (Maybe a) -> f (Maybe b)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> WhenMatched f x y a -> Int -> x -> y -> f (Maybe a)
    forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    runWhenMatched WhenMatched f x y a
    t Int
    k x
    x y
    y
    {-# INLINE mapGentlyWhenMatched #-}

    -- | Map contravariantly over a @'WhenMissing' f _ x@.
    --
    -- @since 0.5.9
    lmapWhenMissing :: (b -> a) -> WhenMissing f a x -> WhenMissing f b x
    lmapWhenMissing :: forall b a (f :: * -> *) x.
    (b -> a) -> WhenMissing f a x -> WhenMissing f b x
    lmapWhenMissing b -> a
    f WhenMissing f a x
    t = WhenMissing
      { missingSubtree :: IntMap b -> f (IntMap x)
    missingSubtree = \IntMap b
    m -> WhenMissing f a x -> IntMap a -> f (IntMap x)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> IntMap x -> f (IntMap y)
    missingSubtree WhenMissing f a x
    t ((b -> a) -> IntMap b -> IntMap a
    forall a b. (a -> b) -> IntMap a -> IntMap b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap b -> a
    f IntMap b
    m)
      , missingKey :: Int -> b -> f (Maybe x)
    missingKey     = \Int
    k b
    x -> WhenMissing f a x -> Int -> a -> f (Maybe x)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey WhenMissing f a x
    t Int
    k (b -> a
    f b
    x) }
    {-# INLINE lmapWhenMissing #-}

    -- | Map contravariantly over a @'WhenMatched' f _ y z@.
    --
    -- @since 0.5.9
    contramapFirstWhenMatched
      :: (b -> a)
      -> WhenMatched f a y z
      -> WhenMatched f b y z
    contramapFirstWhenMatched :: forall b a (f :: * -> *) y z.
    (b -> a) -> WhenMatched f a y z -> WhenMatched f b y z
    contramapFirstWhenMatched b -> a
    f WhenMatched f a y z
    t =
      (Int -> b -> y -> f (Maybe z)) -> WhenMatched f b y z
    forall (f :: * -> *) x y z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    WhenMatched ((Int -> b -> y -> f (Maybe z)) -> WhenMatched f b y z)
    -> (Int -> b -> y -> f (Maybe z)) -> WhenMatched f b y z
    forall a b. (a -> b) -> a -> b
    $ \Int
    k b
    x y
    y -> WhenMatched f a y z -> Int -> a -> y -> f (Maybe z)
    forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    runWhenMatched WhenMatched f a y z
    t Int
    k (b -> a
    f b
    x) y
    y
    {-# INLINE contramapFirstWhenMatched #-}

    -- | Map contravariantly over a @'WhenMatched' f x _ z@.
    --
    -- @since 0.5.9
    contramapSecondWhenMatched
      :: (b -> a)
      -> WhenMatched f x a z
      -> WhenMatched f x b z
    contramapSecondWhenMatched :: forall b a (f :: * -> *) x z.
    (b -> a) -> WhenMatched f x a z -> WhenMatched f x b z
    contramapSecondWhenMatched b -> a
    f WhenMatched f x a z
    t =
      (Int -> x -> b -> f (Maybe z)) -> WhenMatched f x b z
    forall (f :: * -> *) x y z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    WhenMatched ((Int -> x -> b -> f (Maybe z)) -> WhenMatched f x b z)
    -> (Int -> x -> b -> f (Maybe z)) -> WhenMatched f x b z
    forall a b. (a -> b) -> a -> b
    $ \Int
    k x
    x b
    y -> WhenMatched f x a z -> Int -> x -> a -> f (Maybe z)
    forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    runWhenMatched WhenMatched f x a z
    t Int
    k x
    x (b -> a
    f b
    y)
    {-# INLINE contramapSecondWhenMatched #-}

    -- | A tactic for dealing with keys present in one map but not the
    -- other in 'merge'.
    --
    -- A tactic of type @SimpleWhenMissing x z@ is an abstract
    -- representation of a function of type @Key -> x -> Maybe z@.
    --
    -- @since 0.5.9
    type SimpleWhenMissing = WhenMissing Identity

    -- | A tactic for dealing with keys present in both maps in 'merge'
    -- or 'mergeA'.
    --
    -- A tactic of type @WhenMatched f x y z@ is an abstract representation
    -- of a function of type @Key -> x -> y -> f (Maybe z)@.
    --
    -- @since 0.5.9
    newtype WhenMatched f x y z = WhenMatched
      { forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    matchedKey :: Key -> x -> y -> f (Maybe z) }

    -- | Along with zipWithMaybeAMatched, witnesses the isomorphism
    -- between @WhenMatched f x y z@ and @Key -> x -> y -> f (Maybe z)@.
    --
    -- @since 0.5.9
    runWhenMatched :: WhenMatched f x y z -> Key -> x -> y -> f (Maybe z)
    runWhenMatched :: forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    runWhenMatched = WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    matchedKey
    {-# INLINE runWhenMatched #-}

    -- | Along with traverseMaybeMissing, witnesses the isomorphism
    -- between @WhenMissing f x y@ and @Key -> x -> f (Maybe y)@.
    --
    -- @since 0.5.9
    runWhenMissing :: WhenMissing f x y -> Key-> x -> f (Maybe y)
    runWhenMissing :: forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    runWhenMissing = WhenMissing f x y -> Int -> x -> f (Maybe y)
    forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey
    {-# INLINE runWhenMissing #-}

    -- | @since 0.5.9
    instance Functor f => Functor (WhenMatched f x y) where
      fmap :: forall a b. (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b
    fmap = (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b
    forall (f :: * -> *) a b x y.
    Functor f =>
    (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b
    mapWhenMatched
      {-# INLINE fmap #-}

    -- | @since 0.5.9
    instance (Monad f, Applicative f) => Category.Category (WhenMatched f x)
      where
        id :: forall a. WhenMatched f x a a
    id = (Int -> x -> a -> a) -> WhenMatched f x a a
    forall (f :: * -> *) x y z.
    Applicative f =>
    (Int -> x -> y -> z) -> WhenMatched f x y z
    zipWithMatched (\Int
    _ x
    _ a
    y -> a
    y)
        WhenMatched f x b c
    f . :: forall b c a.
    WhenMatched f x b c -> WhenMatched f x a b -> WhenMatched f x a c
    . WhenMatched f x a b
    g =
          (Int -> x -> a -> f (Maybe c)) -> WhenMatched f x a c
    forall x y (f :: * -> *) z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    zipWithMaybeAMatched ((Int -> x -> a -> f (Maybe c)) -> WhenMatched f x a c)
    -> (Int -> x -> a -> f (Maybe c)) -> WhenMatched f x a c
    forall a b. (a -> b) -> a -> b
    $ \Int
    k x
    x a
    y -> do
            res <- WhenMatched f x a b -> Int -> x -> a -> f (Maybe b)
    forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    runWhenMatched WhenMatched f x a b
    g Int
    k x
    x a
    y
            case res of
              Maybe b
    Nothing -> Maybe c -> f (Maybe c)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Maybe c
    forall a. Maybe a
    Nothing
              Just b
    r  -> WhenMatched f x b c -> Int -> x -> b -> f (Maybe c)
    forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    runWhenMatched WhenMatched f x b c
    f Int
    k x
    x b
    r
        {-# INLINE id #-}
        {-# INLINE (.) #-}

    -- | Equivalent to @ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))@
    --
    -- @since 0.5.9
    instance (Monad f, Applicative f) => Applicative (WhenMatched f x y) where
      pure :: forall a. a -> WhenMatched f x y a
    pure a
    x = (Int -> x -> y -> a) -> WhenMatched f x y a
    forall (f :: * -> *) x y z.
    Applicative f =>
    (Int -> x -> y -> z) -> WhenMatched f x y z
    zipWithMatched (\Int
    _ x
    _ y
    _ -> a
    x)
      WhenMatched f x y (a -> b)
    fs <*> :: forall a b.
    WhenMatched f x y (a -> b)
    -> WhenMatched f x y a -> WhenMatched f x y b
    <*> WhenMatched f x y a
    xs =
        (Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b
    forall x y (f :: * -> *) z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    zipWithMaybeAMatched ((Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b)
    -> (Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b
    forall a b. (a -> b) -> a -> b
    $ \Int
    k x
    x y
    y -> do
          res <- WhenMatched f x y (a -> b) -> Int -> x -> y -> f (Maybe (a -> b))
    forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    runWhenMatched WhenMatched f x y (a -> b)
    fs Int
    k x
    x y
    y
          case res of
            Maybe (a -> b)
    Nothing -> Maybe b -> f (Maybe b)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Maybe b
    forall a. Maybe a
    Nothing
            Just a -> b
    r  -> (Maybe b -> f (Maybe b)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (Maybe b -> f (Maybe b)) -> Maybe b -> f (Maybe b)
    forall a b. (a -> b) -> a -> b
    $!) (Maybe b -> f (Maybe b))
    -> (Maybe a -> Maybe b) -> Maybe a -> f (Maybe b)
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (a -> b) -> Maybe a -> Maybe b
    forall a b. (a -> b) -> Maybe a -> Maybe b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap a -> b
    r (Maybe a -> f (Maybe b)) -> f (Maybe a) -> f (Maybe b)
    forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
    =<< WhenMatched f x y a -> Int -> x -> y -> f (Maybe a)
    forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    runWhenMatched WhenMatched f x y a
    xs Int
    k x
    x y
    y
      {-# INLINE pure #-}
      {-# INLINE (<*>) #-}

    -- | Equivalent to @ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))@
    --
    -- @since 0.5.9
    instance (Monad f, Applicative f) => Monad (WhenMatched f x y) where
      WhenMatched f x y a
    m >>= :: forall a b.
    WhenMatched f x y a
    -> (a -> WhenMatched f x y b) -> WhenMatched f x y b
    >>= a -> WhenMatched f x y b
    f =
        (Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b
    forall x y (f :: * -> *) z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    zipWithMaybeAMatched ((Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b)
    -> (Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b
    forall a b. (a -> b) -> a -> b
    $ \Int
    k x
    x y
    y -> do
          res <- WhenMatched f x y a -> Int -> x -> y -> f (Maybe a)
    forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    runWhenMatched WhenMatched f x y a
    m Int
    k x
    x y
    y
          case res of
            Maybe a
    Nothing -> Maybe b -> f (Maybe b)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Maybe b
    forall a. Maybe a
    Nothing
            Just a
    r  -> WhenMatched f x y b -> Int -> x -> y -> f (Maybe b)
    forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    runWhenMatched (a -> WhenMatched f x y b
    f a
    r) Int
    k x
    x y
    y
      {-# INLINE (>>=) #-}

    -- | Map covariantly over a @'WhenMatched' f x y@.
    --
    -- @since 0.5.9
    mapWhenMatched
      :: Functor f
      => (a -> b)
      -> WhenMatched f x y a
      -> WhenMatched f x y b
    mapWhenMatched :: forall (f :: * -> *) a b x y.
    Functor f =>
    (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b
    mapWhenMatched a -> b
    f (WhenMatched Int -> x -> y -> f (Maybe a)
    g) =
      (Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b
    forall (f :: * -> *) x y z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    WhenMatched ((Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b)
    -> (Int -> x -> y -> f (Maybe b)) -> WhenMatched f x y b
    forall a b. (a -> b) -> a -> b
    $ \Int
    k x
    x y
    y -> (Maybe a -> Maybe b) -> f (Maybe a) -> f (Maybe b)
    forall a b. (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap ((a -> b) -> Maybe a -> Maybe b
    forall a b. (a -> b) -> Maybe a -> Maybe b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap a -> b
    f) (Int -> x -> y -> f (Maybe a)
    g Int
    k x
    x y
    y)
    {-# INLINE mapWhenMatched #-}

    -- | A tactic for dealing with keys present in both maps in 'merge'.
    --
    -- A tactic of type @SimpleWhenMatched x y z@ is an abstract
    -- representation of a function of type @Key -> x -> y -> Maybe z@.
    --
    -- @since 0.5.9
    type SimpleWhenMatched = WhenMatched Identity

    -- | When a key is found in both maps, apply a function to the key
    -- and values and use the result in the merged map.
    --
    -- > zipWithMatched
    -- >   :: (Key -> x -> y -> z)
    -- >   -> SimpleWhenMatched x y z
    --
    -- @since 0.5.9
    zipWithMatched
      :: Applicative f
      => (Key -> x -> y -> z)
      -> WhenMatched f x y z
    zipWithMatched :: forall (f :: * -> *) x y z.
    Applicative f =>
    (Int -> x -> y -> z) -> WhenMatched f x y z
    zipWithMatched Int -> x -> y -> z
    f = (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    forall (f :: * -> *) x y z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    WhenMatched ((Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z)
    -> (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    forall a b. (a -> b) -> a -> b
    $ \ Int
    k x
    x y
    y -> Maybe z -> f (Maybe z)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (Maybe z -> f (Maybe z)) -> (z -> Maybe z) -> z -> f (Maybe z)
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . z -> Maybe z
    forall a. a -> Maybe a
    Just (z -> f (Maybe z)) -> z -> f (Maybe z)
    forall a b. (a -> b) -> a -> b
    $ Int -> x -> y -> z
    f Int
    k x
    x y
    y
    {-# INLINE zipWithMatched #-}

    -- | When a key is found in both maps, apply a function to the key
    -- and values to produce an action and use its result in the merged
    -- map.
    --
    -- @since 0.5.9
    zipWithAMatched
      :: Applicative f
      => (Key -> x -> y -> f z)
      -> WhenMatched f x y z
    zipWithAMatched :: forall (f :: * -> *) x y z.
    Applicative f =>
    (Int -> x -> y -> f z) -> WhenMatched f x y z
    zipWithAMatched Int -> x -> y -> f z
    f = (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    forall (f :: * -> *) x y z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    WhenMatched ((Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z)
    -> (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    forall a b. (a -> b) -> a -> b
    $ \ Int
    k x
    x y
    y -> z -> Maybe z
    forall a. a -> Maybe a
    Just (z -> Maybe z) -> f z -> f (Maybe z)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Int -> x -> y -> f z
    f Int
    k x
    x y
    y
    {-# INLINE zipWithAMatched #-}

    -- | When a key is found in both maps, apply a function to the key
    -- and values and maybe use the result in the merged map.
    --
    -- > zipWithMaybeMatched
    -- >   :: (Key -> x -> y -> Maybe z)
    -- >   -> SimpleWhenMatched x y z
    --
    -- @since 0.5.9
    zipWithMaybeMatched
      :: Applicative f
      => (Key -> x -> y -> Maybe z)
      -> WhenMatched f x y z
    zipWithMaybeMatched :: forall (f :: * -> *) x y z.
    Applicative f =>
    (Int -> x -> y -> Maybe z) -> WhenMatched f x y z
    zipWithMaybeMatched Int -> x -> y -> Maybe z
    f = (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    forall (f :: * -> *) x y z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    WhenMatched ((Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z)
    -> (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    forall a b. (a -> b) -> a -> b
    $ \ Int
    k x
    x y
    y -> Maybe z -> f (Maybe z)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (Maybe z -> f (Maybe z)) -> Maybe z -> f (Maybe z)
    forall a b. (a -> b) -> a -> b
    $ Int -> x -> y -> Maybe z
    f Int
    k x
    x y
    y
    {-# INLINE zipWithMaybeMatched #-}

    -- | When a key is found in both maps, apply a function to the key
    -- and values, perform the resulting action, and maybe use the
    -- result in the merged map.
    --
    -- This is the fundamental 'WhenMatched' tactic.
    --
    -- @since 0.5.9
    zipWithMaybeAMatched
      :: (Key -> x -> y -> f (Maybe z))
      -> WhenMatched f x y z
    zipWithMaybeAMatched :: forall x y (f :: * -> *) z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    zipWithMaybeAMatched Int -> x -> y -> f (Maybe z)
    f = (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    forall (f :: * -> *) x y z.
    (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    WhenMatched ((Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z)
    -> (Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
    forall a b. (a -> b) -> a -> b
    $ \ Int
    k x
    x y
    y -> Int -> x -> y -> f (Maybe z)
    f Int
    k x
    x y
    y
    {-# INLINE zipWithMaybeAMatched #-}

    -- | Drop all the entries whose keys are missing from the other
    -- map.
    --
    -- > dropMissing :: SimpleWhenMissing x y
    --
    -- prop> dropMissing = mapMaybeMissing (\_ _ -> Nothing)
    --
    -- but @dropMissing@ is much faster.
    --
    -- @since 0.5.9
    dropMissing :: Applicative f => WhenMissing f x y
    dropMissing :: forall (f :: * -> *) x y. Applicative f => WhenMissing f x y
    dropMissing = WhenMissing
      { missingSubtree :: IntMap x -> f (IntMap y)
    missingSubtree = f (IntMap y) -> IntMap x -> f (IntMap y)
    forall a b. a -> b -> a
    const (IntMap y -> f (IntMap y)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure IntMap y
    forall a. IntMap a
    Nil)
      , missingKey :: Int -> x -> f (Maybe y)
    missingKey     = \Int
    _ x
    _ -> Maybe y -> f (Maybe y)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Maybe y
    forall a. Maybe a
    Nothing }
    {-# INLINE dropMissing #-}

    -- | Preserve, unchanged, the entries whose keys are missing from
    -- the other map.
    --
    -- > preserveMissing :: SimpleWhenMissing x x
    --
    -- prop> preserveMissing = Merge.Lazy.mapMaybeMissing (\_ x -> Just x)
    --
    -- but @preserveMissing@ is much faster.
    --
    -- @since 0.5.9
    preserveMissing :: Applicative f => WhenMissing f x x
    preserveMissing :: forall (f :: * -> *) x. Applicative f => WhenMissing f x x
    preserveMissing = WhenMissing
      { missingSubtree :: IntMap x -> f (IntMap x)
    missingSubtree = IntMap x -> f (IntMap x)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure
      , missingKey :: Int -> x -> f (Maybe x)
    missingKey     = \Int
    _ x
    v -> Maybe x -> f (Maybe x)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (x -> Maybe x
    forall a. a -> Maybe a
    Just x
    v) }
    {-# INLINE preserveMissing #-}

    -- | Map over the entries whose keys are missing from the other map.
    --
    -- > mapMissing :: (k -> x -> y) -> SimpleWhenMissing x y
    --
    -- prop> mapMissing f = mapMaybeMissing (\k x -> Just $ f k x)
    --
    -- but @mapMissing@ is somewhat faster.
    --
    -- @since 0.5.9
    mapMissing :: Applicative f => (Key -> x -> y) -> WhenMissing f x y
    mapMissing :: forall (f :: * -> *) x y.
    Applicative f =>
    (Int -> x -> y) -> WhenMissing f x y
    mapMissing Int -> x -> y
    f = WhenMissing
      { missingSubtree :: IntMap x -> f (IntMap y)
    missingSubtree = \IntMap x
    m -> IntMap y -> f (IntMap y)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (IntMap y -> f (IntMap y)) -> IntMap y -> f (IntMap y)
    forall a b. (a -> b) -> a -> b
    $! (Int -> x -> y) -> IntMap x -> IntMap y
    forall a b. (Int -> a -> b) -> IntMap a -> IntMap b
    mapWithKey Int -> x -> y
    f IntMap x
    m
      , missingKey :: Int -> x -> f (Maybe y)
    missingKey     = \Int
    k x
    x -> Maybe y -> f (Maybe y)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (Maybe y -> f (Maybe y)) -> Maybe y -> f (Maybe y)
    forall a b. (a -> b) -> a -> b
    $ y -> Maybe y
    forall a. a -> Maybe a
    Just (Int -> x -> y
    f Int
    k x
    x) }
    {-# INLINE mapMissing #-}

    -- | Map over the entries whose keys are missing from the other
    -- map, optionally removing some. This is the most powerful
    -- 'SimpleWhenMissing' tactic, but others are usually more efficient.
    --
    -- > mapMaybeMissing :: (Key -> x -> Maybe y) -> SimpleWhenMissing x y
    --
    -- prop> mapMaybeMissing f = traverseMaybeMissing (\k x -> pure (f k x))
    --
    -- but @mapMaybeMissing@ uses fewer unnecessary 'Applicative'
    -- operations.
    --
    -- @since 0.5.9
    mapMaybeMissing
      :: Applicative f => (Key -> x -> Maybe y) -> WhenMissing f x y
    mapMaybeMissing :: forall (f :: * -> *) x y.
    Applicative f =>
    (Int -> x -> Maybe y) -> WhenMissing f x y
    mapMaybeMissing Int -> x -> Maybe y
    f = WhenMissing
      { missingSubtree :: IntMap x -> f (IntMap y)
    missingSubtree = \IntMap x
    m -> IntMap y -> f (IntMap y)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (IntMap y -> f (IntMap y)) -> IntMap y -> f (IntMap y)
    forall a b. (a -> b) -> a -> b
    $! (Int -> x -> Maybe y) -> IntMap x -> IntMap y
    forall a b. (Int -> a -> Maybe b) -> IntMap a -> IntMap b
    mapMaybeWithKey Int -> x -> Maybe y
    f IntMap x
    m
      , missingKey :: Int -> x -> f (Maybe y)
    missingKey     = \Int
    k x
    x -> Maybe y -> f (Maybe y)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (Maybe y -> f (Maybe y)) -> Maybe y -> f (Maybe y)
    forall a b. (a -> b) -> a -> b
    $! Int -> x -> Maybe y
    f Int
    k x
    x }
    {-# INLINE mapMaybeMissing #-}

    -- | Filter the entries whose keys are missing from the other map.
    --
    -- > filterMissing :: (k -> x -> Bool) -> SimpleWhenMissing x x
    --
    -- prop> filterMissing f = Merge.Lazy.mapMaybeMissing $ \k x -> guard (f k x) *> Just x
    --
    -- but this should be a little faster.
    --
    -- @since 0.5.9
    filterMissing
      :: Applicative f => (Key -> x -> Bool) -> WhenMissing f x x
    filterMissing :: forall (f :: * -> *) x.
    Applicative f =>
    (Int -> x -> Bool) -> WhenMissing f x x
    filterMissing Int -> x -> Bool
    f = WhenMissing
      { missingSubtree :: IntMap x -> f (IntMap x)
    missingSubtree = \IntMap x
    m -> IntMap x -> f (IntMap x)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (IntMap x -> f (IntMap x)) -> IntMap x -> f (IntMap x)
    forall a b. (a -> b) -> a -> b
    $! (Int -> x -> Bool) -> IntMap x -> IntMap x
    forall a. (Int -> a -> Bool) -> IntMap a -> IntMap a
    filterWithKey Int -> x -> Bool
    f IntMap x
    m
      , missingKey :: Int -> x -> f (Maybe x)
    missingKey     = \Int
    k x
    x -> Maybe x -> f (Maybe x)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (Maybe x -> f (Maybe x)) -> Maybe x -> f (Maybe x)
    forall a b. (a -> b) -> a -> b
    $! if Int -> x -> Bool
    f Int
    k x
    x then x -> Maybe x
    forall a. a -> Maybe a
    Just x
    x else Maybe x
    forall a. Maybe a
    Nothing }
    {-# INLINE filterMissing #-}

    -- | Filter the entries whose keys are missing from the other map
    -- using some 'Applicative' action.
    --
    -- > filterAMissing f = Merge.Lazy.traverseMaybeMissing $
    -- >   \k x -> (\b -> guard b *> Just x) <$> f k x
    --
    -- but this should be a little faster.
    --
    -- @since 0.5.9
    filterAMissing
      :: Applicative f => (Key -> x -> f Bool) -> WhenMissing f x x
    filterAMissing :: forall (f :: * -> *) x.
    Applicative f =>
    (Int -> x -> f Bool) -> WhenMissing f x x
    filterAMissing Int -> x -> f Bool
    f = WhenMissing
      { missingSubtree :: IntMap x -> f (IntMap x)
    missingSubtree = \IntMap x
    m -> (Int -> x -> f Bool) -> IntMap x -> f (IntMap x)
    forall (f :: * -> *) a.
    Applicative f =>
    (Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
    filterWithKeyA Int -> x -> f Bool
    f IntMap x
    m
      , missingKey :: Int -> x -> f (Maybe x)
    missingKey     = \Int
    k x
    x -> Maybe x -> Maybe x -> Bool -> Maybe x
    forall a. a -> a -> Bool -> a
    bool Maybe x
    forall a. Maybe a
    Nothing (x -> Maybe x
    forall a. a -> Maybe a
    Just x
    x) (Bool -> Maybe x) -> f Bool -> f (Maybe x)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Int -> x -> f Bool
    f Int
    k x
    x }
    {-# INLINE filterAMissing #-}

    -- | \(O(n)\). Filter keys and values using an 'Applicative' predicate.
    filterWithKeyA
      :: Applicative f => (Key -> a -> f Bool) -> IntMap a -> f (IntMap a)
    filterWithKeyA :: forall (f :: * -> *) a.
    Applicative f =>
    (Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
    filterWithKeyA Int -> a -> f Bool
    _ IntMap a
    Nil           = IntMap a -> f (IntMap a)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure IntMap a
    forall a. IntMap a
    Nil
    filterWithKeyA Int -> a -> f Bool
    f t :: IntMap a
    t@(Tip Int
    k a
    x)   = (\Bool
    b -> if Bool
    b then IntMap a
    t else IntMap a
    forall a. IntMap a
    Nil) (Bool -> IntMap a) -> f Bool -> f (IntMap a)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Int -> a -> f Bool
    f Int
    k a
    x
    filterWithKeyA Int -> a -> f Bool
    f (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = (IntMap a -> IntMap a -> IntMap a)
    -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    forall a b c. (a -> b -> c) -> f a -> f b -> f c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 ((IntMap a -> IntMap a -> IntMap a)
    -> IntMap a -> IntMap a -> IntMap a
    forall a b c. (a -> b -> c) -> b -> a -> c
    flip (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m)) ((Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
    forall (f :: * -> *) a.
    Applicative f =>
    (Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
    filterWithKeyA Int -> a -> f Bool
    f IntMap a
    r) ((Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
    forall (f :: * -> *) a.
    Applicative f =>
    (Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
    filterWithKeyA Int -> a -> f Bool
    f IntMap a
    l)
      | Bool
    otherwise = (IntMap a -> IntMap a -> IntMap a)
    -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    forall a b c. (a -> b -> c) -> f a -> f b -> f c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m) ((Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
    forall (f :: * -> *) a.
    Applicative f =>
    (Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
    filterWithKeyA Int -> a -> f Bool
    f IntMap a
    l) ((Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
    forall (f :: * -> *) a.
    Applicative f =>
    (Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
    filterWithKeyA Int -> a -> f Bool
    f IntMap a
    r)

    -- | This wasn't in Data.Bool until 4.7.0, so we define it here
    bool :: a -> a -> Bool -> a
    bool :: forall a. a -> a -> Bool -> a
    bool a
    f a
    _ Bool
    False = a
    f
    bool a
    _ a
    t Bool
    True  = a
    t

    -- | Traverse over the entries whose keys are missing from the other
    -- map.
    --
    -- @since 0.5.9
    traverseMissing
      :: Applicative f => (Key -> x -> f y) -> WhenMissing f x y
    traverseMissing :: forall (f :: * -> *) x y.
    Applicative f =>
    (Int -> x -> f y) -> WhenMissing f x y
    traverseMissing Int -> x -> f y
    f = WhenMissing
      { missingSubtree :: IntMap x -> f (IntMap y)
    missingSubtree = (Int -> x -> f y) -> IntMap x -> f (IntMap y)
    forall (t :: * -> *) a b.
    Applicative t =>
    (Int -> a -> t b) -> IntMap a -> t (IntMap b)
    traverseWithKey Int -> x -> f y
    f
      , missingKey :: Int -> x -> f (Maybe y)
    missingKey = \Int
    k x
    x -> y -> Maybe y
    forall a. a -> Maybe a
    Just (y -> Maybe y) -> f y -> f (Maybe y)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Int -> x -> f y
    f Int
    k x
    x }
    {-# INLINE traverseMissing #-}

    -- | Traverse over the entries whose keys are missing from the other
    -- map, optionally producing values to put in the result. This is
    -- the most powerful 'WhenMissing' tactic, but others are usually
    -- more efficient.
    --
    -- @since 0.5.9
    traverseMaybeMissing
      :: Applicative f => (Key -> x -> f (Maybe y)) -> WhenMissing f x y
    traverseMaybeMissing :: forall (f :: * -> *) x y.
    Applicative f =>
    (Int -> x -> f (Maybe y)) -> WhenMissing f x y
    traverseMaybeMissing Int -> x -> f (Maybe y)
    f = WhenMissing
      { missingSubtree :: IntMap x -> f (IntMap y)
    missingSubtree = (Int -> x -> f (Maybe y)) -> IntMap x -> f (IntMap y)
    forall (f :: * -> *) a b.
    Applicative f =>
    (Int -> a -> f (Maybe b)) -> IntMap a -> f (IntMap b)
    traverseMaybeWithKey Int -> x -> f (Maybe y)
    f
      , missingKey :: Int -> x -> f (Maybe y)
    missingKey = Int -> x -> f (Maybe y)
    f }
    {-# INLINE traverseMaybeMissing #-}

    -- | \(O(n)\). Traverse keys\/values and collect the 'Just' results.
    --
    -- @since 0.6.4
    traverseMaybeWithKey
      :: Applicative f => (Key -> a -> f (Maybe b)) -> IntMap a -> f (IntMap b)
    traverseMaybeWithKey :: forall (f :: * -> *) a b.
    Applicative f =>
    (Int -> a -> f (Maybe b)) -> IntMap a -> f (IntMap b)
    traverseMaybeWithKey Int -> a -> f (Maybe b)
    f = IntMap a -> f (IntMap b)
    go
        where
        go :: IntMap a -> f (IntMap b)
    go IntMap a
    Nil           = IntMap b -> f (IntMap b)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure IntMap b
    forall a. IntMap a
    Nil
        go (Tip Int
    k a
    x)     = IntMap b -> (b -> IntMap b) -> Maybe b -> IntMap b
    forall b a. b -> (a -> b) -> Maybe a -> b
    maybe IntMap b
    forall a. IntMap a
    Nil (Int -> b -> IntMap b
    forall a. Int -> a -> IntMap a
    Tip Int
    k) (Maybe b -> IntMap b) -> f (Maybe b) -> f (IntMap b)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Int -> a -> f (Maybe b)
    f Int
    k a
    x
        go (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = (IntMap b -> IntMap b -> IntMap b)
    -> f (IntMap b) -> f (IntMap b) -> f (IntMap b)
    forall a b c. (a -> b -> c) -> f a -> f b -> f c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 ((IntMap b -> IntMap b -> IntMap b)
    -> IntMap b -> IntMap b -> IntMap b
    forall a b c. (a -> b -> c) -> b -> a -> c
    flip (Int -> Int -> IntMap b -> IntMap b -> IntMap b
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m)) (IntMap a -> f (IntMap b)
    go IntMap a
    r) (IntMap a -> f (IntMap b)
    go IntMap a
    l)
          | Bool
    otherwise = (IntMap b -> IntMap b -> IntMap b)
    -> f (IntMap b) -> f (IntMap b) -> f (IntMap b)
    forall a b c. (a -> b -> c) -> f a -> f b -> f c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 (Int -> Int -> IntMap b -> IntMap b -> IntMap b
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m) (IntMap a -> f (IntMap b)
    go IntMap a
    l) (IntMap a -> f (IntMap b)
    go IntMap a
    r)

    -- | Merge two maps.
    --
    -- 'merge' takes two 'WhenMissing' tactics, a 'WhenMatched' tactic
    -- and two maps. It uses the tactics to merge the maps. Its behavior
    -- is best understood via its fundamental tactics, 'mapMaybeMissing'
    -- and 'zipWithMaybeMatched'.
    --
    -- Consider
    --
    -- @
    -- merge (mapMaybeMissing g1)
    --              (mapMaybeMissing g2)
    --              (zipWithMaybeMatched f)
    --              m1 m2
    -- @
    --
    -- Take, for example,
    --
    -- @
    -- m1 = [(0, \'a\'), (1, \'b\'), (3, \'c\'), (4, \'d\')]
    -- m2 = [(1, "one"), (2, "two"), (4, "three")]
    -- @
    --
    -- 'merge' will first \"align\" these maps by key:
    --
    -- @
    -- m1 = [(0, \'a\'), (1, \'b\'),               (3, \'c\'), (4, \'d\')]
    -- m2 =           [(1, "one"), (2, "two"),           (4, "three")]
    -- @
    --
    -- It will then pass the individual entries and pairs of entries
    -- to @g1@, @g2@, or @f@ as appropriate:
    --
    -- @
    -- maybes = [g1 0 \'a\', f 1 \'b\' "one", g2 2 "two", g1 3 \'c\', f 4 \'d\' "three"]
    -- @
    --
    -- This produces a 'Maybe' for each key:
    --
    -- @
    -- keys =     0        1          2           3        4
    -- results = [Nothing, Just True, Just False, Nothing, Just True]
    -- @
    --
    -- Finally, the @Just@ results are collected into a map:
    --
    -- @
    -- return value = [(1, True), (2, False), (4, True)]
    -- @
    --
    -- The other tactics below are optimizations or simplifications of
    -- 'mapMaybeMissing' for special cases. Most importantly,
    --
    -- * 'dropMissing' drops all the keys.
    -- * 'preserveMissing' leaves all the entries alone.
    --
    -- When 'merge' is given three arguments, it is inlined at the call
    -- site. To prevent excessive inlining, you should typically use
    -- 'merge' to define your custom combining functions.
    --
    --
    -- Examples:
    --
    -- prop> unionWithKey f = merge preserveMissing preserveMissing (zipWithMatched f)
    -- prop> intersectionWithKey f = merge dropMissing dropMissing (zipWithMatched f)
    -- prop> differenceWith f = merge diffPreserve diffDrop f
    -- prop> symmetricDifference = merge diffPreserve diffPreserve (\ _ _ _ -> Nothing)
    -- prop> mapEachPiece f g h = merge (diffMapWithKey f) (diffMapWithKey g)
    --
    -- @since 0.5.9
    merge
      :: SimpleWhenMissing a c -- ^ What to do with keys in @m1@ but not @m2@
      -> SimpleWhenMissing b c -- ^ What to do with keys in @m2@ but not @m1@
      -> SimpleWhenMatched a b c -- ^ What to do with keys in both @m1@ and @m2@
      -> IntMap a -- ^ Map @m1@
      -> IntMap b -- ^ Map @m2@
      -> IntMap c
    merge :: forall a c b.
    SimpleWhenMissing a c
    -> SimpleWhenMissing b c
    -> SimpleWhenMatched a b c
    -> IntMap a
    -> IntMap b
    -> IntMap c
    merge SimpleWhenMissing a c
    g1 SimpleWhenMissing b c
    g2 SimpleWhenMatched a b c
    f IntMap a
    m1 IntMap b
    m2 =
      Identity (IntMap c) -> IntMap c
    forall a. Identity a -> a
    runIdentity (Identity (IntMap c) -> IntMap c)
    -> Identity (IntMap c) -> IntMap c
    forall a b. (a -> b) -> a -> b
    $ SimpleWhenMissing a c
    -> SimpleWhenMissing b c
    -> SimpleWhenMatched a b c
    -> IntMap a
    -> IntMap b
    -> Identity (IntMap c)
    forall (f :: * -> *) a c b.
    Applicative f =>
    WhenMissing f a c
    -> WhenMissing f b c
    -> WhenMatched f a b c
    -> IntMap a
    -> IntMap b
    -> f (IntMap c)
    mergeA SimpleWhenMissing a c
    g1 SimpleWhenMissing b c
    g2 SimpleWhenMatched a b c
    f IntMap a
    m1 IntMap b
    m2
    {-# INLINE merge #-}

    -- | An applicative version of 'merge'.
    --
    -- 'mergeA' takes two 'WhenMissing' tactics, a 'WhenMatched'
    -- tactic and two maps. It uses the tactics to merge the maps.
    -- Its behavior is best understood via its fundamental tactics,
    -- 'traverseMaybeMissing' and 'zipWithMaybeAMatched'.
    --
    -- Consider
    --
    -- @
    -- mergeA (traverseMaybeMissing g1)
    --               (traverseMaybeMissing g2)
    --               (zipWithMaybeAMatched f)
    --               m1 m2
    -- @
    --
    -- Take, for example,
    --
    -- @
    -- m1 = [(0, \'a\'), (1, \'b\'), (3,\'c\'), (4, \'d\')]
    -- m2 = [(1, "one"), (2, "two"), (4, "three")]
    -- @
    --
    -- 'mergeA' will first \"align\" these maps by key:
    --
    -- @
    -- m1 = [(0, \'a\'), (1, \'b\'),               (3, \'c\'), (4, \'d\')]
    -- m2 =           [(1, "one"), (2, "two"),           (4, "three")]
    -- @
    --
    -- It will then pass the individual entries and pairs of entries
    -- to @g1@, @g2@, or @f@ as appropriate:
    --
    -- @
    -- actions = [g1 0 \'a\', f 1 \'b\' "one", g2 2 "two", g1 3 \'c\', f 4 \'d\' "three"]
    -- @
    --
    -- Next, it will perform the actions in the @actions@ list in order from
    -- left to right.
    --
    -- @
    -- keys =     0        1          2           3        4
    -- results = [Nothing, Just True, Just False, Nothing, Just True]
    -- @
    --
    -- Finally, the @Just@ results are collected into a map:
    --
    -- @
    -- return value = [(1, True), (2, False), (4, True)]
    -- @
    --
    -- The other tactics below are optimizations or simplifications of
    -- 'traverseMaybeMissing' for special cases. Most importantly,
    --
    -- * 'dropMissing' drops all the keys.
    -- * 'preserveMissing' leaves all the entries alone.
    -- * 'mapMaybeMissing' does not use the 'Applicative' context.
    --
    -- When 'mergeA' is given three arguments, it is inlined at the call
    -- site. To prevent excessive inlining, you should generally only use
    -- 'mergeA' to define custom combining functions.
    --
    -- @since 0.5.9
    mergeA
      :: (Applicative f)
      => WhenMissing f a c -- ^ What to do with keys in @m1@ but not @m2@
      -> WhenMissing f b c -- ^ What to do with keys in @m2@ but not @m1@
      -> WhenMatched f a b c -- ^ What to do with keys in both @m1@ and @m2@
      -> IntMap a -- ^ Map @m1@
      -> IntMap b -- ^ Map @m2@
      -> f (IntMap c)
    mergeA :: forall (f :: * -> *) a c b.
    Applicative f =>
    WhenMissing f a c
    -> WhenMissing f b c
    -> WhenMatched f a b c
    -> IntMap a
    -> IntMap b
    -> f (IntMap c)
    mergeA
        WhenMissing{missingSubtree :: forall (f :: * -> *) x y.
    WhenMissing f x y -> IntMap x -> f (IntMap y)
    missingSubtree = IntMap a -> f (IntMap c)
    g1t, missingKey :: forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey = Int -> a -> f (Maybe c)
    g1k}
        WhenMissing{missingSubtree :: forall (f :: * -> *) x y.
    WhenMissing f x y -> IntMap x -> f (IntMap y)
    missingSubtree = IntMap b -> f (IntMap c)
    g2t, missingKey :: forall (f :: * -> *) x y.
    WhenMissing f x y -> Int -> x -> f (Maybe y)
    missingKey = Int -> b -> f (Maybe c)
    g2k}
        WhenMatched{matchedKey :: forall (f :: * -> *) x y z.
    WhenMatched f x y z -> Int -> x -> y -> f (Maybe z)
    matchedKey = Int -> a -> b -> f (Maybe c)
    f}
        = IntMap a -> IntMap b -> f (IntMap c)
    go
      where
        go :: IntMap a -> IntMap b -> f (IntMap c)
    go IntMap a
    t1  IntMap b
    Nil = IntMap a -> f (IntMap c)
    g1t IntMap a
    t1
        go IntMap a
    Nil IntMap b
    t2  = IntMap b -> f (IntMap c)
    g2t IntMap b
    t2

        -- This case is already covered below.
        -- go (Tip k1 x1) (Tip k2 x2) = mergeTips k1 x1 k2 x2

        go (Tip Int
    k1 a
    x1) IntMap b
    t2' = IntMap b -> f (IntMap c)
    merge2 IntMap b
    t2'
          where
            merge2 :: IntMap b -> f (IntMap c)
    merge2 t2 :: IntMap b
    t2@(Bin Int
    p2 Int
    m2 IntMap b
    l2 IntMap b
    r2)
              | Int -> Int -> Int -> Bool
    nomatch Int
    k1 Int
    p2 Int
    m2 = Int -> f (IntMap c) -> Int -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> f (IntMap a) -> Int -> f (IntMap a) -> f (IntMap a)
    linkA Int
    k1 ((Int -> a -> f (Maybe c)) -> Int -> a -> f (IntMap c)
    forall {f :: * -> *} {t} {a}.
    Functor f =>
    (Int -> t -> f (Maybe a)) -> Int -> t -> f (IntMap a)
    subsingletonBy Int -> a -> f (Maybe c)
    g1k Int
    k1 a
    x1) Int
    p2 (IntMap b -> f (IntMap c)
    g2t IntMap b
    t2)
              | Int -> Int -> Bool
    zero Int
    k1 Int
    m2       = Int -> Int -> f (IntMap c) -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p2 Int
    m2 (IntMap b -> f (IntMap c)
    merge2 IntMap b
    l2) (IntMap b -> f (IntMap c)
    g2t IntMap b
    r2)
              | Bool
    otherwise        = Int -> Int -> f (IntMap c) -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p2 Int
    m2 (IntMap b -> f (IntMap c)
    g2t IntMap b
    l2) (IntMap b -> f (IntMap c)
    merge2 IntMap b
    r2)
            merge2 (Tip Int
    k2 b
    x2)   = Int -> a -> Int -> b -> f (IntMap c)
    mergeTips Int
    k1 a
    x1 Int
    k2 b
    x2
            merge2 IntMap b
    Nil           = (Int -> a -> f (Maybe c)) -> Int -> a -> f (IntMap c)
    forall {f :: * -> *} {t} {a}.
    Functor f =>
    (Int -> t -> f (Maybe a)) -> Int -> t -> f (IntMap a)
    subsingletonBy Int -> a -> f (Maybe c)
    g1k Int
    k1 a
    x1

        go IntMap a
    t1' (Tip Int
    k2 b
    x2) = IntMap a -> f (IntMap c)
    merge1 IntMap a
    t1'
          where
            merge1 :: IntMap a -> f (IntMap c)
    merge1 t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1)
              | Int -> Int -> Int -> Bool
    nomatch Int
    k2 Int
    p1 Int
    m1 = Int -> f (IntMap c) -> Int -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> f (IntMap a) -> Int -> f (IntMap a) -> f (IntMap a)
    linkA Int
    p1 (IntMap a -> f (IntMap c)
    g1t IntMap a
    t1) Int
    k2 ((Int -> b -> f (Maybe c)) -> Int -> b -> f (IntMap c)
    forall {f :: * -> *} {t} {a}.
    Functor f =>
    (Int -> t -> f (Maybe a)) -> Int -> t -> f (IntMap a)
    subsingletonBy Int -> b -> f (Maybe c)
    g2k Int
    k2 b
    x2)
              | Int -> Int -> Bool
    zero Int
    k2 Int
    m1       = Int -> Int -> f (IntMap c) -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p1 Int
    m1 (IntMap a -> f (IntMap c)
    merge1 IntMap a
    l1) (IntMap a -> f (IntMap c)
    g1t IntMap a
    r1)
              | Bool
    otherwise        = Int -> Int -> f (IntMap c) -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p1 Int
    m1 (IntMap a -> f (IntMap c)
    g1t IntMap a
    l1) (IntMap a -> f (IntMap c)
    merge1 IntMap a
    r1)
            merge1 (Tip Int
    k1 a
    x1)   = Int -> a -> Int -> b -> f (IntMap c)
    mergeTips Int
    k1 a
    x1 Int
    k2 b
    x2
            merge1 IntMap a
    Nil           = (Int -> b -> f (Maybe c)) -> Int -> b -> f (IntMap c)
    forall {f :: * -> *} {t} {a}.
    Functor f =>
    (Int -> t -> f (Maybe a)) -> Int -> t -> f (IntMap a)
    subsingletonBy Int -> b -> f (Maybe c)
    g2k Int
    k2 b
    x2

        go t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1) t2 :: IntMap b
    t2@(Bin Int
    p2 Int
    m2 IntMap b
    l2 IntMap b
    r2)
          | Int -> Int -> Bool
    shorter Int
    m1 Int
    m2  = f (IntMap c)
    merge1
          | Int -> Int -> Bool
    shorter Int
    m2 Int
    m1  = f (IntMap c)
    merge2
          | Int
    p1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    p2       = Int -> Int -> f (IntMap c) -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p1 Int
    m1 (IntMap a -> IntMap b -> f (IntMap c)
    go IntMap a
    l1 IntMap b
    l2) (IntMap a -> IntMap b -> f (IntMap c)
    go IntMap a
    r1 IntMap b
    r2)
          | Bool
    otherwise      = Int -> f (IntMap c) -> Int -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> f (IntMap a) -> Int -> f (IntMap a) -> f (IntMap a)
    linkA Int
    p1 (IntMap a -> f (IntMap c)
    g1t IntMap a
    t1) Int
    p2 (IntMap b -> f (IntMap c)
    g2t IntMap b
    t2)
          where
            merge1 :: f (IntMap c)
    merge1 | Int -> Int -> Int -> Bool
    nomatch Int
    p2 Int
    p1 Int
    m1  = Int -> f (IntMap c) -> Int -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> f (IntMap a) -> Int -> f (IntMap a) -> f (IntMap a)
    linkA Int
    p1 (IntMap a -> f (IntMap c)
    g1t IntMap a
    t1) Int
    p2 (IntMap b -> f (IntMap c)
    g2t IntMap b
    t2)
                   | Int -> Int -> Bool
    zero Int
    p2 Int
    m1        = Int -> Int -> f (IntMap c) -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p1 Int
    m1 (IntMap a -> IntMap b -> f (IntMap c)
    go  IntMap a
    l1 IntMap b
    t2) (IntMap a -> f (IntMap c)
    g1t IntMap a
    r1)
                   | Bool
    otherwise         = Int -> Int -> f (IntMap c) -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p1 Int
    m1 (IntMap a -> f (IntMap c)
    g1t IntMap a
    l1)    (IntMap a -> IntMap b -> f (IntMap c)
    go  IntMap a
    r1 IntMap b
    t2)
            merge2 :: f (IntMap c)
    merge2 | Int -> Int -> Int -> Bool
    nomatch Int
    p1 Int
    p2 Int
    m2  = Int -> f (IntMap c) -> Int -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> f (IntMap a) -> Int -> f (IntMap a) -> f (IntMap a)
    linkA Int
    p1 (IntMap a -> f (IntMap c)
    g1t IntMap a
    t1) Int
    p2 (IntMap b -> f (IntMap c)
    g2t IntMap b
    t2)
                   | Int -> Int -> Bool
    zero Int
    p1 Int
    m2        = Int -> Int -> f (IntMap c) -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p2 Int
    m2 (IntMap a -> IntMap b -> f (IntMap c)
    go  IntMap a
    t1 IntMap b
    l2) (IntMap b -> f (IntMap c)
    g2t    IntMap b
    r2)
                   | Bool
    otherwise         = Int -> Int -> f (IntMap c) -> f (IntMap c) -> f (IntMap c)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p2 Int
    m2 (IntMap b -> f (IntMap c)
    g2t    IntMap b
    l2) (IntMap a -> IntMap b -> f (IntMap c)
    go  IntMap a
    t1 IntMap b
    r2)

        subsingletonBy :: (Int -> t -> f (Maybe a)) -> Int -> t -> f (IntMap a)
    subsingletonBy Int -> t -> f (Maybe a)
    gk Int
    k t
    x = IntMap a -> (a -> IntMap a) -> Maybe a -> IntMap a
    forall b a. b -> (a -> b) -> Maybe a -> b
    maybe IntMap a
    forall a. IntMap a
    Nil (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k) (Maybe a -> IntMap a) -> f (Maybe a) -> f (IntMap a)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Int -> t -> f (Maybe a)
    gk Int
    k t
    x
        {-# INLINE subsingletonBy #-}

        mergeTips :: Int -> a -> Int -> b -> f (IntMap c)
    mergeTips Int
    k1 a
    x1 Int
    k2 b
    x2
          | Int
    k1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    k2  = IntMap c -> (c -> IntMap c) -> Maybe c -> IntMap c
    forall b a. b -> (a -> b) -> Maybe a -> b
    maybe IntMap c
    forall a. IntMap a
    Nil (Int -> c -> IntMap c
    forall a. Int -> a -> IntMap a
    Tip Int
    k1) (Maybe c -> IntMap c) -> f (Maybe c) -> f (IntMap c)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Int -> a -> b -> f (Maybe c)
    f Int
    k1 a
    x1 b
    x2
          | Int
    k1 Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    <  Int
    k2  = (Maybe c -> Maybe c -> IntMap c)
    -> f (Maybe c) -> f (Maybe c) -> f (IntMap c)
    forall a b c. (a -> b -> c) -> f a -> f b -> f c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 (Int -> Int -> Maybe c -> Maybe c -> IntMap c
    forall {a}. Int -> Int -> Maybe a -> Maybe a -> IntMap a
    subdoubleton Int
    k1 Int
    k2) (Int -> a -> f (Maybe c)
    g1k Int
    k1 a
    x1) (Int -> b -> f (Maybe c)
    g2k Int
    k2 b
    x2)
            {-
            = link_ k1 k2 <$> subsingletonBy g1k k1 x1 <*> subsingletonBy g2k k2 x2
            -}
          | Bool
    otherwise = (Maybe c -> Maybe c -> IntMap c)
    -> f (Maybe c) -> f (Maybe c) -> f (IntMap c)
    forall a b c. (a -> b -> c) -> f a -> f b -> f c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 (Int -> Int -> Maybe c -> Maybe c -> IntMap c
    forall {a}. Int -> Int -> Maybe a -> Maybe a -> IntMap a
    subdoubleton Int
    k2 Int
    k1) (Int -> b -> f (Maybe c)
    g2k Int
    k2 b
    x2) (Int -> a -> f (Maybe c)
    g1k Int
    k1 a
    x1)
        {-# INLINE mergeTips #-}

        subdoubleton :: Int -> Int -> Maybe a -> Maybe a -> IntMap a
    subdoubleton Int
    _ Int
    _   Maybe a
    Nothing Maybe a
    Nothing     = IntMap a
    forall a. IntMap a
    Nil
        subdoubleton Int
    _ Int
    k2  Maybe a
    Nothing (Just a
    y2)   = Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k2 a
    y2
        subdoubleton Int
    k1 Int
    _  (Just a
    y1) Maybe a
    Nothing   = Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k1 a
    y1
        subdoubleton Int
    k1 Int
    k2 (Just a
    y1) (Just a
    y2) = Int -> IntMap a -> Int -> IntMap a -> IntMap a
    forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    k1 (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k1 a
    y1) Int
    k2 (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k2 a
    y2)
        {-# INLINE subdoubleton #-}

        -- | A variant of 'link_' which makes sure to execute side-effects
        -- in the right order.
        linkA
            :: Applicative f
            => Prefix -> f (IntMap a)
            -> Prefix -> f (IntMap a)
            -> f (IntMap a)
        linkA :: forall (f :: * -> *) a.
    Applicative f =>
    Int -> f (IntMap a) -> Int -> f (IntMap a) -> f (IntMap a)
    linkA Int
    p1 f (IntMap a)
    t1 Int
    p2 f (IntMap a)
    t2
          | Int -> Int -> Bool
    zero Int
    p1 Int
    m = Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p Int
    m f (IntMap a)
    t1 f (IntMap a)
    t2
          | Bool
    otherwise = Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p Int
    m f (IntMap a)
    t2 f (IntMap a)
    t1
          where
            m :: Int
    m = Int -> Int -> Int
    branchMask Int
    p1 Int
    p2
            p :: Int
    p = Int -> Int -> Int
    mask Int
    p1 Int
    m
        {-# INLINE linkA #-}

        -- A variant of 'bin' that ensures that effects for negative keys are executed
        -- first.
        binA
            :: Applicative f
            => Prefix
            -> Mask
            -> f (IntMap a)
            -> f (IntMap a)
            -> f (IntMap a)
        binA :: forall (f :: * -> *) a.
    Applicative f =>
    Int -> Int -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    binA Int
    p Int
    m f (IntMap a)
    a f (IntMap a)
    b
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = (IntMap a -> IntMap a -> IntMap a)
    -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    forall a b c. (a -> b -> c) -> f a -> f b -> f c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 ((IntMap a -> IntMap a -> IntMap a)
    -> IntMap a -> IntMap a -> IntMap a
    forall a b c. (a -> b -> c) -> b -> a -> c
    flip (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m)) f (IntMap a)
    b f (IntMap a)
    a
          | Bool
    otherwise = (IntMap a -> IntMap a -> IntMap a)
    -> f (IntMap a) -> f (IntMap a) -> f (IntMap a)
    forall a b c. (a -> b -> c) -> f a -> f b -> f c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2       (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m)  f (IntMap a)
    a f (IntMap a)
    b
        {-# INLINE binA #-}
    {-# INLINE mergeA #-}

    {--------------------------------------------------------------------
      Min\/Max
    --------------------------------------------------------------------}

    -- | \(O(\min(n,W))\). 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 -> Maybe a) -> IntMap a -> IntMap a
    updateMinWithKey :: forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    updateMinWithKey Int -> a -> Maybe a
    f IntMap a
    t =
      case IntMap a
    t of Bin Int
    p Int
    m IntMap a
    l IntMap a
    r | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    p Int
    m IntMap a
    l ((Int -> a -> Maybe a) -> IntMap a -> IntMap a
    forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    go Int -> a -> Maybe a
    f IntMap a
    r)
                IntMap a
    _ -> (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    go Int -> a -> Maybe a
    f IntMap a
    t
      where
        go :: (Int -> t -> Maybe t) -> IntMap t -> IntMap t
    go Int -> t -> Maybe t
    f' (Bin Int
    p Int
    m IntMap t
    l IntMap t
    r) = Int -> Int -> IntMap t -> IntMap t -> IntMap t
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    p Int
    m ((Int -> t -> Maybe t) -> IntMap t -> IntMap t
    go Int -> t -> Maybe t
    f' IntMap t
    l) IntMap t
    r
        go Int -> t -> Maybe t
    f' (Tip Int
    k t
    y) = case Int -> t -> Maybe t
    f' Int
    k t
    y of
                            Just t
    y' -> Int -> t -> IntMap t
    forall a. Int -> a -> IntMap a
    Tip Int
    k t
    y'
                            Maybe t
    Nothing -> IntMap t
    forall a. IntMap a
    Nil
        go Int -> t -> Maybe t
    _ IntMap t
    Nil = [Char] -> IntMap t
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "updateMinWithKey Nil"

    -- | \(O(\min(n,W))\). 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 -> Maybe a) -> IntMap a -> IntMap a
    updateMaxWithKey :: forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    updateMaxWithKey Int -> a -> Maybe a
    f IntMap a
    t =
      case IntMap a
    t of Bin Int
    p Int
    m IntMap a
    l IntMap a
    r | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    p Int
    m ((Int -> a -> Maybe a) -> IntMap a -> IntMap a
    forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    go Int -> a -> Maybe a
    f IntMap a
    l) IntMap a
    r
                IntMap a
    _ -> (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    go Int -> a -> Maybe a
    f IntMap a
    t
      where
        go :: (Int -> t -> Maybe t) -> IntMap t -> IntMap t
    go Int -> t -> Maybe t
    f' (Bin Int
    p Int
    m IntMap t
    l IntMap t
    r) = Int -> Int -> IntMap t -> IntMap t -> IntMap t
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    p Int
    m IntMap t
    l ((Int -> t -> Maybe t) -> IntMap t -> IntMap t
    go Int -> t -> Maybe t
    f' IntMap t
    r)
        go Int -> t -> Maybe t
    f' (Tip Int
    k t
    y) = case Int -> t -> Maybe t
    f' Int
    k t
    y of
                            Just t
    y' -> Int -> t -> IntMap t
    forall a. Int -> a -> IntMap a
    Tip Int
    k t
    y'
                            Maybe t
    Nothing -> IntMap t
    forall a. IntMap a
    Nil
        go Int -> t -> Maybe t
    _ IntMap t
    Nil = [Char] -> IntMap t
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "updateMaxWithKey Nil"

    data View a = View {-# UNPACK #-} !Key a !(IntMap a)

    -- | \(O(\min(n,W))\). 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 :: forall a. IntMap a -> Maybe ((Int, a), IntMap a)
    maxViewWithKey IntMap a
    t = case IntMap a
    t of
      IntMap a
    Nil -> Maybe ((Int, a), IntMap a)
    forall a. Maybe a
    Nothing
      IntMap a
    _ -> ((Int, a), IntMap a) -> Maybe ((Int, a), IntMap a)
    forall a. a -> Maybe a
    Just (((Int, a), IntMap a) -> Maybe ((Int, a), IntMap a))
    -> ((Int, a), IntMap a) -> Maybe ((Int, a), IntMap a)
    forall a b. (a -> b) -> a -> b
    $ case IntMap a -> View a
    forall a. IntMap a -> View a
    maxViewWithKeySure IntMap a
    t of
                    View Int
    k a
    v IntMap a
    t' -> ((Int
    k, a
    v), IntMap a
    t')
    {-# INLINE maxViewWithKey #-}

    maxViewWithKeySure :: IntMap a -> View a
    maxViewWithKeySure :: forall a. IntMap a -> View a
    maxViewWithKeySure IntMap a
    t =
      case IntMap a
    t of
        IntMap a
    Nil -> [Char] -> View a
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "maxViewWithKeySure Nil"
        Bin Int
    p Int
    m IntMap a
    l IntMap a
    r | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 ->
          case IntMap a -> View a
    forall a. IntMap a -> View a
    go IntMap a
    l of View Int
    k a
    a IntMap a
    l' -> Int -> a -> IntMap a -> View a
    forall a. Int -> a -> IntMap a -> View a
    View Int
    k a
    a (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    p Int
    m IntMap a
    l' IntMap a
    r)
        IntMap a
    _ -> IntMap a -> View a
    forall a. IntMap a -> View a
    go IntMap a
    t
      where
        go :: IntMap a -> View a
    go (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r) =
            case IntMap a -> View a
    go IntMap a
    r of View Int
    k a
    a IntMap a
    r' -> Int -> a -> IntMap a -> View a
    forall a. Int -> a -> IntMap a -> View a
    View Int
    k a
    a (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    p Int
    m IntMap a
    l IntMap a
    r')
        go (Tip Int
    k a
    y) = Int -> a -> IntMap a -> View a
    forall a. Int -> a -> IntMap a -> View a
    View Int
    k a
    y IntMap a
    forall a. IntMap a
    Nil
        go IntMap a
    Nil = [Char] -> View a
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "maxViewWithKey_go Nil"
    -- See note on NOINLINE at minViewWithKeySure
    {-# NOINLINE maxViewWithKeySure #-}

    -- | \(O(\min(n,W))\). 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 :: forall a. IntMap a -> Maybe ((Int, a), IntMap a)
    minViewWithKey IntMap a
    t =
      case IntMap a
    t of
        IntMap a
    Nil -> Maybe ((Int, a), IntMap a)
    forall a. Maybe a
    Nothing
        IntMap a
    _ -> ((Int, a), IntMap a) -> Maybe ((Int, a), IntMap a)
    forall a. a -> Maybe a
    Just (((Int, a), IntMap a) -> Maybe ((Int, a), IntMap a))
    -> ((Int, a), IntMap a) -> Maybe ((Int, a), IntMap a)
    forall a b. (a -> b) -> a -> b
    $ case IntMap a -> View a
    forall a. IntMap a -> View a
    minViewWithKeySure IntMap a
    t of
                      View Int
    k a
    v IntMap a
    t' -> ((Int
    k, a
    v), IntMap a
    t')
    -- We inline this to give GHC the best possible chance of
    -- getting rid of the Maybe, pair, and Int constructors, as
    -- well as a thunk under the Just. That is, we really want to
    -- be certain this inlines!
    {-# INLINE minViewWithKey #-}

    minViewWithKeySure :: IntMap a -> View a
    minViewWithKeySure :: forall a. IntMap a -> View a
    minViewWithKeySure IntMap a
    t =
      case IntMap a
    t of
        IntMap a
    Nil -> [Char] -> View a
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "minViewWithKeySure Nil"
        Bin Int
    p Int
    m IntMap a
    l IntMap a
    r | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 ->
          case IntMap a -> View a
    forall a. IntMap a -> View a
    go IntMap a
    r of
            View Int
    k a
    a IntMap a
    r' -> Int -> a -> IntMap a -> View a
    forall a. Int -> a -> IntMap a -> View a
    View Int
    k a
    a (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    p Int
    m IntMap a
    l IntMap a
    r')
        IntMap a
    _ -> IntMap a -> View a
    forall a. IntMap a -> View a
    go IntMap a
    t
      where
        go :: IntMap a -> View a
    go (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r) =
            case IntMap a -> View a
    go IntMap a
    l of View Int
    k a
    a IntMap a
    l' -> Int -> a -> IntMap a -> View a
    forall a. Int -> a -> IntMap a -> View a
    View Int
    k a
    a (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    p Int
    m IntMap a
    l' IntMap a
    r)
        go (Tip Int
    k a
    y) = Int -> a -> IntMap a -> View a
    forall a. Int -> a -> IntMap a -> View a
    View Int
    k a
    y IntMap a
    forall a. IntMap a
    Nil
        go IntMap a
    Nil = [Char] -> View a
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "minViewWithKey_go Nil"
    -- There's never anything significant to be gained by inlining
    -- this. Sufficiently recent GHC versions will inline the wrapper
    -- anyway, which should be good enough.
    {-# NOINLINE minViewWithKeySure #-}

    -- | \(O(\min(n,W))\). 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 -> Maybe a) -> IntMap a -> IntMap a
    updateMax :: forall a. (a -> Maybe a) -> IntMap a -> IntMap a
    updateMax a -> Maybe a
    f = (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    updateMaxWithKey ((a -> Maybe a) -> Int -> a -> Maybe a
    forall a b. a -> b -> a
    const a -> Maybe a
    f)

    -- | \(O(\min(n,W))\). 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 -> Maybe a) -> IntMap a -> IntMap a
    updateMin :: forall a. (a -> Maybe a) -> IntMap a -> IntMap a
    updateMin a -> Maybe a
    f = (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
    updateMinWithKey ((a -> Maybe a) -> Int -> a -> Maybe a
    forall a b. a -> b -> a
    const a -> Maybe a
    f)

    -- | \(O(\min(n,W))\). 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 :: forall a. IntMap a -> Maybe (a, IntMap a)
    maxView IntMap a
    t = (((Int, a), IntMap a) -> (a, IntMap a))
    -> Maybe ((Int, a), IntMap a) -> Maybe (a, IntMap a)
    forall a b. (a -> b) -> Maybe a -> Maybe b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap (\((Int
    _, a
    x), IntMap a
    t') -> (a
    x, IntMap a
    t')) (IntMap a -> Maybe ((Int, a), IntMap a)
    forall a. IntMap a -> Maybe ((Int, a), IntMap a)
    maxViewWithKey IntMap a
    t)

    -- | \(O(\min(n,W))\). 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 :: forall a. IntMap a -> Maybe (a, IntMap a)
    minView IntMap a
    t = (((Int, a), IntMap a) -> (a, IntMap a))
    -> Maybe ((Int, a), IntMap a) -> Maybe (a, IntMap a)
    forall a b. (a -> b) -> Maybe a -> Maybe b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap (\((Int
    _, a
    x), IntMap a
    t') -> (a
    x, IntMap a
    t')) (IntMap a -> Maybe ((Int, a), IntMap a)
    forall a. IntMap a -> Maybe ((Int, a), IntMap a)
    minViewWithKey IntMap a
    t)

    -- | \(O(\min(n,W))\). Delete and find the maximal element.
    -- This function throws an error if the map is empty. Use 'maxViewWithKey'
    -- if the map may be empty.
    deleteFindMax :: IntMap a -> ((Key, a), IntMap a)
    deleteFindMax :: forall a. IntMap a -> ((Int, a), IntMap a)
    deleteFindMax = ((Int, a), IntMap a)
    -> Maybe ((Int, a), IntMap a) -> ((Int, a), IntMap a)
    forall a. a -> Maybe a -> a
    fromMaybe ([Char] -> ((Int, a), IntMap a)
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "deleteFindMax: empty map has no maximal element") (Maybe ((Int, a), IntMap a) -> ((Int, a), IntMap a))
    -> (IntMap a -> Maybe ((Int, a), IntMap a))
    -> IntMap a
    -> ((Int, a), IntMap a)
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . IntMap a -> Maybe ((Int, a), IntMap a)
    forall a. IntMap a -> Maybe ((Int, a), IntMap a)
    maxViewWithKey

    -- | \(O(\min(n,W))\). Delete and find the minimal element.
    -- This function throws an error if the map is empty. Use 'minViewWithKey'
    -- if the map may be empty.
    deleteFindMin :: IntMap a -> ((Key, a), IntMap a)
    deleteFindMin :: forall a. IntMap a -> ((Int, a), IntMap a)
    deleteFindMin = ((Int, a), IntMap a)
    -> Maybe ((Int, a), IntMap a) -> ((Int, a), IntMap a)
    forall a. a -> Maybe a -> a
    fromMaybe ([Char] -> ((Int, a), IntMap a)
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "deleteFindMin: empty map has no minimal element") (Maybe ((Int, a), IntMap a) -> ((Int, a), IntMap a))
    -> (IntMap a -> Maybe ((Int, a), IntMap a))
    -> IntMap a
    -> ((Int, a), IntMap a)
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . IntMap a -> Maybe ((Int, a), IntMap a)
    forall a. IntMap a -> Maybe ((Int, a), IntMap a)
    minViewWithKey

    -- | \(O(\min(n,W))\). The minimal key of the map. Returns 'Nothing' if the map is empty.
    lookupMin :: IntMap a -> Maybe (Key, a)
    lookupMin :: forall a. IntMap a -> Maybe (Int, a)
    lookupMin IntMap a
    Nil = Maybe (Int, a)
    forall a. Maybe a
    Nothing
    lookupMin (Tip Int
    k a
    v) = (Int, a) -> Maybe (Int, a)
    forall a. a -> Maybe a
    Just (Int
    k,a
    v)
    lookupMin (Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r)
      | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    go IntMap a
    r
      | Bool
    otherwise = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    go IntMap a
    l
        where go :: IntMap b -> Maybe (Int, b)
    go (Tip Int
    k b
    v)      = (Int, b) -> Maybe (Int, b)
    forall a. a -> Maybe a
    Just (Int
    k,b
    v)
              go (Bin Int
    _ Int
    _ IntMap b
    l' IntMap b
    _) = IntMap b -> Maybe (Int, b)
    go IntMap b
    l'
              go IntMap b
    Nil            = Maybe (Int, b)
    forall a. Maybe a
    Nothing

    -- | \(O(\min(n,W))\). The minimal key of the map. Calls 'error' if the map is empty.
    -- Use 'minViewWithKey' if the map may be empty.
    findMin :: IntMap a -> (Key, a)
    findMin :: forall a. IntMap a -> (Int, a)
    findMin IntMap a
    t
      | Just (Int, a)
    r <- IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    lookupMin IntMap a
    t = (Int, a)
    r
      | Bool
    otherwise = [Char] -> (Int, a)
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "findMin: empty map has no minimal element"

    -- | \(O(\min(n,W))\). The maximal key of the map. Returns 'Nothing' if the map is empty.
    lookupMax :: IntMap a -> Maybe (Key, a)
    lookupMax :: forall a. IntMap a -> Maybe (Int, a)
    lookupMax IntMap a
    Nil = Maybe (Int, a)
    forall a. Maybe a
    Nothing
    lookupMax (Tip Int
    k a
    v) = (Int, a) -> Maybe (Int, a)
    forall a. a -> Maybe a
    Just (Int
    k,a
    v)
    lookupMax (Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r)
      | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    go IntMap a
    l
      | Bool
    otherwise = IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    go IntMap a
    r
        where go :: IntMap b -> Maybe (Int, b)
    go (Tip Int
    k b
    v)      = (Int, b) -> Maybe (Int, b)
    forall a. a -> Maybe a
    Just (Int
    k,b
    v)
              go (Bin Int
    _ Int
    _ IntMap b
    _ IntMap b
    r') = IntMap b -> Maybe (Int, b)
    go IntMap b
    r'
              go IntMap b
    Nil            = Maybe (Int, b)
    forall a. Maybe a
    Nothing

    -- | \(O(\min(n,W))\). The maximal key of the map. Calls 'error' if the map is empty.
    -- Use 'maxViewWithKey' if the map may be empty.
    findMax :: IntMap a -> (Key, a)
    findMax :: forall a. IntMap a -> (Int, a)
    findMax IntMap a
    t
      | Just (Int, a)
    r <- IntMap a -> Maybe (Int, a)
    forall a. IntMap a -> Maybe (Int, a)
    lookupMax IntMap a
    t = (Int, a)
    r
      | Bool
    otherwise = [Char] -> (Int, a)
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "findMax: empty map has no maximal element"

    -- | \(O(\min(n,W))\). Delete the minimal key. Returns an empty map if the map is empty.
    --
    -- Note that this is a change of behaviour for consistency with 'Data.Map.Map' &#8211;
    -- versions prior to 0.5 threw an error if the 'IntMap' was already empty.
    deleteMin :: IntMap a -> IntMap a
    deleteMin :: forall a. IntMap a -> IntMap a
    deleteMin = IntMap a
    -> ((a, IntMap a) -> IntMap a) -> Maybe (a, IntMap a) -> IntMap a
    forall b a. b -> (a -> b) -> Maybe a -> b
    maybe IntMap a
    forall a. IntMap a
    Nil (a, IntMap a) -> IntMap a
    forall a b. (a, b) -> b
    snd (Maybe (a, IntMap a) -> IntMap a)
    -> (IntMap a -> Maybe (a, IntMap a)) -> IntMap a -> IntMap a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . IntMap a -> Maybe (a, IntMap a)
    forall a. IntMap a -> Maybe (a, IntMap a)
    minView

    -- | \(O(\min(n,W))\). Delete the maximal key. Returns an empty map if the map is empty.
    --
    -- Note that this is a change of behaviour for consistency with 'Data.Map.Map' &#8211;
    -- versions prior to 0.5 threw an error if the 'IntMap' was already empty.
    deleteMax :: IntMap a -> IntMap a
    deleteMax :: forall a. IntMap a -> IntMap a
    deleteMax = IntMap a
    -> ((a, IntMap a) -> IntMap a) -> Maybe (a, IntMap a) -> IntMap a
    forall b a. b -> (a -> b) -> Maybe a -> b
    maybe IntMap a
    forall a. IntMap a
    Nil (a, IntMap a) -> IntMap a
    forall a b. (a, b) -> b
    snd (Maybe (a, IntMap a) -> IntMap a)
    -> (IntMap a -> Maybe (a, IntMap a)) -> IntMap a -> IntMap a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . IntMap a -> Maybe (a, IntMap a)
    forall a. IntMap a -> Maybe (a, IntMap a)
    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 :: forall a. Eq a => IntMap a -> IntMap a -> Bool
    isProperSubmapOf IntMap a
    m1 IntMap a
    m2
      = (a -> a -> Bool) -> IntMap a -> IntMap a -> Bool
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    isProperSubmapOfBy a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    (==) IntMap a
    m1 IntMap a
    m2

    {- | \(O(n+m)\). Is this a proper submap? (ie. a submap but not equal).
     The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
     @keys m1@ and @keys 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 :: forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    isProperSubmapOfBy a -> b -> Bool
    predicate IntMap a
    t1 IntMap b
    t2
      = case (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    submapCmp a -> b -> Bool
    predicate IntMap a
    t1 IntMap b
    t2 of
          Ordering
    LT -> Bool
    True
          Ordering
    _  -> Bool
    False

    submapCmp :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    submapCmp :: forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    submapCmp a -> b -> Bool
    predicate t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1) (Bin Int
    p2 Int
    m2 IntMap b
    l2 IntMap b
    r2)
      | Int -> Int -> Bool
    shorter Int
    m1 Int
    m2  = Ordering
    GT
      | Int -> Int -> Bool
    shorter Int
    m2 Int
    m1  = Ordering
    submapCmpLt
      | Int
    p1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    p2       = Ordering
    submapCmpEq
      | Bool
    otherwise      = Ordering
    GT  -- disjoint
      where
        submapCmpLt :: Ordering
    submapCmpLt | Int -> Int -> Int -> Bool
    nomatch Int
    p1 Int
    p2 Int
    m2  = Ordering
    GT
                    | Int -> Int -> Bool
    zero Int
    p1 Int
    m2        = (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    submapCmp a -> b -> Bool
    predicate IntMap a
    t1 IntMap b
    l2
                    | Bool
    otherwise         = (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    submapCmp a -> b -> Bool
    predicate IntMap a
    t1 IntMap b
    r2
        submapCmpEq :: Ordering
    submapCmpEq = case ((a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    submapCmp a -> b -> Bool
    predicate IntMap a
    l1 IntMap b
    l2, (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
    submapCmp a -> b -> Bool
    predicate IntMap a
    r1 IntMap b
    r2) of
                        (Ordering
    GT,Ordering
    _ ) -> Ordering
    GT
                        (Ordering
    _ ,Ordering
    GT) -> Ordering
    GT
                        (Ordering
    EQ,Ordering
    EQ) -> Ordering
    EQ
                        (Ordering, Ordering)
    _       -> Ordering
    LT

    submapCmp a -> b -> Bool
    _         (Bin Int
    _ Int
    _ IntMap a
    _ IntMap a
    _) IntMap b
    _  = Ordering
    GT
    submapCmp a -> b -> Bool
    predicate (Tip Int
    kx a
    x) (Tip Int
    ky b
    y)
      | (Int
    kx Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    ky) Bool -> Bool -> Bool
    && a -> b -> Bool
    predicate a
    x b
    y = Ordering
    EQ
      | Bool
    otherwise                   = Ordering
    GT  -- disjoint
    submapCmp a -> b -> Bool
    predicate (Tip Int
    k a
    x) IntMap b
    t
      = case Int -> IntMap b -> Maybe b
    forall a. Int -> IntMap a -> Maybe a
    lookup Int
    k IntMap b
    t of
         Just b
    y | a -> b -> Bool
    predicate a
    x b
    y -> Ordering
    LT
         Maybe b
    _                      -> Ordering
    GT -- disjoint
    submapCmp a -> b -> Bool
    _    IntMap a
    Nil IntMap b
    Nil = Ordering
    EQ
    submapCmp a -> b -> Bool
    _    IntMap a
    Nil IntMap b
    _   = Ordering
    LT

    -- | \(O(n+m)\). Is this a submap?
    -- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
    isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
    isSubmapOf :: forall a. Eq a => IntMap a -> IntMap a -> Bool
    isSubmapOf IntMap a
    m1 IntMap a
    m2
      = (a -> a -> Bool) -> IntMap a -> IntMap a -> Bool
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    isSubmapOfBy a -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    (==) IntMap a
    m1 IntMap a
    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 :: forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    isSubmapOfBy a -> b -> Bool
    predicate t1 :: IntMap a
    t1@(Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1) (Bin Int
    p2 Int
    m2 IntMap b
    l2 IntMap b
    r2)
      | Int -> Int -> Bool
    shorter Int
    m1 Int
    m2  = Bool
    False
      | Int -> Int -> Bool
    shorter Int
    m2 Int
    m1  = Int -> Int -> Int -> Bool
    match Int
    p1 Int
    p2 Int
    m2 Bool -> Bool -> Bool
    &&
                           if Int -> Int -> Bool
    zero Int
    p1 Int
    m2
                           then (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    isSubmapOfBy a -> b -> Bool
    predicate IntMap a
    t1 IntMap b
    l2
                           else (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    isSubmapOfBy a -> b -> Bool
    predicate IntMap a
    t1 IntMap b
    r2
      | Bool
    otherwise      = (Int
    p1Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    ==Int
    p2) Bool -> Bool -> Bool
    && (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    isSubmapOfBy a -> b -> Bool
    predicate IntMap a
    l1 IntMap b
    l2 Bool -> Bool -> Bool
    && (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    isSubmapOfBy a -> b -> Bool
    predicate IntMap a
    r1 IntMap b
    r2
    isSubmapOfBy a -> b -> Bool
    _         (Bin Int
    _ Int
    _ IntMap a
    _ IntMap a
    _) IntMap b
    _ = Bool
    False
    isSubmapOfBy a -> b -> Bool
    predicate (Tip Int
    k a
    x) IntMap b
    t     = case Int -> IntMap b -> Maybe b
    forall a. Int -> IntMap a -> Maybe a
    lookup Int
    k IntMap b
    t of
                                             Just b
    y  -> a -> b -> Bool
    predicate a
    x b
    y
                                             Maybe b
    Nothing -> Bool
    False
    isSubmapOfBy a -> b -> Bool
    _         IntMap a
    Nil IntMap b
    _           = Bool
    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 :: forall a b. (a -> b) -> IntMap a -> IntMap b
    map a -> b
    f = IntMap a -> IntMap b
    go
      where
        go :: IntMap a -> IntMap b
    go (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r) = Int -> Int -> IntMap b -> IntMap b -> IntMap b
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m (IntMap a -> IntMap b
    go IntMap a
    l) (IntMap a -> IntMap b
    go IntMap a
    r)
        go (Tip Int
    k a
    x)     = Int -> b -> IntMap b
    forall a. Int -> a -> IntMap a
    Tip Int
    k (a -> b
    f a
    x)
        go IntMap a
    Nil           = IntMap b
    forall a. IntMap a
    Nil

    #ifdef __GLASGOW_HASKELL__
    {-# NOINLINE [1] map #-}
    {-# RULES
    "map/map" forall f g xs . map f (map g xs) = map (f . g) xs
    "map/coerce" map coerce = coerce
     #-}
    #endif

    -- | \(O(n)\). 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 :: forall a b. (Int -> a -> b) -> IntMap a -> IntMap b
    mapWithKey Int -> a -> b
    f IntMap a
    t
      = case IntMap a
    t of
          Bin Int
    p Int
    m IntMap a
    l IntMap a
    r -> Int -> Int -> IntMap b -> IntMap b -> IntMap b
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m ((Int -> a -> b) -> IntMap a -> IntMap b
    forall a b. (Int -> a -> b) -> IntMap a -> IntMap b
    mapWithKey Int -> a -> b
    f IntMap a
    l) ((Int -> a -> b) -> IntMap a -> IntMap b
    forall a b. (Int -> a -> b) -> IntMap a -> IntMap b
    mapWithKey Int -> a -> b
    f IntMap a
    r)
          Tip Int
    k a
    x     -> Int -> b -> IntMap b
    forall a. Int -> a -> IntMap a
    Tip Int
    k (Int -> a -> b
    f Int
    k a
    x)
          IntMap a
    Nil         -> IntMap b
    forall a. IntMap a
    Nil

    #ifdef __GLASGOW_HASKELL__
    {-# NOINLINE [1] mapWithKey #-}
    {-# RULES
    "mapWithKey/mapWithKey" forall f g xs . mapWithKey f (mapWithKey g xs) =
      mapWithKey (\k a -> f k (g k a)) xs
    "mapWithKey/map" forall f g xs . mapWithKey f (map g xs) =
      mapWithKey (\k a -> f k (g a)) xs
    "map/mapWithKey" forall f g xs . map f (mapWithKey g xs) =
      mapWithKey (\k a -> f (g k a)) xs
     #-}
    #endif

    -- | \(O(n)\).
    -- @'traverseWithKey' f s == 'fromList' <$> 'traverse' (\(k, v) -> (,) k <$> f k v) ('toList' m)@
    -- That is, behaves exactly like a regular 'traverse' except that the traversing
    -- function also has access to the key associated with a value.
    --
    -- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')])
    -- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')])           == Nothing
    traverseWithKey :: Applicative t => (Key -> a -> t b) -> IntMap a -> t (IntMap b)
    traverseWithKey :: forall (t :: * -> *) a b.
    Applicative t =>
    (Int -> a -> t b) -> IntMap a -> t (IntMap b)
    traverseWithKey Int -> a -> t b
    f = IntMap a -> t (IntMap b)
    go
      where
        go :: IntMap a -> t (IntMap b)
    go IntMap a
    Nil = IntMap b -> t (IntMap b)
    forall a. a -> t a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure IntMap b
    forall a. IntMap a
    Nil
        go (Tip Int
    k a
    v) = Int -> b -> IntMap b
    forall a. Int -> a -> IntMap a
    Tip Int
    k (b -> IntMap b) -> t b -> t (IntMap b)
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    <$> Int -> a -> t b
    f Int
    k a
    v
        go (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = (IntMap b -> IntMap b -> IntMap b)
    -> t (IntMap b) -> t (IntMap b) -> t (IntMap b)
    forall a b c. (a -> b -> c) -> t a -> t b -> t c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 ((IntMap b -> IntMap b -> IntMap b)
    -> IntMap b -> IntMap b -> IntMap b
    forall a b c. (a -> b -> c) -> b -> a -> c
    flip (Int -> Int -> IntMap b -> IntMap b -> IntMap b
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m)) (IntMap a -> t (IntMap b)
    go IntMap a
    r) (IntMap a -> t (IntMap b)
    go IntMap a
    l)
          | Bool
    otherwise = (IntMap b -> IntMap b -> IntMap b)
    -> t (IntMap b) -> t (IntMap b) -> t (IntMap b)
    forall a b c. (a -> b -> c) -> t a -> t b -> t c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 (Int -> Int -> IntMap b -> IntMap b -> IntMap b
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m) (IntMap a -> t (IntMap b)
    go IntMap a
    l) (IntMap a -> t (IntMap b)
    go IntMap a
    r)
    {-# INLINE traverseWithKey #-}

    -- | \(O(n)\). 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 :: forall a b c. (a -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccum a -> b -> (a, c)
    f = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumWithKey (\a
    a' Int
    _ b
    x -> a -> b -> (a, c)
    f a
    a' b
    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 :: forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumWithKey a -> Int -> b -> (a, c)
    f a
    a IntMap b
    t
      = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumL a -> Int -> b -> (a, c)
    f a
    a IntMap b
    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 :: forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumL a -> Int -> b -> (a, c)
    f a
    a IntMap b
    t
      = case IntMap b
    t of
          Bin Int
    p Int
    m IntMap b
    l IntMap b
    r
            | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 ->
                let (a
    a1,IntMap c
    r') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumL a -> Int -> b -> (a, c)
    f a
    a IntMap b
    r
                    (a
    a2,IntMap c
    l') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumL a -> Int -> b -> (a, c)
    f a
    a1 IntMap b
    l
                in (a
    a2,Int -> Int -> IntMap c -> IntMap c -> IntMap c
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap c
    l' IntMap c
    r')
            | Bool
    otherwise  ->
                let (a
    a1,IntMap c
    l') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumL a -> Int -> b -> (a, c)
    f a
    a IntMap b
    l
                    (a
    a2,IntMap c
    r') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumL a -> Int -> b -> (a, c)
    f a
    a1 IntMap b
    r
                in (a
    a2,Int -> Int -> IntMap c -> IntMap c -> IntMap c
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap c
    l' IntMap c
    r')
          Tip Int
    k b
    x     -> let (a
    a',c
    x') = a -> Int -> b -> (a, c)
    f a
    a Int
    k b
    x in (a
    a',Int -> c -> IntMap c
    forall a. Int -> a -> IntMap a
    Tip Int
    k c
    x')
          IntMap b
    Nil         -> (a
    a,IntMap c
    forall a. IntMap a
    Nil)

    -- | \(O(n)\). The function @'mapAccumRWithKey'@ 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 :: forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumRWithKey a -> Int -> b -> (a, c)
    f a
    a IntMap b
    t
      = case IntMap b
    t of
          Bin Int
    p Int
    m IntMap b
    l IntMap b
    r
            | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 ->
                let (a
    a1,IntMap c
    l') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumRWithKey a -> Int -> b -> (a, c)
    f a
    a IntMap b
    l
                    (a
    a2,IntMap c
    r') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumRWithKey a -> Int -> b -> (a, c)
    f a
    a1 IntMap b
    r
                in (a
    a2,Int -> Int -> IntMap c -> IntMap c -> IntMap c
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap c
    l' IntMap c
    r')
            | Bool
    otherwise  ->
                let (a
    a1,IntMap c
    r') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumRWithKey a -> Int -> b -> (a, c)
    f a
    a IntMap b
    r
                    (a
    a2,IntMap c
    l') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    forall a b c.
    (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
    mapAccumRWithKey a -> Int -> b -> (a, c)
    f a
    a1 IntMap b
    l
                in (a
    a2,Int -> Int -> IntMap c -> IntMap c -> IntMap c
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap c
    l' IntMap c
    r')
          Tip Int
    k b
    x     -> let (a
    a',c
    x') = a -> Int -> b -> (a, c)
    f a
    a Int
    k b
    x in (a
    a',Int -> c -> IntMap c
    forall a. Int -> a -> IntMap a
    Tip Int
    k c
    x')
          IntMap b
    Nil         -> (a
    a,IntMap c
    forall a. IntMap a
    Nil)

    -- | \(O(n \min(n,W))\).
    -- @'mapKeys' f s@ is the map obtained by applying @f@ to each key of @s@.
    --
    -- The size of the result may be smaller if @f@ maps two or more distinct
    -- keys to the same new key.  In this case the value at the greatest of the
    -- original keys is retained.
    --
    -- > mapKeys (+ 1) (fromList [(5,"a"), (3,"b")])                        == fromList [(4, "b"), (6, "a")]
    -- > mapKeys (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "c"
    -- > mapKeys (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "c"

    mapKeys :: (Key->Key) -> IntMap a -> IntMap a
    mapKeys :: forall a. (Int -> Int) -> IntMap a -> IntMap a
    mapKeys Int -> Int
    f = [(Int, a)] -> IntMap a
    forall a. [(Int, a)] -> IntMap a
    fromList ([(Int, a)] -> IntMap a)
    -> (IntMap a -> [(Int, a)]) -> IntMap a -> IntMap a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (Int -> a -> [(Int, a)] -> [(Int, a)])
    -> [(Int, a)] -> IntMap a -> [(Int, a)]
    forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
    foldrWithKey (\Int
    k a
    x [(Int, a)]
    xs -> (Int -> Int
    f Int
    k, a
    x) (Int, a) -> [(Int, a)] -> [(Int, a)]
    forall a. a -> [a] -> [a]
    : [(Int, a)]
    xs) []

    -- | \(O(n \min(n,W))\).
    -- @'mapKeysWith' c f s@ is the map obtained by applying @f@ to each key of @s@.
    --
    -- The size of the result may be smaller if @f@ maps two or more distinct
    -- keys to the same new key.  In this case the associated values will be
    -- combined using @c@.
    --
    -- > mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab"
    -- > mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab"
    --
    -- Also see the performance note on 'fromListWith'.

    mapKeysWith :: (a -> a -> a) -> (Key->Key) -> IntMap a -> IntMap a
    mapKeysWith :: forall a. (a -> a -> a) -> (Int -> Int) -> IntMap a -> IntMap a
    mapKeysWith a -> a -> a
    c Int -> Int
    f
      = (a -> a -> a) -> [(Int, a)] -> IntMap a
    forall a. (a -> a -> a) -> [(Int, a)] -> IntMap a
    fromListWith a -> a -> a
    c ([(Int, a)] -> IntMap a)
    -> (IntMap a -> [(Int, a)]) -> IntMap a -> IntMap a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (Int -> a -> [(Int, a)] -> [(Int, a)])
    -> [(Int, a)] -> IntMap a -> [(Int, a)]
    forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
    foldrWithKey (\Int
    k a
    x [(Int, a)]
    xs -> (Int -> Int
    f Int
    k, a
    x) (Int, a) -> [(Int, a)] -> [(Int, a)]
    forall a. a -> [a] -> [a]
    : [(Int, a)]
    xs) []

    -- | \(O(n)\).
    -- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@
    -- is strictly monotonic.
    -- That is, for any values @x@ and @y@, if @x@ < @y@ then @f x@ < @f y@.
    -- /The precondition is not checked./
    -- Semi-formally, we have:
    --
    -- > and [x < y ==> f x < f y | x <- ls, y <- ls]
    -- >                     ==> mapKeysMonotonic f s == mapKeys f s
    -- >     where ls = keys s
    --
    -- This means that @f@ maps distinct original keys to distinct resulting keys.
    -- This function has slightly better performance than 'mapKeys'.
    --
    -- > mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")]

    mapKeysMonotonic :: (Key->Key) -> IntMap a -> IntMap a
    mapKeysMonotonic :: forall a. (Int -> Int) -> IntMap a -> IntMap a
    mapKeysMonotonic Int -> Int
    f
      = [(Int, a)] -> IntMap a
    forall a. [(Int, a)] -> IntMap a
    fromDistinctAscList ([(Int, a)] -> IntMap a)
    -> (IntMap a -> [(Int, a)]) -> IntMap a -> IntMap a
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . (Int -> a -> [(Int, a)] -> [(Int, a)])
    -> [(Int, a)] -> IntMap a -> [(Int, a)]
    forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
    foldrWithKey (\Int
    k a
    x [(Int, a)]
    xs -> (Int -> Int
    f Int
    k, a
    x) (Int, a) -> [(Int, a)] -> [(Int, a)]
    forall a. a -> [a] -> [a]
    : [(Int, a)]
    xs) []

    {--------------------------------------------------------------------
      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 :: forall a. (a -> Bool) -> IntMap a -> IntMap a
    filter a -> Bool
    p IntMap a
    m
      = (Int -> a -> Bool) -> IntMap a -> IntMap a
    forall a. (Int -> a -> Bool) -> IntMap a -> IntMap a
    filterWithKey (\Int
    _ a
    x -> a -> Bool
    p a
    x) IntMap a
    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 :: forall a. (Int -> a -> Bool) -> IntMap a -> IntMap a
    filterWithKey Int -> a -> Bool
    predicate = IntMap a -> IntMap a
    go
        where
        go :: IntMap a -> IntMap a
    go IntMap a
    Nil           = IntMap a
    forall a. IntMap a
    Nil
        go t :: IntMap a
    t@(Tip Int
    k a
    x)   = if Int -> a -> Bool
    predicate Int
    k a
    x then IntMap a
    t else IntMap a
    forall a. IntMap a
    Nil
        go (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r) = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m (IntMap a -> IntMap a
    go IntMap a
    l) (IntMap a -> IntMap a
    go IntMap a
    r)

    -- | \(O(n)\). 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 :: forall a. (a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
    partition a -> Bool
    p IntMap a
    m
      = (Int -> a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
    forall a. (Int -> a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
    partitionWithKey (\Int
    _ a
    x -> a -> Bool
    p a
    x) IntMap a
    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 :: forall a. (Int -> a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
    partitionWithKey Int -> a -> Bool
    predicate0 IntMap a
    t0 = StrictPair (IntMap a) (IntMap a) -> (IntMap a, IntMap a)
    forall a b. StrictPair a b -> (a, b)
    toPair (StrictPair (IntMap a) (IntMap a) -> (IntMap a, IntMap a))
    -> StrictPair (IntMap a) (IntMap a) -> (IntMap a, IntMap a)
    forall a b. (a -> b) -> a -> b
    $ (Int -> a -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall {a}.
    (Int -> a -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int -> a -> Bool
    predicate0 IntMap a
    t0
      where
        go :: (Int -> a -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int -> a -> Bool
    predicate IntMap a
    t =
          case IntMap a
    t of
            Bin Int
    p Int
    m IntMap a
    l IntMap a
    r ->
              let (IntMap a
    l1 :*: IntMap a
    l2) = (Int -> a -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int -> a -> Bool
    predicate IntMap a
    l
                  (IntMap a
    r1 :*: IntMap a
    r2) = (Int -> a -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int -> a -> Bool
    predicate IntMap a
    r
              in Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l1 IntMap a
    r1 IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l2 IntMap a
    r2
            Tip Int
    k a
    x
              | Int -> a -> Bool
    predicate Int
    k a
    x -> (IntMap a
    t IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    forall a. IntMap a
    Nil)
              | Bool
    otherwise     -> (IntMap a
    forall a. IntMap a
    Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    t)
            IntMap a
    Nil -> (IntMap a
    forall a. IntMap a
    Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    forall a. IntMap a
    Nil)

    -- | \(O(\min(n,W))\). Take while a predicate on the keys holds.
    -- The user is responsible for ensuring that for all @Int@s, @j \< k ==\> p j \>= p k@.
    -- See note at 'spanAntitone'.
    --
    -- @
    -- takeWhileAntitone p = 'fromDistinctAscList' . 'Data.List.takeWhile' (p . fst) . 'toList'
    -- takeWhileAntitone p = 'filterWithKey' (\\k _ -> p k)
    -- @
    --
    -- @since 0.6.7
    takeWhileAntitone :: (Key -> Bool) -> IntMap a -> IntMap a
    takeWhileAntitone :: forall a. (Int -> Bool) -> IntMap a -> IntMap a
    takeWhileAntitone Int -> Bool
    predicate IntMap a
    t =
      case IntMap a
    t of
        Bin Int
    p Int
    m IntMap a
    l IntMap a
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 ->
            if Int -> Bool
    predicate Int
    0 -- handle negative numbers.
            then Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m ((Int -> Bool) -> IntMap a -> IntMap a
    forall a. (Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate IntMap a
    l) IntMap a
    r
            else (Int -> Bool) -> IntMap a -> IntMap a
    forall a. (Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate IntMap a
    r
        IntMap a
    _ -> (Int -> Bool) -> IntMap a -> IntMap a
    forall a. (Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate IntMap a
    t
      where
        go :: (Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate' (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int -> Bool
    predicate' (Int -> Bool) -> Int -> Bool
    forall a b. (a -> b) -> a -> b
    $! Int
    pInt -> Int -> Int
    forall a. Num a => a -> a -> a
    +Int
    m = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l ((Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate' IntMap a
    r)
          | Bool
    otherwise         = (Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate' IntMap a
    l
        go Int -> Bool
    predicate' t' :: IntMap a
    t'@(Tip Int
    ky a
    _)
          | Int -> Bool
    predicate' Int
    ky = IntMap a
    t'
          | Bool
    otherwise     = IntMap a
    forall a. IntMap a
    Nil
        go Int -> Bool
    _ IntMap a
    Nil = IntMap a
    forall a. IntMap a
    Nil

    -- | \(O(\min(n,W))\). Drop while a predicate on the keys holds.
    -- The user is responsible for ensuring that for all @Int@s, @j \< k ==\> p j \>= p k@.
    -- See note at 'spanAntitone'.
    --
    -- @
    -- dropWhileAntitone p = 'fromDistinctAscList' . 'Data.List.dropWhile' (p . fst) . 'toList'
    -- dropWhileAntitone p = 'filterWithKey' (\\k _ -> not (p k))
    -- @
    --
    -- @since 0.6.7
    dropWhileAntitone :: (Key -> Bool) -> IntMap a -> IntMap a
    dropWhileAntitone :: forall a. (Int -> Bool) -> IntMap a -> IntMap a
    dropWhileAntitone Int -> Bool
    predicate IntMap a
    t =
      case IntMap a
    t of
        Bin Int
    p Int
    m IntMap a
    l IntMap a
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 ->
            if Int -> Bool
    predicate Int
    0 -- handle negative numbers.
            then (Int -> Bool) -> IntMap a -> IntMap a
    forall a. (Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate IntMap a
    l
            else Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l ((Int -> Bool) -> IntMap a -> IntMap a
    forall a. (Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate IntMap a
    r)
        IntMap a
    _ -> (Int -> Bool) -> IntMap a -> IntMap a
    forall a. (Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate IntMap a
    t
      where
        go :: (Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate' (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int -> Bool
    predicate' (Int -> Bool) -> Int -> Bool
    forall a b. (a -> b) -> a -> b
    $! Int
    pInt -> Int -> Int
    forall a. Num a => a -> a -> a
    +Int
    m = (Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate' IntMap a
    r
          | Bool
    otherwise         = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m ((Int -> Bool) -> IntMap a -> IntMap a
    go Int -> Bool
    predicate' IntMap a
    l) IntMap a
    r
        go Int -> Bool
    predicate' t' :: IntMap a
    t'@(Tip Int
    ky a
    _)
          | Int -> Bool
    predicate' Int
    ky = IntMap a
    forall a. IntMap a
    Nil
          | Bool
    otherwise     = IntMap a
    t'
        go Int -> Bool
    _ IntMap a
    Nil = IntMap a
    forall a. IntMap a
    Nil

    -- | \(O(\min(n,W))\). Divide a map at the point where a predicate on the keys stops holding.
    -- The user is responsible for ensuring that for all @Int@s, @j \< k ==\> p j \>= p k@.
    --
    -- @
    -- spanAntitone p xs = ('takeWhileAntitone' p xs, 'dropWhileAntitone' p xs)
    -- spanAntitone p xs = 'partitionWithKey' (\\k _ -> p k) xs
    -- @
    --
    -- Note: if @p@ is not actually antitone, then @spanAntitone@ will split the map
    -- at some /unspecified/ point.
    --
    -- @since 0.6.7
    spanAntitone :: (Key -> Bool) -> IntMap a -> (IntMap a, IntMap a)
    spanAntitone :: forall a. (Int -> Bool) -> IntMap a -> (IntMap a, IntMap a)
    spanAntitone Int -> Bool
    predicate IntMap a
    t =
      case IntMap a
    t of
        Bin Int
    p Int
    m IntMap a
    l IntMap a
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 ->
            if Int -> Bool
    predicate Int
    0 -- handle negative numbers.
            then
              case (Int -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall {a}.
    (Int -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int -> Bool
    predicate IntMap a
    l of
                (IntMap a
    lt :*: IntMap a
    gt) ->
                  let !lt' :: IntMap a
    lt' = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    lt IntMap a
    r
                  in (IntMap a
    lt', IntMap a
    gt)
            else
              case (Int -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall {a}.
    (Int -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int -> Bool
    predicate IntMap a
    r of
                (IntMap a
    lt :*: IntMap a
    gt) ->
                  let !gt' :: IntMap a
    gt' = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l IntMap a
    gt
                  in (IntMap a
    lt, IntMap a
    gt')
        IntMap a
    _ -> case (Int -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall {a}.
    (Int -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int -> Bool
    predicate IntMap a
    t of
              (IntMap a
    lt :*: IntMap a
    gt) -> (IntMap a
    lt, IntMap a
    gt)
      where
        go :: (Int -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int -> Bool
    predicate' (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int -> Bool
    predicate' (Int -> Bool) -> Int -> Bool
    forall a b. (a -> b) -> a -> b
    $! Int
    pInt -> Int -> Int
    forall a. Num a => a -> a -> a
    +Int
    m = case (Int -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int -> Bool
    predicate' IntMap a
    r of (IntMap a
    lt :*: IntMap a
    gt) -> Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l IntMap a
    lt IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    gt
          | Bool
    otherwise         = case (Int -> Bool) -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int -> Bool
    predicate' IntMap a
    l of (IntMap a
    lt :*: IntMap a
    gt) -> IntMap a
    lt IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    gt IntMap a
    r
        go Int -> Bool
    predicate' t' :: IntMap a
    t'@(Tip Int
    ky a
    _)
          | Int -> Bool
    predicate' Int
    ky = (IntMap a
    t' IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    forall a. IntMap a
    Nil)
          | Bool
    otherwise     = (IntMap a
    forall a. IntMap a
    Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    t')
        go Int -> Bool
    _ IntMap a
    Nil = (IntMap a
    forall a. IntMap a
    Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    forall a. IntMap a
    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 :: forall a b. (a -> Maybe b) -> IntMap a -> IntMap b
    mapMaybe a -> Maybe b
    f = (Int -> a -> Maybe b) -> IntMap a -> IntMap b
    forall a b. (Int -> a -> Maybe b) -> IntMap a -> IntMap b
    mapMaybeWithKey (\Int
    _ a
    x -> a -> Maybe b
    f a
    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 :: forall a b. (Int -> a -> Maybe b) -> IntMap a -> IntMap b
    mapMaybeWithKey Int -> a -> Maybe b
    f (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      = Int -> Int -> IntMap b -> IntMap b -> IntMap b
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m ((Int -> a -> Maybe b) -> IntMap a -> IntMap b
    forall a b. (Int -> a -> Maybe b) -> IntMap a -> IntMap b
    mapMaybeWithKey Int -> a -> Maybe b
    f IntMap a
    l) ((Int -> a -> Maybe b) -> IntMap a -> IntMap b
    forall a b. (Int -> a -> Maybe b) -> IntMap a -> IntMap b
    mapMaybeWithKey Int -> a -> Maybe b
    f IntMap a
    r)
    mapMaybeWithKey Int -> a -> Maybe b
    f (Tip Int
    k a
    x) = case Int -> a -> Maybe b
    f Int
    k a
    x of
      Just b
    y  -> Int -> b -> IntMap b
    forall a. Int -> a -> IntMap a
    Tip Int
    k b
    y
      Maybe b
    Nothing -> IntMap b
    forall a. IntMap a
    Nil
    mapMaybeWithKey Int -> a -> Maybe b
    _ IntMap a
    Nil = IntMap b
    forall a. IntMap a
    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 :: forall a b c. (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
    mapEither a -> Either b c
    f IntMap a
    m
      = (Int -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
    forall a b c.
    (Int -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
    mapEitherWithKey (\Int
    _ a
    x -> a -> Either b c
    f a
    x) IntMap a
    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 :: forall a b c.
    (Int -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
    mapEitherWithKey Int -> a -> Either b c
    f0 IntMap a
    t0 = StrictPair (IntMap b) (IntMap c) -> (IntMap b, IntMap c)
    forall a b. StrictPair a b -> (a, b)
    toPair (StrictPair (IntMap b) (IntMap c) -> (IntMap b, IntMap c))
    -> StrictPair (IntMap b) (IntMap c) -> (IntMap b, IntMap c)
    forall a b. (a -> b) -> a -> b
    $ (Int -> a -> Either b c)
    -> IntMap a -> StrictPair (IntMap b) (IntMap c)
    forall {t} {a} {a}.
    (Int -> t -> Either a a)
    -> IntMap t -> StrictPair (IntMap a) (IntMap a)
    go Int -> a -> Either b c
    f0 IntMap a
    t0
      where
        go :: (Int -> t -> Either a a)
    -> IntMap t -> StrictPair (IntMap a) (IntMap a)
    go Int -> t -> Either a a
    f (Bin Int
    p Int
    m IntMap t
    l IntMap t
    r) =
          Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l1 IntMap a
    r1 IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l2 IntMap a
    r2
          where
            (IntMap a
    l1 :*: IntMap a
    l2) = (Int -> t -> Either a a)
    -> IntMap t -> StrictPair (IntMap a) (IntMap a)
    go Int -> t -> Either a a
    f IntMap t
    l
            (IntMap a
    r1 :*: IntMap a
    r2) = (Int -> t -> Either a a)
    -> IntMap t -> StrictPair (IntMap a) (IntMap a)
    go Int -> t -> Either a a
    f IntMap t
    r
        go Int -> t -> Either a a
    f (Tip Int
    k t
    x) = case Int -> t -> Either a a
    f Int
    k t
    x of
          Left a
    y  -> (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    y IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    forall a. IntMap a
    Nil)
          Right a
    z -> (IntMap a
    forall a. IntMap a
    Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    z)
        go Int -> t -> Either a a
    _ IntMap t
    Nil = (IntMap a
    forall a. IntMap a
    Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    forall a. IntMap a
    Nil)

    -- | \(O(\min(n,W))\). 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@. Any key equal to @k@ is found in neither @map1@ nor @map2@.
    --
    -- > 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 :: forall a. Int -> IntMap a -> (IntMap a, IntMap a)
    split Int
    k IntMap a
    t =
      case IntMap a
    t of
        Bin Int
    p Int
    m IntMap a
    l IntMap a
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 ->
            if Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    >= Int
    0 -- handle negative numbers.
            then
              case Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall {a}. Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int
    k IntMap a
    l of
                (IntMap a
    lt :*: IntMap a
    gt) ->
                  let !lt' :: IntMap a
    lt' = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    lt IntMap a
    r
                  in (IntMap a
    lt', IntMap a
    gt)
            else
              case Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall {a}. Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int
    k IntMap a
    r of
                (IntMap a
    lt :*: IntMap a
    gt) ->
                  let !gt' :: IntMap a
    gt' = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l IntMap a
    gt
                  in (IntMap a
    lt, IntMap a
    gt')
        IntMap a
    _ -> case Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall {a}. Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int
    k IntMap a
    t of
              (IntMap a
    lt :*: IntMap a
    gt) -> (IntMap a
    lt, IntMap a
    gt)
      where
        go :: Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int
    k' t' :: IntMap a
    t'@(Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int -> Int -> Int -> Bool
    nomatch Int
    k' Int
    p Int
    m = if Int
    k' Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > Int
    p then IntMap a
    t' IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    forall a. IntMap a
    Nil else IntMap a
    forall a. IntMap a
    Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    t'
          | Int -> Int -> Bool
    zero Int
    k' Int
    m = case Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int
    k' IntMap a
    l of (IntMap a
    lt :*: IntMap a
    gt) -> IntMap a
    lt IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    gt IntMap a
    r
          | Bool
    otherwise = case Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    go Int
    k' IntMap a
    r of (IntMap a
    lt :*: IntMap a
    gt) -> Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l IntMap a
    lt IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    gt
        go Int
    k' t' :: IntMap a
    t'@(Tip Int
    ky a
    _)
          | Int
    k' Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > Int
    ky   = (IntMap a
    t' IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    forall a. IntMap a
    Nil)
          | Int
    k' Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    ky   = (IntMap a
    forall a. IntMap a
    Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    t')
          | Bool
    otherwise = (IntMap a
    forall a. IntMap a
    Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    forall a. IntMap a
    Nil)
        go Int
    _ IntMap a
    Nil = (IntMap a
    forall a. IntMap a
    Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
    forall a b. a -> b -> StrictPair a b
    :*: IntMap a
    forall a. IntMap a
    Nil)

    data SplitLookup a = SplitLookup !(IntMap a) !(Maybe a) !(IntMap a)

    mapLT :: (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    mapLT :: forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    mapLT IntMap a -> IntMap a
    f (SplitLookup IntMap a
    lt Maybe a
    fnd IntMap a
    gt) = IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    SplitLookup (IntMap a -> IntMap a
    f IntMap a
    lt) Maybe a
    fnd IntMap a
    gt
    {-# INLINE mapLT #-}

    mapGT :: (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    mapGT :: forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    mapGT IntMap a -> IntMap a
    f (SplitLookup IntMap a
    lt Maybe a
    fnd IntMap a
    gt) = IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    SplitLookup IntMap a
    lt Maybe a
    fnd (IntMap a -> IntMap a
    f IntMap a
    gt)
    {-# INLINE mapGT #-}

    -- | \(O(\min(n,W))\). 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 :: forall a. Int -> IntMap a -> (IntMap a, Maybe a, IntMap a)
    splitLookup Int
    k IntMap a
    t =
      case
        case IntMap a
    t of
          Bin Int
    p Int
    m IntMap a
    l IntMap a
    r
            | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 ->
              if Int
    k Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    >= Int
    0 -- handle negative numbers.
              then (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    mapLT ((IntMap a -> IntMap a -> IntMap a)
    -> IntMap a -> IntMap a -> IntMap a
    forall a b c. (a -> b -> c) -> b -> a -> c
    flip (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m) IntMap a
    r) (Int -> IntMap a -> SplitLookup a
    forall {a}. Int -> IntMap a -> SplitLookup a
    go Int
    k IntMap a
    l)
              else (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    mapGT (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l) (Int -> IntMap a -> SplitLookup a
    forall {a}. Int -> IntMap a -> SplitLookup a
    go Int
    k IntMap a
    r)
          IntMap a
    _ -> Int -> IntMap a -> SplitLookup a
    forall {a}. Int -> IntMap a -> SplitLookup a
    go Int
    k IntMap a
    t
      of SplitLookup IntMap a
    lt Maybe a
    fnd IntMap a
    gt -> (IntMap a
    lt, Maybe a
    fnd, IntMap a
    gt)
      where
        go :: Int -> IntMap a -> SplitLookup a
    go Int
    k' t' :: IntMap a
    t'@(Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
          | Int -> Int -> Int -> Bool
    nomatch Int
    k' Int
    p Int
    m =
              if Int
    k' Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > Int
    p
              then IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    SplitLookup IntMap a
    t' Maybe a
    forall a. Maybe a
    Nothing IntMap a
    forall a. IntMap a
    Nil
              else IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    SplitLookup IntMap a
    forall a. IntMap a
    Nil Maybe a
    forall a. Maybe a
    Nothing IntMap a
    t'
          | Int -> Int -> Bool
    zero Int
    k' Int
    m = (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    mapGT ((IntMap a -> IntMap a -> IntMap a)
    -> IntMap a -> IntMap a -> IntMap a
    forall a b c. (a -> b -> c) -> b -> a -> c
    flip (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m) IntMap a
    r) (Int -> IntMap a -> SplitLookup a
    go Int
    k' IntMap a
    l)
          | Bool
    otherwise = (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
    mapLT (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    p Int
    m IntMap a
    l) (Int -> IntMap a -> SplitLookup a
    go Int
    k' IntMap a
    r)
        go Int
    k' t' :: IntMap a
    t'@(Tip Int
    ky a
    y)
          | Int
    k' Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > Int
    ky   = IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    SplitLookup IntMap a
    t'  Maybe a
    forall a. Maybe a
    Nothing  IntMap a
    forall a. IntMap a
    Nil
          | Int
    k' Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    ky   = IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    SplitLookup IntMap a
    forall a. IntMap a
    Nil Maybe a
    forall a. Maybe a
    Nothing  IntMap a
    t'
          | Bool
    otherwise = IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    SplitLookup IntMap a
    forall a. IntMap a
    Nil (a -> Maybe a
    forall a. a -> Maybe a
    Just a
    y) IntMap a
    forall a. IntMap a
    Nil
        go Int
    _ IntMap a
    Nil      = IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
    SplitLookup IntMap a
    forall a. IntMap a
    Nil Maybe a
    forall a. Maybe a
    Nothing  IntMap a
    forall a. IntMap a
    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 :: forall a b. (a -> b -> b) -> b -> IntMap a -> b
    foldr a -> b -> b
    f b
    z = \IntMap a
    t ->      -- Use lambda t to be inlinable with two arguments only.
      case IntMap a
    t of
        Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z IntMap a
    l) IntMap a
    r -- put negative numbers before
          | Bool
    otherwise -> b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z IntMap a
    r) IntMap a
    l
        IntMap a
    _ -> b -> IntMap a -> b
    go b
    z IntMap a
    t
      where
        go :: b -> IntMap a -> b
    go b
    z' IntMap a
    Nil           = b
    z'
        go b
    z' (Tip Int
    _ a
    x)     = a -> b -> b
    f a
    x b
    z'
        go b
    z' (Bin Int
    _ Int
    _ IntMap a
    l IntMap a
    r) = b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z' IntMap a
    r) IntMap a
    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' :: forall a b. (a -> b -> b) -> b -> IntMap a -> b
    foldr' a -> b -> b
    f b
    z = \IntMap a
    t ->      -- Use lambda t to be inlinable with two arguments only.
      case IntMap a
    t of
        Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z IntMap a
    l) IntMap a
    r -- put negative numbers before
          | Bool
    otherwise -> b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z IntMap a
    r) IntMap a
    l
        IntMap a
    _ -> b -> IntMap a -> b
    go b
    z IntMap a
    t
      where
        go :: b -> IntMap a -> b
    go !b
    z' IntMap a
    Nil          = b
    z'
        go b
    z' (Tip Int
    _ a
    x)     = a -> b -> b
    f a
    x b
    z'
        go b
    z' (Bin Int
    _ Int
    _ IntMap a
    l IntMap a
    r) = b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z' IntMap a
    r) IntMap a
    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 :: forall b a. (b -> a -> b) -> b -> IntMap a -> b
    foldl a -> b -> a
    f a
    z = \IntMap b
    t ->      -- Use lambda t to be inlinable with two arguments only.
      case IntMap b
    t of
        Bin Int
    _ Int
    m IntMap b
    l IntMap b
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z IntMap b
    r) IntMap b
    l -- put negative numbers before
          | Bool
    otherwise -> a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z IntMap b
    l) IntMap b
    r
        IntMap b
    _ -> a -> IntMap b -> a
    go a
    z IntMap b
    t
      where
        go :: a -> IntMap b -> a
    go a
    z' IntMap b
    Nil           = a
    z'
        go a
    z' (Tip Int
    _ b
    x)     = a -> b -> a
    f a
    z' b
    x
        go a
    z' (Bin Int
    _ Int
    _ IntMap b
    l IntMap b
    r) = a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z' IntMap b
    l) IntMap b
    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' :: forall b a. (b -> a -> b) -> b -> IntMap a -> b
    foldl' a -> b -> a
    f a
    z = \IntMap b
    t ->      -- Use lambda t to be inlinable with two arguments only.
      case IntMap b
    t of
        Bin Int
    _ Int
    m IntMap b
    l IntMap b
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z IntMap b
    r) IntMap b
    l -- put negative numbers before
          | Bool
    otherwise -> a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z IntMap b
    l) IntMap b
    r
        IntMap b
    _ -> a -> IntMap b -> a
    go a
    z IntMap b
    t
      where
        go :: a -> IntMap b -> a
    go !a
    z' IntMap b
    Nil          = a
    z'
        go a
    z' (Tip Int
    _ b
    x)     = a -> b -> a
    f a
    z' b
    x
        go a
    z' (Bin Int
    _ Int
    _ IntMap b
    l IntMap b
    r) = a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z' IntMap b
    l) IntMap b
    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 :: (Key -> a -> b -> b) -> b -> IntMap a -> b
    foldrWithKey :: forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
    foldrWithKey Int -> a -> b -> b
    f b
    z = \IntMap a
    t ->      -- Use lambda t to be inlinable with two arguments only.
      case IntMap a
    t of
        Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z IntMap a
    l) IntMap a
    r -- put negative numbers before
          | Bool
    otherwise -> b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z IntMap a
    r) IntMap a
    l
        IntMap a
    _ -> b -> IntMap a -> b
    go b
    z IntMap a
    t
      where
        go :: b -> IntMap a -> b
    go b
    z' IntMap a
    Nil           = b
    z'
        go b
    z' (Tip Int
    kx a
    x)    = Int -> a -> b -> b
    f Int
    kx a
    x b
    z'
        go b
    z' (Bin Int
    _ Int
    _ IntMap a
    l IntMap a
    r) = b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z' IntMap a
    r) IntMap a
    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' :: (Key -> a -> b -> b) -> b -> IntMap a -> b
    foldrWithKey' :: forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
    foldrWithKey' Int -> a -> b -> b
    f b
    z = \IntMap a
    t ->      -- Use lambda t to be inlinable with two arguments only.
      case IntMap a
    t of
        Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z IntMap a
    l) IntMap a
    r -- put negative numbers before
          | Bool
    otherwise -> b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z IntMap a
    r) IntMap a
    l
        IntMap a
    _ -> b -> IntMap a -> b
    go b
    z IntMap a
    t
      where
        go :: b -> IntMap a -> b
    go !b
    z' IntMap a
    Nil          = b
    z'
        go b
    z' (Tip Int
    kx a
    x)    = Int -> a -> b -> b
    f Int
    kx a
    x b
    z'
        go b
    z' (Bin Int
    _ Int
    _ IntMap a
    l IntMap a
    r) = b -> IntMap a -> b
    go (b -> IntMap a -> b
    go b
    z' IntMap a
    r) IntMap a
    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 -> Key -> b -> a) -> a -> IntMap b -> a
    foldlWithKey :: forall a b. (a -> Int -> b -> a) -> a -> IntMap b -> a
    foldlWithKey a -> Int -> b -> a
    f a
    z = \IntMap b
    t ->      -- Use lambda t to be inlinable with two arguments only.
      case IntMap b
    t of
        Bin Int
    _ Int
    m IntMap b
    l IntMap b
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z IntMap b
    r) IntMap b
    l -- put negative numbers before
          | Bool
    otherwise -> a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z IntMap b
    l) IntMap b
    r
        IntMap b
    _ -> a -> IntMap b -> a
    go a
    z IntMap b
    t
      where
        go :: a -> IntMap b -> a
    go a
    z' IntMap b
    Nil           = a
    z'
        go a
    z' (Tip Int
    kx b
    x)    = a -> Int -> b -> a
    f a
    z' Int
    kx b
    x
        go a
    z' (Bin Int
    _ Int
    _ IntMap b
    l IntMap b
    r) = a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z' IntMap b
    l) IntMap b
    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 -> Key -> b -> a) -> a -> IntMap b -> a
    foldlWithKey' :: forall a b. (a -> Int -> b -> a) -> a -> IntMap b -> a
    foldlWithKey' a -> Int -> b -> a
    f a
    z = \IntMap b
    t ->      -- Use lambda t to be inlinable with two arguments only.
      case IntMap b
    t of
        Bin Int
    _ Int
    m IntMap b
    l IntMap b
    r
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z IntMap b
    r) IntMap b
    l -- put negative numbers before
          | Bool
    otherwise -> a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z IntMap b
    l) IntMap b
    r
        IntMap b
    _ -> a -> IntMap b -> a
    go a
    z IntMap b
    t
      where
        go :: a -> IntMap b -> a
    go !a
    z' IntMap b
    Nil          = a
    z'
        go a
    z' (Tip Int
    kx b
    x)    = a -> Int -> b -> a
    f a
    z' Int
    kx b
    x
        go a
    z' (Bin Int
    _ Int
    _ IntMap b
    l IntMap b
    r) = a -> IntMap b -> a
    go (a -> IntMap b -> a
    go a
    z' IntMap b
    l) IntMap b
    r
    {-# INLINE foldlWithKey' #-}

    -- | \(O(n)\). Fold the keys and values in the map using the given monoid, such that
    --
    -- @'foldMapWithKey' f = 'Prelude.fold' . 'mapWithKey' f@
    --
    -- This can be an asymptotically faster than 'foldrWithKey' or 'foldlWithKey' for some monoids.
    --
    -- @since 0.5.4
    foldMapWithKey :: Monoid m => (Key -> a -> m) -> IntMap a -> m
    foldMapWithKey :: forall m a. Monoid m => (Int -> a -> m) -> IntMap a -> m
    foldMapWithKey Int -> a -> m
    f = IntMap a -> m
    go
      where
        go :: IntMap a -> m
    go IntMap a
    Nil           = m
    forall a. Monoid a => a
    mempty
        go (Tip Int
    kx a
    x)    = Int -> a -> m
    f Int
    kx a
    x
        go (Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r)
          | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0     = IntMap a -> m
    go IntMap a
    r m -> m -> m
    forall a. Monoid a => a -> a -> a
    `mappend` IntMap a -> m
    go IntMap a
    l
          | Bool
    otherwise = IntMap a -> m
    go IntMap a
    l m -> m -> m
    forall a. Monoid a => a -> a -> a
    `mappend` IntMap a -> m
    go IntMap a
    r
    {-# INLINE foldMapWithKey #-}

    {--------------------------------------------------------------------
      List variations
    --------------------------------------------------------------------}
    -- | \(O(n)\).
    -- Return all elements of the map in the ascending order of their keys.
    -- Subject to list fusion.
    --
    -- > elems (fromList [(5,"a"), (3,"b")]) == ["b","a"]
    -- > elems empty == []

    elems :: IntMap a -> [a]
    elems :: forall a. IntMap a -> [a]
    elems = (a -> [a] -> [a]) -> [a] -> IntMap a -> [a]
    forall a b. (a -> b -> b) -> b -> IntMap a -> b
    foldr (:) []

    -- | \(O(n)\). Return all keys of the map in ascending order. Subject to list
    -- fusion.
    --
    -- > keys (fromList [(5,"a"), (3,"b")]) == [3,5]
    -- > keys empty == []

    keys  :: IntMap a -> [Key]
    keys :: forall a. IntMap a -> [Int]
    keys = (Int -> a -> [Int] -> [Int]) -> [Int] -> IntMap a -> [Int]
    forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
    foldrWithKey (\Int
    k a
    _ [Int]
    ks -> Int
    k Int -> [Int] -> [Int]
    forall a. a -> [a] -> [a]
    : [Int]
    ks) []

    -- | \(O(n)\). An alias for 'toAscList'. Returns all key\/value pairs in the
    -- map in ascending key order. Subject to list fusion.
    --
    -- > assocs (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
    -- > assocs empty == []

    assocs :: IntMap a -> [(Key,a)]
    assocs :: forall a. IntMap a -> [(Int, a)]
    assocs = IntMap a -> [(Int, a)]
    forall a. IntMap a -> [(Int, a)]
    toAscList

    -- | \(O(n)\). 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 :: forall a. IntMap a -> IntSet
    keysSet IntMap a
    Nil = IntSet
    IntSet.Nil
    keysSet (Tip Int
    kx a
    _) = Int -> IntSet
    IntSet.singleton Int
    kx
    keysSet (Bin Int
    p Int
    m IntMap a
    l IntMap a
    r)
      | Int
    m Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.suffixBitMask Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    0 = Int -> Int -> IntSet -> IntSet -> IntSet
    IntSet.Bin Int
    p Int
    m (IntMap a -> IntSet
    forall a. IntMap a -> IntSet
    keysSet IntMap a
    l) (IntMap a -> IntSet
    forall a. IntMap a -> IntSet
    keysSet IntMap a
    r)
      | Bool
    otherwise = Int -> Nat -> IntSet
    IntSet.Tip (Int
    p Int -> Int -> Int
    forall a. Bits a => a -> a -> a
    .&. Int
    IntSet.prefixBitMask) (Nat -> IntMap a -> Nat
    forall {a}. Nat -> IntMap a -> Nat
    computeBm (Nat -> IntMap a -> Nat
    forall {a}. Nat -> IntMap a -> Nat
    computeBm Nat
    0 IntMap a
    l) IntMap a
    r)
      where computeBm :: Nat -> IntMap a -> Nat
    computeBm !Nat
    acc (Bin Int
    _ Int
    _ IntMap a
    l' IntMap a
    r') = Nat -> IntMap a -> Nat
    computeBm (Nat -> IntMap a -> Nat
    computeBm Nat
    acc IntMap a
    l') IntMap a
    r'
            computeBm Nat
    acc (Tip Int
    kx a
    _) = Nat
    acc Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .|. Int -> Nat
    IntSet.bitmapOf Int
    kx
            computeBm Nat
    _   IntMap a
    Nil = [Char] -> Nat
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "Data.IntSet.keysSet: Nil"

    -- | \(O(n)\). Build a map from a set of keys and a function which for each key
    -- computes its value.
    --
    -- > fromSet (\k -> replicate k 'a') (Data.IntSet.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")]
    -- > fromSet undefined Data.IntSet.empty == empty

    fromSet :: (Key -> a) -> IntSet.IntSet -> IntMap a
    fromSet :: forall a. (Int -> a) -> IntSet -> IntMap a
    fromSet Int -> a
    _ IntSet
    IntSet.Nil = IntMap a
    forall a. IntMap a
    Nil
    fromSet Int -> a
    f (IntSet.Bin Int
    p Int
    m IntSet
    l IntSet
    r) = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m ((Int -> a) -> IntSet -> IntMap a
    forall a. (Int -> a) -> IntSet -> IntMap a
    fromSet Int -> a
    f IntSet
    l) ((Int -> a) -> IntSet -> IntMap a
    forall a. (Int -> a) -> IntSet -> IntMap a
    fromSet Int -> a
    f IntSet
    r)
    fromSet Int -> a
    f (IntSet.Tip Int
    kx Nat
    bm) = (Int -> a) -> Int -> Nat -> Int -> IntMap a
    forall {a}. (Int -> a) -> Int -> Nat -> Int -> IntMap a
    buildTree Int -> a
    f Int
    kx Nat
    bm (Int
    IntSet.suffixBitMask Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + Int
    1)
      where
        -- This is slightly complicated, as we to convert the dense
        -- representation of IntSet into tree representation of IntMap.
        --
        -- We are given a nonzero bit mask 'bmask' of 'bits' bits with
        -- prefix 'prefix'. We split bmask into halves corresponding
        -- to left and right subtree. If they are both nonempty, we
        -- create a Bin node, otherwise exactly one of them is nonempty
        -- and we construct the IntMap from that half.
        buildTree :: (Int -> a) -> Int -> Nat -> Int -> IntMap a
    buildTree Int -> a
    g !Int
    prefix !Nat
    bmask Int
    bits = case Int
    bits of
          Int
    0 -> Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    prefix (Int -> a
    g Int
    prefix)
          Int
    _ -> case Nat -> Int
    intFromNat ((Int -> Nat
    natFromInt Int
    bits) Nat -> Int -> Nat
    `shiftRL` Int
    1) of
            Int
    bits2
              | Nat
    bmask Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .&. ((Nat
    1 Nat -> Int -> Nat
    `shiftLL` Int
    bits2) Nat -> Nat -> Nat
    forall a. Num a => a -> a -> a
    - Nat
    1) Nat -> Nat -> Bool
    forall a. Eq a => a -> a -> Bool
    == Nat
    0 ->
                  (Int -> a) -> Int -> Nat -> Int -> IntMap a
    buildTree Int -> a
    g (Int
    prefix Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + Int
    bits2) (Nat
    bmask Nat -> Int -> Nat
    `shiftRL` Int
    bits2) Int
    bits2
              | (Nat
    bmask Nat -> Int -> Nat
    `shiftRL` Int
    bits2) Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .&. ((Nat
    1 Nat -> Int -> Nat
    `shiftLL` Int
    bits2) Nat -> Nat -> Nat
    forall a. Num a => a -> a -> a
    - Nat
    1) Nat -> Nat -> Bool
    forall a. Eq a => a -> a -> Bool
    == Nat
    0 ->
                  (Int -> a) -> Int -> Nat -> Int -> IntMap a
    buildTree Int -> a
    g Int
    prefix Nat
    bmask Int
    bits2
              | Bool
    otherwise ->
                  Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    prefix Int
    bits2
                    ((Int -> a) -> Int -> Nat -> Int -> IntMap a
    buildTree Int -> a
    g Int
    prefix Nat
    bmask Int
    bits2)
                    ((Int -> a) -> Int -> Nat -> Int -> IntMap a
    buildTree Int -> a
    g (Int
    prefix Int -> Int -> Int
    forall a. Num a => a -> a -> a
    + Int
    bits2) (Nat
    bmask Nat -> Int -> Nat
    `shiftRL` Int
    bits2) Int
    bits2)

    {--------------------------------------------------------------------
      Lists
    --------------------------------------------------------------------}

    #ifdef __GLASGOW_HASKELL__
    -- | @since 0.5.6.2
    instance GHCExts.IsList (IntMap a) where
      type Item (IntMap a) = (Key,a)
      fromList :: [Item (IntMap a)] -> IntMap a
    fromList = [(Int, a)] -> IntMap a
    [Item (IntMap a)] -> IntMap a
    forall a. [(Int, a)] -> IntMap a
    fromList
      toList :: IntMap a -> [Item (IntMap a)]
    toList   = IntMap a -> [(Int, a)]
    IntMap a -> [Item (IntMap a)]
    forall a. IntMap a -> [(Int, a)]
    toList
    #endif

    -- | \(O(n)\). Convert the map to a list of key\/value pairs. Subject to list
    -- fusion.
    --
    -- > toList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]
    -- > toList empty == []

    toList :: IntMap a -> [(Key,a)]
    toList :: forall a. IntMap a -> [(Int, a)]
    toList = IntMap a -> [(Int, a)]
    forall a. IntMap a -> [(Int, a)]
    toAscList

    -- | \(O(n)\). Convert the map to a list of key\/value pairs where the
    -- keys are in ascending order. Subject to list fusion.
    --
    -- > toAscList (fromList [(5,"a"), (3,"b")]) == [(3,"b"), (5,"a")]

    toAscList :: IntMap a -> [(Key,a)]
    toAscList :: forall a. IntMap a -> [(Int, a)]
    toAscList = (Int -> a -> [(Int, a)] -> [(Int, a)])
    -> [(Int, a)] -> IntMap a -> [(Int, a)]
    forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
    foldrWithKey (\Int
    k a
    x [(Int, a)]
    xs -> (Int
    k,a
    x)(Int, a) -> [(Int, a)] -> [(Int, a)]
    forall a. a -> [a] -> [a]
    :[(Int, a)]
    xs) []

    -- | \(O(n)\). Convert the map to a list of key\/value pairs where the keys
    -- are in descending order. Subject to list fusion.
    --
    -- > toDescList (fromList [(5,"a"), (3,"b")]) == [(5,"a"), (3,"b")]

    toDescList :: IntMap a -> [(Key,a)]
    toDescList :: forall a. IntMap a -> [(Int, a)]
    toDescList = ([(Int, a)] -> Int -> a -> [(Int, a)])
    -> [(Int, a)] -> IntMap a -> [(Int, a)]
    forall a b. (a -> Int -> b -> a) -> a -> IntMap b -> a
    foldlWithKey (\[(Int, a)]
    xs Int
    k a
    x -> (Int
    k,a
    x)(Int, a) -> [(Int, a)] -> [(Int, a)]
    forall a. a -> [a] -> [a]
    :[(Int, a)]
    xs) []

    -- List fusion for the list generating functions.
    #if __GLASGOW_HASKELL__
    -- The foldrFB and foldlFB are fold{r,l}WithKey equivalents, used for list fusion.
    -- They are important to convert unfused methods back, see mapFB in prelude.
    foldrFB :: (Key -> a -> b -> b) -> b -> IntMap a -> b
    foldrFB :: forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
    foldrFB = (Int -> a -> b -> b) -> b -> IntMap a -> b
    forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
    foldrWithKey
    {-# INLINE[0] foldrFB #-}
    foldlFB :: (a -> Key -> b -> a) -> a -> IntMap b -> a
    foldlFB :: forall a b. (a -> Int -> b -> a) -> a -> IntMap b -> a
    foldlFB = (a -> Int -> b -> a) -> a -> IntMap b -> a
    forall a b. (a -> Int -> b -> a) -> a -> IntMap b -> a
    foldlWithKey
    {-# INLINE[0] foldlFB #-}

    -- Inline assocs and toList, so that we need to fuse only toAscList.
    {-# INLINE assocs #-}
    {-# INLINE toList #-}

    -- The fusion is enabled up to phase 2 included. If it does not succeed,
    -- convert in phase 1 the expanded elems,keys,to{Asc,Desc}List calls back to
    -- elems,keys,to{Asc,Desc}List.  In phase 0, we inline fold{lr}FB (which were
    -- used in a list fusion, otherwise it would go away in phase 1), and let compiler
    -- do whatever it wants with elems,keys,to{Asc,Desc}List -- it was forbidden to
    -- inline it before phase 0, otherwise the fusion rules would not fire at all.
    {-# NOINLINE[0] elems #-}
    {-# NOINLINE[0] keys #-}
    {-# NOINLINE[0] toAscList #-}
    {-# NOINLINE[0] toDescList #-}
    {-# RULES "IntMap.elems" [~1] forall m . elems m = build (\c n -> foldrFB (\_ x xs -> c x xs) n m) #-}
    {-# RULES "IntMap.elemsBack" [1] foldrFB (\_ x xs -> x : xs) [] = elems #-}
    {-# RULES "IntMap.keys" [~1] forall m . keys m = build (\c n -> foldrFB (\k _ xs -> c k xs) n m) #-}
    {-# RULES "IntMap.keysBack" [1] foldrFB (\k _ xs -> k : xs) [] = keys #-}
    {-# RULES "IntMap.toAscList" [~1] forall m . toAscList m = build (\c n -> foldrFB (\k x xs -> c (k,x) xs) n m) #-}
    {-# RULES "IntMap.toAscListBack" [1] foldrFB (\k x xs -> (k, x) : xs) [] = toAscList #-}
    {-# RULES "IntMap.toDescList" [~1] forall m . toDescList m = build (\c n -> foldlFB (\xs k x -> c (k,x) xs) n m) #-}
    {-# RULES "IntMap.toDescListBack" [1] foldlFB (\xs k x -> (k, x) : xs) [] = toDescList #-}
    #endif

    -- | \(O(n \min(n,W))\). 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 :: forall a. [(Int, a)] -> IntMap a
    fromList [(Int, a)]
    xs
      = (IntMap a -> (Int, a) -> IntMap a)
    -> IntMap a -> [(Int, a)] -> IntMap a
    forall b a. (b -> a -> b) -> b -> [a] -> b
    forall (t :: * -> *) b a.
    Foldable t =>
    (b -> a -> b) -> b -> t a -> b
    Foldable.foldl' IntMap a -> (Int, a) -> IntMap a
    forall {a}. IntMap a -> (Int, a) -> IntMap a
    ins IntMap a
    forall a. IntMap a
    empty [(Int, a)]
    xs
      where
        ins :: IntMap a -> (Int, a) -> IntMap a
    ins IntMap a
    t (Int
    k,a
    x)  = Int -> a -> IntMap a -> IntMap a
    forall a. Int -> a -> IntMap a -> IntMap a
    insert Int
    k a
    x IntMap a
    t

    -- | \(O(n \min(n,W))\). Build a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
    --
    -- > fromListWith (++) [(5,"a"), (5,"b"), (3,"x"), (5,"c")] == fromList [(3, "x"), (5, "cba")]
    -- > fromListWith (++) [] == empty
    --
    -- Note the reverse ordering of @"cba"@ in the example.
    --
    -- The symmetric combining function @f@ is applied in a left-fold over the list, as @f new old@.
    --
    -- === Performance
    --
    -- You should ensure that the given @f@ is fast with this order of arguments.
    --
    -- Symmetric functions may be slow in one order, and fast in another.
    -- For the common case of collecting values of matching keys in a list, as above:
    --
    -- The complexity of @(++) a b@ is \(O(a)\), so it is fast when given a short list as its first argument.
    -- Thus:
    --
    -- > fromListWith       (++)  (replicate 1000000 (3, "x"))   -- O(n),  fast
    -- > fromListWith (flip (++)) (replicate 1000000 (3, "x"))   -- O(n²), extremely slow
    --
    -- because they evaluate as, respectively:
    --
    -- > fromList [(3, "x" ++ ("x" ++ "xxxxx..xxxxx"))]   -- O(n)
    -- > fromList [(3, ("xxxxx..xxxxx" ++ "x") ++ "x")]   -- O(n²)
    --
    -- Thus, to get good performance with an operation like @(++)@ while also preserving
    -- the same order as in the input list, reverse the input:
    --
    -- > fromListWith (++) (reverse [(5,"a"), (5,"b"), (5,"c")]) == fromList [(5, "abc")]
    --
    -- and it is always fast to combine singleton-list values @[v]@ with @fromListWith (++)@, as in:
    --
    -- > fromListWith (++) $ reverse $ map (\(k, v) -> (k, [v])) someListOfTuples

    fromListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
    fromListWith :: forall a. (a -> a -> a) -> [(Int, a)] -> IntMap a
    fromListWith a -> a -> a
    f [(Int, a)]
    xs
      = (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    forall a. (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    fromListWithKey (\Int
    _ a
    x a
    y -> a -> a -> a
    f a
    x a
    y) [(Int, a)]
    xs

    -- | \(O(n \min(n,W))\). Build a map from a list of key\/value pairs with a combining function. See also fromAscListWithKey'.
    --
    -- > let f key new_value old_value = show key ++ ":" ++ new_value ++ "|" ++ old_value
    -- > fromListWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")] == fromList [(3, "3:a|b"), (5, "5:c|5:b|a")]
    -- > fromListWithKey f [] == empty
    --
    -- Also see the performance note on 'fromListWith'.

    fromListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
    fromListWithKey :: forall a. (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    fromListWithKey Int -> a -> a -> a
    f [(Int, a)]
    xs
      = (IntMap a -> (Int, a) -> IntMap a)
    -> IntMap a -> [(Int, a)] -> IntMap a
    forall b a. (b -> a -> b) -> b -> [a] -> b
    forall (t :: * -> *) b a.
    Foldable t =>
    (b -> a -> b) -> b -> t a -> b
    Foldable.foldl' IntMap a -> (Int, a) -> IntMap a
    ins IntMap a
    forall a. IntMap a
    empty [(Int, a)]
    xs
      where
        ins :: IntMap a -> (Int, a) -> IntMap a
    ins IntMap a
    t (Int
    k,a
    x) = (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
    forall a. (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
    insertWithKey Int -> a -> a -> a
    f Int
    k a
    x IntMap a
    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 :: forall a. [(Int, a)] -> IntMap a
    fromAscList = Distinct -> (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    forall a.
    Distinct -> (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    fromMonoListWithKey Distinct
    Nondistinct (\Int
    _ a
    x a
    _ -> a
    x)
    {-# NOINLINE fromAscList #-}

    -- | \(O(n)\). 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")]
    --
    -- Also see the performance note on 'fromListWith'.

    fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
    fromAscListWith :: forall a. (a -> a -> a) -> [(Int, a)] -> IntMap a
    fromAscListWith a -> a -> a
    f = Distinct -> (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    forall a.
    Distinct -> (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    fromMonoListWithKey Distinct
    Nondistinct (\Int
    _ a
    x a
    y -> a -> a -> a
    f a
    x a
    y)
    {-# NOINLINE fromAscListWith #-}

    -- | \(O(n)\). 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./
    --
    -- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
    -- > fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "5:b|a")]
    --
    -- Also see the performance note on 'fromListWith'.

    fromAscListWithKey :: (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
    fromAscListWithKey :: forall a. (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    fromAscListWithKey Int -> a -> a -> a
    f = Distinct -> (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    forall a.
    Distinct -> (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    fromMonoListWithKey Distinct
    Nondistinct Int -> a -> a -> a
    f
    {-# NOINLINE fromAscListWithKey #-}

    -- | \(O(n)\). 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")]

    fromDistinctAscList :: [(Key,a)] -> IntMap a
    fromDistinctAscList :: forall a. [(Int, a)] -> IntMap a
    fromDistinctAscList = Distinct -> (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    forall a.
    Distinct -> (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    fromMonoListWithKey Distinct
    Distinct (\Int
    _ a
    x a
    _ -> a
    x)
    {-# NOINLINE fromDistinctAscList #-}

    -- | \(O(n)\). Build a map from a list of key\/value pairs with monotonic keys
    -- and a combining function.
    --
    -- The precise conditions under which this function works are subtle:
    -- For any branch mask, keys with the same prefix w.r.t. the branch
    -- mask must occur consecutively in the list.
    --
    -- Also see the performance note on 'fromListWith'.

    fromMonoListWithKey :: Distinct -> (Key -> a -> a -> a) -> [(Key,a)] -> IntMap a
    fromMonoListWithKey :: forall a.
    Distinct -> (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
    fromMonoListWithKey Distinct
    distinct Int -> a -> a -> a
    f = [(Int, a)] -> IntMap a
    go
      where
        go :: [(Int, a)] -> IntMap a
    go []              = IntMap a
    forall a. IntMap a
    Nil
        go ((Int
    kx,a
    vx) : [(Int, a)]
    zs1) = Int -> a -> [(Int, a)] -> IntMap a
    addAll' Int
    kx a
    vx [(Int, a)]
    zs1

        -- `addAll'` collects all keys equal to `kx` into a single value,
        -- and then proceeds with `addAll`.
        addAll' :: Int -> a -> [(Int, a)] -> IntMap a
    addAll' !Int
    kx a
    vx []
            = Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    kx a
    vx
        addAll' !Int
    kx a
    vx ((Int
    ky,a
    vy) : [(Int, a)]
    zs)
            | Distinct
    Nondistinct <- Distinct
    distinct, Int
    kx Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    ky
            = let v :: a
    v = Int -> a -> a -> a
    f Int
    kx a
    vy a
    vx in Int -> a -> [(Int, a)] -> IntMap a
    addAll' Int
    ky a
    v [(Int, a)]
    zs
            -- inlined: | otherwise = addAll kx (Tip kx vx) (ky : zs)
            | Int
    m <- Int -> Int -> Int
    branchMask Int
    kx Int
    ky
            , Inserted IntMap a
    ty [(Int, a)]
    zs' <- Int -> Int -> a -> [(Int, a)] -> Inserted a
    addMany' Int
    m Int
    ky a
    vy [(Int, a)]
    zs
            = Int -> IntMap a -> [(Int, a)] -> IntMap a
    addAll Int
    kx (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    linkWithMask Int
    m Int
    ky IntMap a
    ty {-kx-} (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    kx a
    vx)) [(Int, a)]
    zs'

        -- for `addAll` and `addMany`, kx is /a/ key inside the tree `tx`
        -- `addAll` consumes the rest of the list, adding to the tree `tx`
        addAll :: Int -> IntMap a -> [(Int, a)] -> IntMap a
    addAll !Int
    _kx !IntMap a
    tx []
            = IntMap a
    tx
        addAll !Int
    kx !IntMap a
    tx ((Int
    ky,a
    vy) : [(Int, a)]
    zs)
            | Int
    m <- Int -> Int -> Int
    branchMask Int
    kx Int
    ky
            , Inserted IntMap a
    ty [(Int, a)]
    zs' <- Int -> Int -> a -> [(Int, a)] -> Inserted a
    addMany' Int
    m Int
    ky a
    vy [(Int, a)]
    zs
            = Int -> IntMap a -> [(Int, a)] -> IntMap a
    addAll Int
    kx (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    linkWithMask Int
    m Int
    ky IntMap a
    ty {-kx-} IntMap a
    tx) [(Int, a)]
    zs'

        -- `addMany'` is similar to `addAll'`, but proceeds with `addMany'`.
        addMany' :: Int -> Int -> a -> [(Int, a)] -> Inserted a
    addMany' !Int
    _m !Int
    kx a
    vx []
            = IntMap a -> [(Int, a)] -> Inserted a
    forall a. IntMap a -> [(Int, a)] -> Inserted a
    Inserted (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    kx a
    vx) []
        addMany' !Int
    m !Int
    kx a
    vx zs0 :: [(Int, a)]
    zs0@((Int
    ky,a
    vy) : [(Int, a)]
    zs)
            | Distinct
    Nondistinct <- Distinct
    distinct, Int
    kx Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    ky
            = let v :: a
    v = Int -> a -> a -> a
    f Int
    kx a
    vy a
    vx in Int -> Int -> a -> [(Int, a)] -> Inserted a
    addMany' Int
    m Int
    ky a
    v [(Int, a)]
    zs
            -- inlined: | otherwise = addMany m kx (Tip kx vx) (ky : zs)
            | Int -> Int -> Int
    mask Int
    kx Int
    m Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    /= Int -> Int -> Int
    mask Int
    ky Int
    m
            = IntMap a -> [(Int, a)] -> Inserted a
    forall a. IntMap a -> [(Int, a)] -> Inserted a
    Inserted (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    kx a
    vx) [(Int, a)]
    zs0
            | Int
    mxy <- Int -> Int -> Int
    branchMask Int
    kx Int
    ky
            , Inserted IntMap a
    ty [(Int, a)]
    zs' <- Int -> Int -> a -> [(Int, a)] -> Inserted a
    addMany' Int
    mxy Int
    ky a
    vy [(Int, a)]
    zs
            = Int -> Int -> IntMap a -> [(Int, a)] -> Inserted a
    addMany Int
    m Int
    kx (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    linkWithMask Int
    mxy Int
    ky IntMap a
    ty {-kx-} (Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    kx a
    vx)) [(Int, a)]
    zs'

        -- `addAll` adds to `tx` all keys whose prefix w.r.t. `m` agrees with `kx`.
        addMany :: Int -> Int -> IntMap a -> [(Int, a)] -> Inserted a
    addMany !Int
    _m !Int
    _kx IntMap a
    tx []
            = IntMap a -> [(Int, a)] -> Inserted a
    forall a. IntMap a -> [(Int, a)] -> Inserted a
    Inserted IntMap a
    tx []
        addMany !Int
    m !Int
    kx IntMap a
    tx zs0 :: [(Int, a)]
    zs0@((Int
    ky,a
    vy) : [(Int, a)]
    zs)
            | Int -> Int -> Int
    mask Int
    kx Int
    m Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    /= Int -> Int -> Int
    mask Int
    ky Int
    m
            = IntMap a -> [(Int, a)] -> Inserted a
    forall a. IntMap a -> [(Int, a)] -> Inserted a
    Inserted IntMap a
    tx [(Int, a)]
    zs0
            | Int
    mxy <- Int -> Int -> Int
    branchMask Int
    kx Int
    ky
            , Inserted IntMap a
    ty [(Int, a)]
    zs' <- Int -> Int -> a -> [(Int, a)] -> Inserted a
    addMany' Int
    mxy Int
    ky a
    vy [(Int, a)]
    zs
            = Int -> Int -> IntMap a -> [(Int, a)] -> Inserted a
    addMany Int
    m Int
    kx (Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    linkWithMask Int
    mxy Int
    ky IntMap a
    ty {-kx-} IntMap a
    tx) [(Int, a)]
    zs'
    {-# INLINE fromMonoListWithKey #-}

    data Inserted a = Inserted !(IntMap a) ![(Key,a)]

    data Distinct = Distinct | Nondistinct

    {--------------------------------------------------------------------
      Eq
    --------------------------------------------------------------------}
    instance Eq a => Eq (IntMap a) where
      IntMap a
    t1 == :: IntMap a -> IntMap a -> Bool
    == IntMap a
    t2  = IntMap a -> IntMap a -> Bool
    forall a. Eq a => IntMap a -> IntMap a -> Bool
    equal IntMap a
    t1 IntMap a
    t2
      IntMap a
    t1 /= :: IntMap a -> IntMap a -> Bool
    /= IntMap a
    t2  = IntMap a -> IntMap a -> Bool
    forall a. Eq a => IntMap a -> IntMap a -> Bool
    nequal IntMap a
    t1 IntMap a
    t2

    equal :: Eq a => IntMap a -> IntMap a -> Bool
    equal :: forall a. Eq a => IntMap a -> IntMap a -> Bool
    equal (Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1) (Bin Int
    p2 Int
    m2 IntMap a
    l2 IntMap a
    r2)
      = (Int
    m1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    m2) Bool -> Bool -> Bool
    && (Int
    p1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    p2) Bool -> Bool -> Bool
    && (IntMap a -> IntMap a -> Bool
    forall a. Eq a => IntMap a -> IntMap a -> Bool
    equal IntMap a
    l1 IntMap a
    l2) Bool -> Bool -> Bool
    && (IntMap a -> IntMap a -> Bool
    forall a. Eq a => IntMap a -> IntMap a -> Bool
    equal IntMap a
    r1 IntMap a
    r2)
    equal (Tip Int
    kx a
    x) (Tip Int
    ky a
    y)
      = (Int
    kx Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    ky) Bool -> Bool -> Bool
    && (a
    xa -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    ==a
    y)
    equal IntMap a
    Nil IntMap a
    Nil = Bool
    True
    equal IntMap a
    _   IntMap a
    _   = Bool
    False

    nequal :: Eq a => IntMap a -> IntMap a -> Bool
    nequal :: forall a. Eq a => IntMap a -> IntMap a -> Bool
    nequal (Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1) (Bin Int
    p2 Int
    m2 IntMap a
    l2 IntMap a
    r2)
      = (Int
    m1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    /= Int
    m2) Bool -> Bool -> Bool
    || (Int
    p1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    /= Int
    p2) Bool -> Bool -> Bool
    || (IntMap a -> IntMap a -> Bool
    forall a. Eq a => IntMap a -> IntMap a -> Bool
    nequal IntMap a
    l1 IntMap a
    l2) Bool -> Bool -> Bool
    || (IntMap a -> IntMap a -> Bool
    forall a. Eq a => IntMap a -> IntMap a -> Bool
    nequal IntMap a
    r1 IntMap a
    r2)
    nequal (Tip Int
    kx a
    x) (Tip Int
    ky a
    y)
      = (Int
    kx Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    /= Int
    ky) Bool -> Bool -> Bool
    || (a
    xa -> a -> Bool
    forall a. Eq a => a -> a -> Bool
    /=a
    y)
    nequal IntMap a
    Nil IntMap a
    Nil = Bool
    False
    nequal IntMap a
    _   IntMap a
    _   = Bool
    True

    -- | @since 0.5.9
    instance Eq1 IntMap where
      liftEq :: forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    liftEq a -> b -> Bool
    eq (Bin Int
    p1 Int
    m1 IntMap a
    l1 IntMap a
    r1) (Bin Int
    p2 Int
    m2 IntMap b
    l2 IntMap b
    r2)
        = (Int
    m1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    m2) Bool -> Bool -> Bool
    && (Int
    p1 Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    p2) Bool -> Bool -> Bool
    && ((a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    forall (f :: * -> *) a b.
    Eq1 f =>
    (a -> b -> Bool) -> f a -> f b -> Bool
    liftEq a -> b -> Bool
    eq IntMap a
    l1 IntMap b
    l2) Bool -> Bool -> Bool
    && ((a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
    forall (f :: * -> *) a b.
    Eq1 f =>
    (a -> b -> Bool) -> f a -> f b -> Bool
    liftEq a -> b -> Bool
    eq IntMap a
    r1 IntMap b
    r2)
      liftEq a -> b -> Bool
    eq (Tip Int
    kx a
    x) (Tip Int
    ky b
    y)
        = (Int
    kx Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    ky) Bool -> Bool -> Bool
    && (a -> b -> Bool
    eq a
    x b
    y)
      liftEq a -> b -> Bool
    _eq IntMap a
    Nil IntMap b
    Nil = Bool
    True
      liftEq a -> b -> Bool
    _eq IntMap a
    _   IntMap b
    _   = Bool
    False

    {--------------------------------------------------------------------
      Ord
    --------------------------------------------------------------------}

    instance Ord a => Ord (IntMap a) where
        compare :: IntMap a -> IntMap a -> Ordering
    compare IntMap a
    m1 IntMap a
    m2 = [(Int, a)] -> [(Int, a)] -> Ordering
    forall a. Ord a => a -> a -> Ordering
    compare (IntMap a -> [(Int, a)]
    forall a. IntMap a -> [(Int, a)]
    toList IntMap a
    m1) (IntMap a -> [(Int, a)]
    forall a. IntMap a -> [(Int, a)]
    toList IntMap a
    m2)

    -- | @since 0.5.9
    instance Ord1 IntMap where
      liftCompare :: forall a b.
    (a -> b -> Ordering) -> IntMap a -> IntMap b -> Ordering
    liftCompare a -> b -> Ordering
    cmp IntMap a
    m IntMap b
    n =
        ((Int, a) -> (Int, b) -> Ordering)
    -> [(Int, a)] -> [(Int, b)] -> Ordering
    forall a b. (a -> b -> Ordering) -> [a] -> [b] -> Ordering
    forall (f :: * -> *) a b.
    Ord1 f =>
    (a -> b -> Ordering) -> f a -> f b -> Ordering
    liftCompare ((a -> b -> Ordering) -> (Int, a) -> (Int, b) -> Ordering
    forall a b.
    (a -> b -> Ordering) -> (Int, a) -> (Int, b) -> Ordering
    forall (f :: * -> *) a b.
    Ord1 f =>
    (a -> b -> Ordering) -> f a -> f b -> Ordering
    liftCompare a -> b -> Ordering
    cmp) (IntMap a -> [(Int, a)]
    forall a. IntMap a -> [(Int, a)]
    toList IntMap a
    m) (IntMap b -> [(Int, b)]
    forall a. IntMap a -> [(Int, a)]
    toList IntMap b
    n)

    {--------------------------------------------------------------------
      Functor
    --------------------------------------------------------------------}

    instance Functor IntMap where
        fmap :: forall a b. (a -> b) -> IntMap a -> IntMap b
    fmap = (a -> b) -> IntMap a -> IntMap b
    forall a b. (a -> b) -> IntMap a -> IntMap b
    map

    #ifdef __GLASGOW_HASKELL__
        a
    a <$ :: forall a b. a -> IntMap b -> IntMap a
    <$ Bin Int
    p Int
    m IntMap b
    l IntMap b
    r = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m (a
    a a -> IntMap b -> IntMap a
    forall a b. a -> IntMap b -> IntMap a
    forall (f :: * -> *) a b. Functor f => a -> f b -> f a
    <$ IntMap b
    l) (a
    a a -> IntMap b -> IntMap a
    forall a b. a -> IntMap b -> IntMap a
    forall (f :: * -> *) a b. Functor f => a -> f b -> f a
    <$ IntMap b
    r)
        a
    a <$ Tip Int
    k b
    _     = Int -> a -> IntMap a
    forall a. Int -> a -> IntMap a
    Tip Int
    k a
    a
        a
    _ <$ IntMap b
    Nil         = IntMap a
    forall a. IntMap a
    Nil
    #endif

    {--------------------------------------------------------------------
      Show
    --------------------------------------------------------------------}

    instance Show a => Show (IntMap a) where
      showsPrec :: Int -> IntMap a -> [Char] -> [Char]
    showsPrec Int
    d IntMap a
    m   = Bool -> ([Char] -> [Char]) -> [Char] -> [Char]
    showParen (Int
    d Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    > Int
    10) (([Char] -> [Char]) -> [Char] -> [Char])
    -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall a b. (a -> b) -> a -> b
    $
        [Char] -> [Char] -> [Char]
    showString [Char]
    "fromList " ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [(Int, a)] -> [Char] -> [Char]
    forall a. Show a => a -> [Char] -> [Char]
    shows (IntMap a -> [(Int, a)]
    forall a. IntMap a -> [(Int, a)]
    toList IntMap a
    m)

    -- | @since 0.5.9
    instance Show1 IntMap where
        liftShowsPrec :: forall a.
    (Int -> a -> [Char] -> [Char])
    -> ([a] -> [Char] -> [Char]) -> Int -> IntMap a -> [Char] -> [Char]
    liftShowsPrec Int -> a -> [Char] -> [Char]
    sp [a] -> [Char] -> [Char]
    sl Int
    d IntMap a
    m =
            (Int -> [(Int, a)] -> [Char] -> [Char])
    -> [Char] -> Int -> [(Int, a)] -> [Char] -> [Char]
    forall a.
    (Int -> a -> [Char] -> [Char])
    -> [Char] -> Int -> a -> [Char] -> [Char]
    showsUnaryWith ((Int -> (Int, a) -> [Char] -> [Char])
    -> ([(Int, a)] -> [Char] -> [Char])
    -> Int
    -> [(Int, a)]
    -> [Char]
    -> [Char]
    forall a.
    (Int -> a -> [Char] -> [Char])
    -> ([a] -> [Char] -> [Char]) -> Int -> [a] -> [Char] -> [Char]
    forall (f :: * -> *) a.
    Show1 f =>
    (Int -> a -> [Char] -> [Char])
    -> ([a] -> [Char] -> [Char]) -> Int -> f a -> [Char] -> [Char]
    liftShowsPrec Int -> (Int, a) -> [Char] -> [Char]
    sp' [(Int, a)] -> [Char] -> [Char]
    sl') [Char]
    "fromList" Int
    d (IntMap a -> [(Int, a)]
    forall a. IntMap a -> [(Int, a)]
    toList IntMap a
    m)
          where
            sp' :: Int -> (Int, a) -> [Char] -> [Char]
    sp' = (Int -> a -> [Char] -> [Char])
    -> ([a] -> [Char] -> [Char]) -> Int -> (Int, a) -> [Char] -> [Char]
    forall a.
    (Int -> a -> [Char] -> [Char])
    -> ([a] -> [Char] -> [Char]) -> Int -> (Int, a) -> [Char] -> [Char]
    forall (f :: * -> *) a.
    Show1 f =>
    (Int -> a -> [Char] -> [Char])
    -> ([a] -> [Char] -> [Char]) -> Int -> f a -> [Char] -> [Char]
    liftShowsPrec Int -> a -> [Char] -> [Char]
    sp [a] -> [Char] -> [Char]
    sl
            sl' :: [(Int, a)] -> [Char] -> [Char]
    sl' = (Int -> a -> [Char] -> [Char])
    -> ([a] -> [Char] -> [Char]) -> [(Int, a)] -> [Char] -> [Char]
    forall a.
    (Int -> a -> [Char] -> [Char])
    -> ([a] -> [Char] -> [Char]) -> [(Int, a)] -> [Char] -> [Char]
    forall (f :: * -> *) a.
    Show1 f =>
    (Int -> a -> [Char] -> [Char])
    -> ([a] -> [Char] -> [Char]) -> [f a] -> [Char] -> [Char]
    liftShowList Int -> a -> [Char] -> [Char]
    sp [a] -> [Char] -> [Char]
    sl

    {--------------------------------------------------------------------
      Read
    --------------------------------------------------------------------}
    instance (Read e) => Read (IntMap e) where
    #ifdef __GLASGOW_HASKELL__
      readPrec :: ReadPrec (IntMap e)
    readPrec = ReadPrec (IntMap e) -> ReadPrec (IntMap e)
    forall a. ReadPrec a -> ReadPrec a
    parens (ReadPrec (IntMap e) -> ReadPrec (IntMap e))
    -> ReadPrec (IntMap e) -> ReadPrec (IntMap e)
    forall a b. (a -> b) -> a -> b
    $ Int -> ReadPrec (IntMap e) -> ReadPrec (IntMap e)
    forall a. Int -> ReadPrec a -> ReadPrec a
    prec Int
    10 (ReadPrec (IntMap e) -> ReadPrec (IntMap e))
    -> ReadPrec (IntMap e) -> ReadPrec (IntMap e)
    forall a b. (a -> b) -> a -> b
    $ do
        Ident "fromList" <- ReadPrec Lexeme
    lexP
        xs <- readPrec
        return (fromList xs)

      readListPrec :: ReadPrec [IntMap e]
    readListPrec = ReadPrec [IntMap e]
    forall a. Read a => ReadPrec [a]
    readListPrecDefault
    #else
      readsPrec p = readParen (p > 10) $ \ r -> do
        ("fromList",s) <- lex r
        (xs,t) <- reads s
        return (fromList xs,t)
    #endif

    -- | @since 0.5.9
    instance Read1 IntMap where
        liftReadsPrec :: forall a. (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (IntMap a)
    liftReadsPrec Int -> ReadS a
    rp ReadS [a]
    rl = ([Char] -> ReadS (IntMap a)) -> Int -> ReadS (IntMap a)
    forall a. ([Char] -> ReadS a) -> Int -> ReadS a
    readsData (([Char] -> ReadS (IntMap a)) -> Int -> ReadS (IntMap a))
    -> ([Char] -> ReadS (IntMap a)) -> Int -> ReadS (IntMap a)
    forall a b. (a -> b) -> a -> b
    $
            (Int -> ReadS [(Int, a)])
    -> [Char] -> ([(Int, a)] -> IntMap a) -> [Char] -> ReadS (IntMap a)
    forall a t.
    (Int -> ReadS a) -> [Char] -> (a -> t) -> [Char] -> ReadS t
    readsUnaryWith ((Int -> ReadS (Int, a))
    -> ReadS [(Int, a)] -> Int -> ReadS [(Int, a)]
    forall a. (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS [a]
    forall (f :: * -> *) a.
    Read1 f =>
    (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)
    liftReadsPrec Int -> ReadS (Int, a)
    rp' ReadS [(Int, a)]
    rl') [Char]
    "fromList" [(Int, a)] -> IntMap a
    forall a. [(Int, a)] -> IntMap a
    fromList
          where
            rp' :: Int -> ReadS (Int, a)
    rp' = (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Int, a)
    forall a. (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Int, a)
    forall (f :: * -> *) a.
    Read1 f =>
    (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (f a)
    liftReadsPrec Int -> ReadS a
    rp ReadS [a]
    rl
            rl' :: ReadS [(Int, a)]
    rl' = (Int -> ReadS a) -> ReadS [a] -> ReadS [(Int, a)]
    forall a. (Int -> ReadS a) -> ReadS [a] -> ReadS [(Int, a)]
    forall (f :: * -> *) a.
    Read1 f =>
    (Int -> ReadS a) -> ReadS [a] -> ReadS [f a]
    liftReadList Int -> ReadS a
    rp ReadS [a]
    rl

    {--------------------------------------------------------------------
      Helpers
    --------------------------------------------------------------------}
    {--------------------------------------------------------------------
      Link
    --------------------------------------------------------------------}
    link :: Prefix -> IntMap a -> Prefix -> IntMap a -> IntMap a
    link :: forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
    link Int
    p1 IntMap a
    t1 Int
    p2 IntMap a
    t2 = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    linkWithMask (Int -> Int -> Int
    branchMask Int
    p1 Int
    p2) Int
    p1 IntMap a
    t1 {-p2-} IntMap a
    t2
    {-# INLINE link #-}

    -- `linkWithMask` is useful when the `branchMask` has already been computed
    linkWithMask :: Mask -> Prefix -> IntMap a -> IntMap a -> IntMap a
    linkWithMask :: forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    linkWithMask Int
    m Int
    p1 IntMap a
    t1 {-p2-} IntMap a
    t2
      | Int -> Int -> Bool
    zero Int
    p1 Int
    m = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap a
    t1 IntMap a
    t2
      | Bool
    otherwise = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap a
    t2 IntMap a
    t1
      where
        p :: Int
    p = Int -> Int -> Int
    mask Int
    p1 Int
    m
    {-# INLINE linkWithMask #-}

    {--------------------------------------------------------------------
      @bin@ assures that we never have empty trees within a tree.
    --------------------------------------------------------------------}
    bin :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
    bin :: forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    bin Int
    _ Int
    _ IntMap a
    l IntMap a
    Nil = IntMap a
    l
    bin Int
    _ Int
    _ IntMap a
    Nil IntMap a
    r = IntMap a
    r
    bin Int
    p Int
    m IntMap a
    l IntMap a
    r   = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap a
    l IntMap a
    r
    {-# INLINE bin #-}

    -- binCheckLeft only checks that the left subtree is non-empty
    binCheckLeft :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft :: forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckLeft Int
    _ Int
    _ IntMap a
    Nil IntMap a
    r = IntMap a
    r
    binCheckLeft Int
    p Int
    m IntMap a
    l IntMap a
    r   = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap a
    l IntMap a
    r
    {-# INLINE binCheckLeft #-}

    -- binCheckRight only checks that the right subtree is non-empty
    binCheckRight :: Prefix -> Mask -> IntMap a -> IntMap a -> IntMap a
    binCheckRight :: forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    binCheckRight Int
    _ Int
    _ IntMap a
    l IntMap a
    Nil = IntMap a
    l
    binCheckRight Int
    p Int
    m IntMap a
    l IntMap a
    r   = Int -> Int -> IntMap a -> IntMap a -> IntMap a
    forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
    Bin Int
    p Int
    m IntMap a
    l IntMap a
    r
    {-# INLINE binCheckRight #-}

    {--------------------------------------------------------------------
      Endian independent bit twiddling
    --------------------------------------------------------------------}

    -- | Should this key follow the left subtree of a 'Bin' with switching
    -- bit @m@? N.B., the answer is only valid when @match i p m@ is true.
    zero :: Key -> Mask -> Bool
    zero :: Int -> Int -> Bool
    zero Int
    i Int
    m
      = (Int -> Nat
    natFromInt Int
    i) Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .&. (Int -> Nat
    natFromInt Int
    m) Nat -> Nat -> Bool
    forall a. Eq a => a -> a -> Bool
    == Nat
    0
    {-# INLINE zero #-}

    nomatch,match :: Key -> Prefix -> Mask -> Bool

    -- | Does the key @i@ differ from the prefix @p@ before getting to
    -- the switching bit @m@?
    nomatch :: Int -> Int -> Int -> Bool
    nomatch Int
    i Int
    p Int
    m
      = (Int -> Int -> Int
    mask Int
    i Int
    m) Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    /= Int
    p
    {-# INLINE nomatch #-}

    -- | Does the key @i@ match the prefix @p@ (up to but not including
    -- bit @m@)?
    match :: Int -> Int -> Int -> Bool
    match Int
    i Int
    p Int
    m
      = (Int -> Int -> Int
    mask Int
    i Int
    m) Int -> Int -> Bool
    forall a. Eq a => a -> a -> Bool
    == Int
    p
    {-# INLINE match #-}

    -- | The prefix of key @i@ up to (but not including) the switching
    -- bit @m@.
    mask :: Key -> Mask -> Prefix
    mask :: Int -> Int -> Int
    mask Int
    i Int
    m
      = Nat -> Nat -> Int
    maskW (Int -> Nat
    natFromInt Int
    i) (Int -> Nat
    natFromInt Int
    m)
    {-# INLINE mask #-}

    {--------------------------------------------------------------------
      Big endian operations
    --------------------------------------------------------------------}

    -- | The prefix of key @i@ up to (but not including) the switching
    -- bit @m@.
    maskW :: Nat -> Nat -> Prefix
    maskW :: Nat -> Nat -> Int
    maskW Nat
    i Nat
    m
      = Nat -> Int
    intFromNat (Nat
    i Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    .&. ((-Nat
    m) Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    `xor` Nat
    m))
    {-# INLINE maskW #-}

    -- | Does the left switching bit specify a shorter prefix?
    shorter :: Mask -> Mask -> Bool
    shorter :: Int -> Int -> Bool
    shorter Int
    m1 Int
    m2
      = (Int -> Nat
    natFromInt Int
    m1) Nat -> Nat -> Bool
    forall a. Ord a => a -> a -> Bool
    > (Int -> Nat
    natFromInt Int
    m2)
    {-# INLINE shorter #-}

    -- | The first switching bit where the two prefixes disagree.
    branchMask :: Prefix -> Prefix -> Mask
    branchMask :: Int -> Int -> Int
    branchMask Int
    p1 Int
    p2
      = Nat -> Int
    intFromNat (Nat -> Nat
    highestBitMask (Int -> Nat
    natFromInt Int
    p1 Nat -> Nat -> Nat
    forall a. Bits a => a -> a -> a
    `xor` Int -> Nat
    natFromInt Int
    p2))
    {-# INLINE branchMask #-}

    {--------------------------------------------------------------------
      Utilities
    --------------------------------------------------------------------}

    -- | \(O(1)\).  Decompose a map into pieces based on the structure
    -- of the underlying tree. This function is useful for consuming a
    -- map in parallel.
    --
    -- No guarantee is made as to the sizes of the pieces; an internal, but
    -- deterministic process determines this.  However, it is guaranteed that the
    -- pieces returned will be in ascending order (all elements in the first submap
    -- less than all elements in the second, and so on).
    --
    -- Examples:
    --
    -- > splitRoot (fromList (zip [1..6::Int] ['a'..])) ==
    -- >   [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d'),(5,'e'),(6,'f')]]
    --
    -- > splitRoot empty == []
    --
    --  Note that the current implementation does not return more than two submaps,
    --  but you should not depend on this behaviour because it can change in the
    --  future without notice.
    splitRoot :: IntMap a -> [IntMap a]
    splitRoot :: forall a. IntMap a -> [IntMap a]
    splitRoot IntMap a
    orig =
      case IntMap a
    orig of
        IntMap a
    Nil -> []
        x :: IntMap a
    x@(Tip Int
    _ a
    _) -> [IntMap a
    x]
        Bin Int
    _ Int
    m IntMap a
    l IntMap a
    r | Int
    m Int -> Int -> Bool
    forall a. Ord a => a -> a -> Bool
    < Int
    0 -> [IntMap a
    r, IntMap a
    l]
                    | Bool
    otherwise -> [IntMap a
    l, IntMap a
    r]
    {-# INLINE splitRoot #-}

    {--------------------------------------------------------------------
      Debugging
    --------------------------------------------------------------------}

    -- | \(O(n \min(n,W))\). Show the tree that implements the map. The tree is shown
    -- in a compressed, hanging format.
    showTree :: Show a => IntMap a -> String
    showTree :: forall a. Show a => IntMap a -> [Char]
    showTree IntMap a
    s
      = Bool -> Bool -> IntMap a -> [Char]
    forall a. Show a => Bool -> Bool -> IntMap a -> [Char]
    showTreeWith Bool
    True Bool
    False IntMap a
    s

    {- | \(O(n \min(n,W))\). 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 :: forall a. Show a => Bool -> Bool -> IntMap a -> [Char]
    showTreeWith Bool
    hang Bool
    wide IntMap a
    t
      | Bool
    hang      = (Bool -> [[Char]] -> IntMap a -> [Char] -> [Char]
    forall a.
    Show a =>
    Bool -> [[Char]] -> IntMap a -> [Char] -> [Char]
    showsTreeHang Bool
    wide [] IntMap a
    t) [Char]
    ""
      | Bool
    otherwise = (Bool -> [[Char]] -> [[Char]] -> IntMap a -> [Char] -> [Char]
    forall a.
    Show a =>
    Bool -> [[Char]] -> [[Char]] -> IntMap a -> [Char] -> [Char]
    showsTree Bool
    wide [] [] IntMap a
    t) [Char]
    ""

    showsTree :: Show a => Bool -> [String] -> [String] -> IntMap a -> ShowS
    showsTree :: forall a.
    Show a =>
    Bool -> [[Char]] -> [[Char]] -> IntMap a -> [Char] -> [Char]
    showsTree Bool
    wide [[Char]]
    lbars [[Char]]
    rbars IntMap a
    t = case IntMap a
    t of
      Bin Int
    p Int
    m IntMap a
    l IntMap a
    r ->
        Bool -> [[Char]] -> [[Char]] -> IntMap a -> [Char] -> [Char]
    forall a.
    Show a =>
    Bool -> [[Char]] -> [[Char]] -> IntMap a -> [Char] -> [Char]
    showsTree Bool
    wide ([[Char]] -> [[Char]]
    withBar [[Char]]
    rbars) ([[Char]] -> [[Char]]
    withEmpty [[Char]]
    rbars) IntMap a
    r ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    .
        Bool -> [[Char]] -> [Char] -> [Char]
    showWide Bool
    wide [[Char]]
    rbars ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    .
        [[Char]] -> [Char] -> [Char]
    showsBars [[Char]]
    lbars ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString (Int -> Int -> [Char]
    showBin Int
    p Int
    m) ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString [Char]
    "\n" ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    .
        Bool -> [[Char]] -> [Char] -> [Char]
    showWide Bool
    wide [[Char]]
    lbars ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    .
        Bool -> [[Char]] -> [[Char]] -> IntMap a -> [Char] -> [Char]
    forall a.
    Show a =>
    Bool -> [[Char]] -> [[Char]] -> IntMap a -> [Char] -> [Char]
    showsTree Bool
    wide ([[Char]] -> [[Char]]
    withEmpty [[Char]]
    lbars) ([[Char]] -> [[Char]]
    withBar [[Char]]
    lbars) IntMap a
    l
      Tip Int
    k a
    x ->
        [[Char]] -> [Char] -> [Char]
    showsBars [[Char]]
    lbars ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    .
        [Char] -> [Char] -> [Char]
    showString [Char]
    " " ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Int -> [Char] -> [Char]
    forall a. Show a => a -> [Char] -> [Char]
    shows Int
    k ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString [Char]
    ":=" ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . a -> [Char] -> [Char]
    forall a. Show a => a -> [Char] -> [Char]
    shows a
    x ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString [Char]
    "\n"
      IntMap a
    Nil -> [[Char]] -> [Char] -> [Char]
    showsBars [[Char]]
    lbars ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString [Char]
    "|\n"

    showsTreeHang :: Show a => Bool -> [String] -> IntMap a -> ShowS
    showsTreeHang :: forall a.
    Show a =>
    Bool -> [[Char]] -> IntMap a -> [Char] -> [Char]
    showsTreeHang Bool
    wide [[Char]]
    bars IntMap a
    t = case IntMap a
    t of
      Bin Int
    p Int
    m IntMap a
    l IntMap a
    r ->
        [[Char]] -> [Char] -> [Char]
    showsBars [[Char]]
    bars ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString (Int -> Int -> [Char]
    showBin Int
    p Int
    m) ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString [Char]
    "\n" ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    .
        Bool -> [[Char]] -> [Char] -> [Char]
    showWide Bool
    wide [[Char]]
    bars ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    .
        Bool -> [[Char]] -> IntMap a -> [Char] -> [Char]
    forall a.
    Show a =>
    Bool -> [[Char]] -> IntMap a -> [Char] -> [Char]
    showsTreeHang Bool
    wide ([[Char]] -> [[Char]]
    withBar [[Char]]
    bars) IntMap a
    l ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    .
        Bool -> [[Char]] -> [Char] -> [Char]
    showWide Bool
    wide [[Char]]
    bars ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    .
        Bool -> [[Char]] -> IntMap a -> [Char] -> [Char]
    forall a.
    Show a =>
    Bool -> [[Char]] -> IntMap a -> [Char] -> [Char]
    showsTreeHang Bool
    wide ([[Char]] -> [[Char]]
    withEmpty [[Char]]
    bars) IntMap a
    r
      Tip Int
    k a
    x ->
        [[Char]] -> [Char] -> [Char]
    showsBars [[Char]]
    bars ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    .
        [Char] -> [Char] -> [Char]
    showString [Char]
    " " ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . Int -> [Char] -> [Char]
    forall a. Show a => a -> [Char] -> [Char]
    shows Int
    k ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString [Char]
    ":=" ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . a -> [Char] -> [Char]
    forall a. Show a => a -> [Char] -> [Char]
    shows a
    x ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString [Char]
    "\n"
      IntMap a
    Nil -> [[Char]] -> [Char] -> [Char]
    showsBars [[Char]]
    bars ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString [Char]
    "|\n"

    showBin :: Prefix -> Mask -> String
    showBin :: Int -> Int -> [Char]
    showBin Int
    _ Int
    _
      = [Char]
    "*" -- ++ show (p,m)

    showWide :: Bool -> [String] -> String -> String
    showWide :: Bool -> [[Char]] -> [Char] -> [Char]
    showWide Bool
    wide [[Char]]
    bars
      | Bool
    wide      = [Char] -> [Char] -> [Char]
    showString ([[Char]] -> [Char]
    forall (t :: * -> *) a. Foldable t => t [a] -> [a]
    concat ([[Char]] -> [[Char]]
    forall a. [a] -> [a]
    reverse [[Char]]
    bars)) ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString [Char]
    "|\n"
      | Bool
    otherwise = [Char] -> [Char]
    forall a. a -> a
    id

    showsBars :: [String] -> ShowS
    showsBars :: [[Char]] -> [Char] -> [Char]
    showsBars [[Char]]
    bars
      = case [[Char]]
    bars of
          [] -> [Char] -> [Char]
    forall a. a -> a
    id
          [Char]
    _ : [[Char]]
    tl -> [Char] -> [Char] -> [Char]
    showString ([[Char]] -> [Char]
    forall (t :: * -> *) a. Foldable t => t [a] -> [a]
    concat ([[Char]] -> [[Char]]
    forall a. [a] -> [a]
    reverse [[Char]]
    tl)) ([Char] -> [Char]) -> ([Char] -> [Char]) -> [Char] -> [Char]
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    . [Char] -> [Char] -> [Char]
    showString [Char]
    node

    node :: String
    node :: [Char]
    node = [Char]
    "+--"

    withBar, withEmpty :: [String] -> [String]
    withBar :: [[Char]] -> [[Char]]
    withBar [[Char]]
    bars   = [Char]
    "|  "[Char] -> [[Char]] -> [[Char]]
    forall a. a -> [a] -> [a]
    :[[Char]]
    bars
    withEmpty :: [[Char]] -> [[Char]]
    withEmpty [[Char]]
    bars = [Char]
    "   "[Char] -> [[Char]] -> [[Char]]
    forall a. a -> [a] -> [a]
    :[[Char]]
    bars