{-# LANGUAGE CPP #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE PatternGuards #-}
#if __GLASGOW_HASKELL__
{-# LANGUAGE MagicHash, DeriveDataTypeable, StandaloneDeriving #-}
{-# LANGUAGE ScopedTypeVariables #-}
#endif
#if !defined(TESTING) && defined(__GLASGOW_HASKELL__)
{-# LANGUAGE Trustworthy #-}
#endif
#if __GLASGOW_HASKELL__ >= 708
{-# LANGUAGE TypeFamilies #-}
#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

    , 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

#if MIN_VERSION_base(4,8,0)
import Data.Functor.Identity (Identity (..))
import Control.Applicative (liftA2)
#else
import Control.Applicative (Applicative(pure, (<*>)), (<$>), liftA2)
import Data.Monoid (Monoid(..))
import Data.Traversable (Traversable(traverse))
import Data.Word (Word)
#endif
#if MIN_VERSION_base(4,9,0)
import Data.Semigroup (Semigroup(stimes))
#endif
#if !(MIN_VERSION_base(4,11,0)) && MIN_VERSION_base(4,9,0)
import Data.Semigroup (Semigroup((<>)))
#endif
#if MIN_VERSION_base(4,9,0)
import Data.Semigroup (stimesIdempotentMonoid)
import Data.Functor.Classes
#endif

import Control.DeepSeq (NFData(rnf))
import Data.Bits
import qualified Data.Foldable as Foldable
#if !MIN_VERSION_base(4,8,0)
import Data.Foldable (Foldable())
#endif
import Data.Maybe (fromMaybe)
import Data.Typeable
import Prelude hiding (lookup, map, filter, foldr, foldl, null)

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

#if __GLASGOW_HASKELL__
import Data.Data (Data(..), Constr, mkConstr, constrIndex, Fixity(Prefix),
                  DataType, mkDataType)
import GHC.Exts (build)
#if !MIN_VERSION_base(4,8,0)
import Data.Functor ((<$))
#endif
#if __GLASGOW_HASKELL__ >= 708
import qualified GHC.Exts as GHCExts
#endif
import Text.Read
#endif
import qualified Control.Category as Category
#if __GLASGOW_HASKELL__ >= 709
import Data.Coerce
#endif


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

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

intFromNat :: Nat -> Key
intFromNat :: Nat -> Int
intFromNat = 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

bitmapOf :: Int -> IntSetBitMap
bitmapOf :: Int -> Nat
bitmapOf Int
x = Nat -> Int -> Nat
shiftLL Nat
1 (Int
x 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 = 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 = 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 = 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  = forall a. IntMap a
empty
    mconcat :: [IntMap a] -> IntMap a
mconcat = forall (f :: * -> *) a. Foldable f => f (IntMap a) -> IntMap a
unions
#if !(MIN_VERSION_base(4,9,0))
    mappend = union
#else
    mappend :: IntMap a -> IntMap a -> IntMap a
mappend = forall a. Semigroup a => a -> a -> a
(<>)

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

-- | Folds in order of increasing key.
instance Foldable.Foldable IntMap where
  fold :: forall m. Monoid m => IntMap m -> m
fold = forall m. Monoid m => IntMap m -> m
go
    where go :: IntMap a -> a
go IntMap a
Nil = forall a. Monoid a => a
mempty
          go (Tip Int
_ a
v) = a
v
          go (Bin Int
_ Int
m IntMap a
l IntMap a
r)
            | Int
m forall a. Ord a => a -> a -> Bool
< Int
0     = IntMap a -> a
go IntMap a
r forall a. Monoid a => a -> a -> a
`mappend` IntMap a -> a
go IntMap a
l
            | Bool
otherwise = IntMap a -> a
go IntMap a
l forall a. Monoid a => a -> a -> a
`mappend` IntMap a -> a
go IntMap a
r
  {-# INLINABLE fold #-}
  foldr :: forall a b. (a -> b -> b) -> b -> IntMap a -> b
foldr = 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 = 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 = 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 forall a. Ord a => a -> a -> Bool
< Int
0     = IntMap a -> m
go IntMap a
r forall a. Monoid a => a -> a -> a
`mappend` IntMap a -> m
go IntMap a
l
            | Bool
otherwise = IntMap a -> m
go IntMap a
l 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' = 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' = forall a b. (a -> b -> b) -> b -> IntMap a -> b
foldr'
  {-# INLINE foldr' #-}
#if MIN_VERSION_base(4,8,0)
  length :: forall a. IntMap a -> Int
length = forall a. IntMap a -> Int
size
  {-# INLINE length #-}
  null :: forall a. IntMap a -> Bool
null   = forall a. IntMap a -> Bool
null
  {-# INLINE null #-}
  toList :: forall a. IntMap a -> [a]
toList = forall a. IntMap a -> [a]
elems -- NB: Foldable.toList /= IntMap.toList
  {-# INLINE toList #-}
  elem :: forall a. Eq a => a -> IntMap a -> Bool
elem = 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 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 = forall a. Ord a => IntMap a -> a
start
    where start :: IntMap a -> a
start IntMap a
Nil = forall a. HasCallStack => [Char] -> a
error [Char]
"Data.Foldable.maximum (for Data.IntMap): empty map"
          start (Tip Int
_ a
y) = a
y
          start (Bin Int
_ Int
m IntMap a
l IntMap a
r)
            | Int
m forall a. Ord a => a -> a -> Bool
< Int
0     = forall {t}. Ord t => t -> IntMap t -> t
go (IntMap a -> a
start IntMap a
r) IntMap a
l
            | Bool
otherwise = forall {t}. Ord t => t -> IntMap t -> t
go (IntMap a -> a
start IntMap a
l) IntMap a
r

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

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

-- | 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 = 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) = forall a. NFData a => a -> ()
rnf a
v
    rnf (Bin Int
_ Int
_ IntMap a
l IntMap a
r) = forall a. NFData a => a -> ()
rnf IntMap a
l seq :: forall a b. a -> b -> b
`seq` 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 = forall g. g -> c g
z forall a. [(Int, a)] -> IntMap a
fromList forall d b. Data d => c (d -> b) -> d -> c b
`f` (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 -> forall b r. Data b => c (b -> r) -> c r
k (forall r. r -> c r
z forall a. [(Int, a)] -> IntMap a
fromList)
    Int
_ -> 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    = 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 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 = 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 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 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 forall a b. (a -> b) -> a -> b
$ 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 -> Int -> Bool
nomatch Int
k Int
p Int
m = forall a. Maybe a
Nothing
                     | 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 forall a. Eq a => a -> a -> Bool
== Int
kx   = forall a. a -> Maybe a
Just a
x
                  | Bool
otherwise = forall a. Maybe a
Nothing
    go IntMap a
Nil = 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 -> Int -> Bool
nomatch Int
k Int
p Int
m = a
not_found
                     | 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 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 = forall a. HasCallStack => [Char] -> a
error ([Char]
"IntMap.!: key " forall a. [a] -> [a] -> [a]
++ forall a. Show a => a -> [Char]
show Int
k 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 forall a. Eq a => a -> a -> Bool
== Int
kx   = a
x
                  | Bool
otherwise = a
def
    go IntMap a
Nil = a
def

-- | /O(log n)/. 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 forall a. Ord a => a -> a -> Bool
< Int
0 -> if Int
k 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 forall a. IntMap a
Nil IntMap a
r
    IntMap a
_ -> IntMap a -> IntMap a -> Maybe (Int, a)
go 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 forall a. Ord a => a -> a -> Bool
< Int
p then forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def else 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 forall a. Ord a => a -> a -> Bool
<= Int
ky   = forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def
      | Bool
otherwise = forall a. a -> Maybe a
Just (Int
ky, a
y)
    go IntMap a
def IntMap a
Nil = forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def

-- | /O(log n)/. 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 forall a. Ord a => a -> a -> Bool
< Int
0 -> if Int
k forall a. Ord a => a -> a -> Bool
>= Int
0 then IntMap a -> IntMap a -> Maybe (Int, a)
go 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 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 forall a. Ord a => a -> a -> Bool
< Int
p then forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
l else 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 forall a. Ord a => a -> a -> Bool
>= Int
ky   = forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
def
      | Bool
otherwise = forall a. a -> Maybe a
Just (Int
ky, a
y)
    go IntMap a
def IntMap a
Nil = forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
def

-- | /O(log n)/. 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 forall a. Ord a => a -> a -> Bool
< Int
0 -> if Int
k 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 forall a. IntMap a
Nil IntMap a
r
    IntMap a
_ -> IntMap a -> IntMap a -> Maybe (Int, a)
go 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 forall a. Ord a => a -> a -> Bool
< Int
p then forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def else 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 forall a. Ord a => a -> a -> Bool
< Int
ky    = forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def
      | Bool
otherwise = forall a. a -> Maybe a
Just (Int
ky, a
y)
    go IntMap a
def IntMap a
Nil = forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def

-- | /O(log n)/. 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 forall a. Ord a => a -> a -> Bool
< Int
0 -> if Int
k forall a. Ord a => a -> a -> Bool
>= Int
0 then IntMap a -> IntMap a -> Maybe (Int, a)
go 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 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 forall a. Ord a => a -> a -> Bool
< Int
p then forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
l else 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 forall a. Ord a => a -> a -> Bool
> Int
ky    = forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
def
      | Bool
otherwise = forall a. a -> Maybe a
Just (Int
ky, a
y)
    go IntMap a
def IntMap a
Nil = 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 = forall a. Maybe a
Nothing
unsafeFindMin (Tip Int
ky a
y) = forall a. a -> Maybe a
Just (Int
ky, a
y)
unsafeFindMin (Bin Int
_ Int
_ IntMap a
l IntMap 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 = forall a. Maybe a
Nothing
unsafeFindMax (Tip Int
ky a
y) = forall a. a -> Maybe a
Just (Int
ky, a
y)
unsafeFindMax (Bin Int
_ Int
_ IntMap a
_ IntMap a
r) = 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 = forall a. Int -> IntMap a -> Bool
notMember Int
kx IntMap b
ys
disjoint IntMap a
xs (Tip Int
ky b
_) = 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 forall a. Eq a => a -> a -> Bool
== Int
p2      = forall a b. IntMap a -> IntMap b -> Bool
disjoint IntMap a
l1 IntMap b
l2 Bool -> Bool -> 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       = forall a b. IntMap a -> IntMap b -> Bool
disjoint IntMap a
l1 IntMap b
t2
              | Bool
otherwise        = 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       = forall a b. IntMap a -> IntMap b -> Bool
disjoint IntMap a
t1 IntMap b
l2
              | Bool
otherwise        = 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
  | forall a. IntMap a -> Bool
null IntMap c
bc = forall a. IntMap a
empty
  | Bool
otherwise = forall a b. (a -> Maybe b) -> IntMap a -> IntMap b
mapMaybe (IntMap c
bc 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
  = 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
  = 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 = forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
p IntMap a
t
  | Int -> Int -> Bool
zero Int
k Int
m      = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m (forall a. Int -> a -> IntMap a -> IntMap a
insert Int
k a
x IntMap a
l) IntMap a
r
  | Bool
otherwise     = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m IntMap a
l (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
kforall a. Eq a => a -> a -> Bool
==Int
ky         = forall a. Int -> a -> IntMap a
Tip Int
k a
x
  | Bool
otherwise     = forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
ky IntMap a
t
insert Int
k a
x IntMap a
Nil = 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"

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
  = 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"

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 = forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
p IntMap a
t
  | Int -> Int -> Bool
zero Int
k Int
m      = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m (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     = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m IntMap a
l (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 forall a. Eq a => a -> a -> Bool
== Int
ky       = forall a. Int -> a -> IntMap a
Tip Int
k (Int -> a -> a -> a
f Int
k a
x a
y)
  | Bool
otherwise     = forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (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 = 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")])

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 = (forall a. Maybe a
Nothing,forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (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') = 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,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') = 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,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 forall a. Eq a => a -> a -> Bool
== Int
ky       = (forall a. a -> Maybe a
Just a
y,forall a. Int -> a -> IntMap a
Tip Int
k (Int -> a -> a -> a
f Int
k a
x a
y))
  | Bool
otherwise     = (forall a. Maybe a
Nothing,forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (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 = (forall a. Maybe a
Nothing,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      = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckLeft Int
p Int
m (forall a. Int -> IntMap a -> IntMap a
delete Int
k IntMap a
l) IntMap a
r
  | Bool
otherwise     = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckRight Int
p Int
m IntMap a
l (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 forall a. Eq a => a -> a -> Bool
== Int
ky       = forall a. IntMap a
Nil
  | Bool
otherwise     = IntMap a
t
delete Int
_k IntMap a
Nil = 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
  = 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 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      = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m (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     = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m IntMap a
l (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 forall a. Eq a => a -> a -> Bool
== Int
ky       = 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 = 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
  = 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 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      = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckLeft Int
p Int
m (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     = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckRight Int
p Int
m IntMap a
l (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 forall a. Eq a => a -> a -> Bool
== Int
ky       = case (Int -> a -> Maybe a
f Int
k a
y) of
                      Just a
y' -> forall a. Int -> a -> IntMap a
Tip Int
ky a
y'
                      Maybe a
Nothing -> forall a. IntMap a
Nil
  | Bool
otherwise     = IntMap a
t
updateWithKey Int -> a -> Maybe a
_ Int
_ IntMap a
Nil = 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 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 = (forall a. Maybe a
Nothing,IntMap a
t)
  | Int -> Int -> Bool
zero Int
k Int
m      = let !(Maybe a
found,IntMap a
l') = 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,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') = 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,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
kforall a. Eq a => a -> a -> Bool
==Int
ky         = case (Int -> a -> Maybe a
f Int
k a
y) of
                      Just a
y' -> (forall a. a -> Maybe a
Just a
y,forall a. Int -> a -> IntMap a
Tip Int
ky a
y')
                      Maybe a
Nothing -> (forall a. a -> Maybe a
Just a
y,forall a. IntMap a
Nil)
  | Bool
otherwise     = (forall a. Maybe a
Nothing,IntMap a
t)
updateLookupWithKey Int -> a -> Maybe a
_ Int
_ IntMap a
Nil = (forall a. Maybe a
Nothing,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 forall a. Maybe a
Nothing of
                      Maybe a
Nothing -> IntMap a
t
                      Just a
x -> forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
p IntMap a
t
  | Int -> Int -> Bool
zero Int
k Int
m      = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckLeft Int
p Int
m (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     = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckRight Int
p Int
m IntMap a
l (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
kforall a. Eq a => a -> a -> Bool
==Int
ky         = case Maybe a -> Maybe a
f (forall a. a -> Maybe a
Just a
y) of
                      Just a
x -> forall a. Int -> a -> IntMap a
Tip Int
ky a
x
                      Maybe a
Nothing -> forall a. IntMap a
Nil
  | Bool
otherwise     = case Maybe a -> Maybe a
f forall a. Maybe a
Nothing of
                      Just a
x -> forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
ky IntMap a
t
                      Maybe a
Nothing -> 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 forall a. Maybe a
Nothing of
                      Just a
x -> forall a. Int -> a -> IntMap a
Tip Int
k a
x
                      Maybe a
Nothing -> forall a. IntMap a
Nil

-- | /O(log n)/. 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 = (forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Maybe a -> f (Maybe a)
f Maybe a
mv) forall a b. (a -> b) -> a -> b
$ \Maybe a
fres ->
  case Maybe a
fres of
    Maybe a
Nothing -> forall b a. b -> (a -> b) -> Maybe a -> b
maybe IntMap a
m (forall a b. a -> b -> a
const (forall a. Int -> IntMap a -> IntMap a
delete Int
k IntMap a
m)) Maybe a
mv
    Just a
v' -> forall a. Int -> a -> IntMap a -> IntMap a
insert Int
k a
v' IntMap a
m
  where mv :: Maybe a
mv = 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
  = forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' forall a. IntMap a -> IntMap a -> IntMap a
union 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
  = forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' (forall a. (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
unionWith a -> a -> a
f) 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
  = 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' forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin forall a b. a -> b -> a
const forall a. a -> a
id 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")]

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
  = 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")]

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
  = 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' forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin (\(Tip Int
k1 a
x1) (Tip Int
_k2 a
x2) -> forall a. Int -> a -> IntMap a
Tip Int
k1 (Int -> a -> a -> a
f Int
k1 a
x1 a
x2)) forall a. a -> a
id 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
  = 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
_ -> forall a. Maybe a
Nothing) forall a. a -> a
id (forall a b. a -> b -> a
const 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
  = 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
  = 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 forall a. a -> a
id (forall a b. a -> b -> a
const 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 forall a. Eq a => a -> a -> Bool
== Int
p2       = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p1 Int
m1 (forall a. IntMap a -> IntSet -> IntMap a
withoutKeys IntMap a
l1 IntSet
l2) (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        = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckLeft Int
p1 Int
m1 (forall a. IntMap a -> IntSet -> IntMap a
withoutKeys IntMap a
l1 IntSet
t2) IntMap a
r1
        | Bool
otherwise         = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckRight Int
p1 Int
m1 IntMap a
l1 (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        = forall a. IntMap a -> IntSet -> IntMap a
withoutKeys IntMap a
t1 IntSet
l2
        | Bool
otherwise         = 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 forall a. Num a => a -> a -> a
- Nat
1
        maxbit :: Nat
maxbit = Int -> Nat
bitmapOf (Int
p1 forall a. Bits a => a -> a -> a
.|. (Int
m1 forall a. Bits a => a -> a -> a
.|. (Int
m1 forall a. Num a => a -> a -> a
- Int
1)))
        gt_maxbit :: Nat
gt_maxbit = (-Nat
maxbit) 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 forall a. Int -> IntMap a -> (IntMap a -> IntMap a) -> IntMap a
updatePrefix Int
p2 IntMap a
t1 forall a b. (a -> b) -> a -> b
$ forall a. Nat -> IntMap a -> IntMap a
withoutBM (Nat
bm2 forall a. Bits a => a -> a -> a
.|. Nat
lt_minbit 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 = forall a. IntMap a
Nil
    | Bool
otherwise = IntMap a
t1
withoutKeys IntMap a
Nil IntSet
_ = 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 forall a. Bits a => a -> a -> a
.&. Int
IntSet.suffixBitMask forall a. Eq a => a -> a -> Bool
/= Int
0 =
        if Int
p forall a. Bits a => a -> a -> a
.&. Int
IntSet.prefixBitMask 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      = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckLeft Int
p Int
m (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      = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckRight Int
p Int
m IntMap a
l (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 forall a. Bits a => a -> a -> a
.&. Int
IntSet.prefixBitMask 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
_ = 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 forall a. Bits a => a -> a -> a
.|. Int
m) forall a. Num a => a -> a -> a
- Nat
1
        bmL :: Nat
bmL = Nat
bm forall a. Bits a => a -> a -> a
.&. Nat
leftBits
        bmR :: Nat
bmR = Nat
bm forall a. Bits a => a -> a -> a
`xor` Nat
bmL -- = (bm .&. complement leftBits)
    in  forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p Int
m (forall a. Nat -> IntMap a -> IntMap a
withoutBM Nat
bmL IntMap a
l) (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 forall a. Bits a => a -> a -> a
.&. Int
IntSet.prefixBitMask) Nat
bm = forall a. IntMap a
Nil
    | Bool
otherwise = IntMap a
t
withoutBM Nat
_ IntMap a
Nil = 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
  = 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' forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin forall a b. a -> b -> a
const (forall a b. a -> b -> a
const forall a. IntMap a
Nil) (forall a b. a -> b -> a
const 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 forall a. Eq a => a -> a -> Bool
== Int
p2       = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p1 Int
m1 (forall a. IntMap a -> IntSet -> IntMap a
restrictKeys IntMap a
l1 IntSet
l2) (forall a. IntMap a -> IntSet -> IntMap a
restrictKeys IntMap a
r1 IntSet
r2)
    | Bool
otherwise      = forall a. IntMap a
Nil
    where
    intersection1 :: IntMap a
intersection1
        | Int -> Int -> Int -> Bool
nomatch Int
p2 Int
p1 Int
m1  = forall a. IntMap a
Nil
        | Int -> Int -> Bool
zero Int
p2 Int
m1        = forall a. IntMap a -> IntSet -> IntMap a
restrictKeys IntMap a
l1 IntSet
t2
        | Bool
otherwise         = 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  = forall a. IntMap a
Nil
        | Int -> Int -> Bool
zero Int
p1 Int
m2        = forall a. IntMap a -> IntSet -> IntMap a
restrictKeys IntMap a
t1 IntSet
l2
        | Bool
otherwise         = 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 = forall a. Bits a => a -> a
complement (Nat
minbit forall a. Num a => a -> a -> a
- Nat
1)
        maxbit :: Nat
maxbit = Int -> Nat
bitmapOf (Int
p1 forall a. Bits a => a -> a -> a
.|. (Int
m1 forall a. Bits a => a -> a -> a
.|. (Int
m1 forall a. Num a => a -> a -> a
- Int
1)))
        le_maxbit :: Nat
le_maxbit = Nat
maxbit forall a. Bits a => a -> a -> a
.|. (Nat
maxbit 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 forall a. Nat -> IntMap a -> IntMap a
restrictBM (Nat
bm2 forall a. Bits a => a -> a -> a
.&. Nat
ge_minbit forall a. Bits a => a -> a -> a
.&. Nat
le_maxbit) (forall a. Int -> IntMap a -> IntMap a
lookupPrefix Int
p2 IntMap a
t1)
restrictKeys (Bin Int
_ Int
_ IntMap a
_ IntMap a
_) IntSet
IntSet.Nil = 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 = forall a. IntMap a
Nil
restrictKeys IntMap a
Nil IntSet
_ = 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 forall a. Bits a => a -> a -> a
.&. Int
IntSet.suffixBitMask forall a. Eq a => a -> a -> Bool
/= Int
0 =
        if Int
p forall a. Bits a => a -> a -> a
.&. Int
IntSet.prefixBitMask forall a. Eq a => a -> a -> Bool
== Int
kp then IntMap a
t else forall a. IntMap a
Nil
    | Int -> Int -> Int -> Bool
nomatch Int
kp Int
p Int
m = forall a. IntMap a
Nil
    | Int -> Int -> Bool
zero Int
kp Int
m      = forall a. Int -> IntMap a -> IntMap a
lookupPrefix Int
kp IntMap a
l
    | Bool
otherwise      = 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 forall a. Bits a => a -> a -> a
.&. Int
IntSet.prefixBitMask) forall a. Eq a => a -> a -> Bool
== Int
kp = IntMap a
t
    | Bool
otherwise = forall a. IntMap a
Nil
lookupPrefix Int
_ IntMap a
Nil = forall a. IntMap a
Nil


restrictBM :: IntSetBitMap -> IntMap a -> IntMap a
restrictBM :: forall a. Nat -> IntMap a -> IntMap a
restrictBM Nat
0 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 forall a. Bits a => a -> a -> a
.|. Int
m) forall a. Num a => a -> a -> a
- Nat
1
        bmL :: Nat
bmL = Nat
bm forall a. Bits a => a -> a -> a
.&. Nat
leftBits
        bmR :: Nat
bmR = Nat
bm forall a. Bits a => a -> a -> a
`xor` Nat
bmL -- = (bm .&. complement leftBits)
    in  forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p Int
m (forall a. Nat -> IntMap a -> IntMap a
restrictBM Nat
bmL IntMap a
l) (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 forall a. Bits a => a -> a -> a
.&. Int
IntSet.prefixBitMask) Nat
bm = IntMap a
t
    | Bool
otherwise = forall a. IntMap a
Nil
restrictBM Nat
_ IntMap a
Nil = 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
  = 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
  = 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' forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin (\(Tip Int
k1 a
x1) (Tip Int
_k2 b
x2) -> forall a. Int -> a -> IntMap a
Tip Int
k1 (Int -> a -> b -> c
f Int
k1 a
x1 b
x2)) (forall a b. a -> b -> a
const forall a. IntMap a
Nil) (forall a b. a -> b -> a
const 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 = 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' 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 -> forall a. IntMap a
Nil
            Just c
x -> 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 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      = 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  = 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  = 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 = 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 forall a. Eq a => a -> a -> Bool
== Int
k2 = IntMap a -> IntMap b -> IntMap c
f IntMap a
t1 IntMap b
t2
          | Bool
otherwise = 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 = 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 forall a. Eq a => a -> a -> Bool
== Int
k2 = IntMap a -> IntMap b -> IntMap c
f IntMap a
t1 IntMap b
t2
          | Bool
otherwise = 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 = 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 = 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 = 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 =
      forall (f :: * -> *) x y.
Applicative f =>
(Int -> x -> f (Maybe y)) -> WhenMissing f x y
traverseMaybeMissing forall a b. (a -> b) -> a -> b
$ \ Int
k a
x -> do
        Maybe b
y <- forall (f :: * -> *) x y.
WhenMissing f x y -> Int -> x -> f (Maybe y)
missingKey WhenMissing f a b
g Int
k a
x
        case Maybe b
y of
          Maybe b
Nothing -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. Maybe a
Nothing
          Just b
q  -> 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 = 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 =
    forall (f :: * -> *) x y.
Applicative f =>
(Int -> x -> f (Maybe y)) -> WhenMissing f x y
traverseMaybeMissing forall a b. (a -> b) -> a -> b
$ \Int
k x
x -> do
      Maybe (a -> b)
res1 <- 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 Maybe (a -> b)
res1 of
        Maybe (a -> b)
Nothing -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. Maybe a
Nothing
        Just a -> b
r  -> (forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$!) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
r forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< 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
#if !MIN_VERSION_base(4,8,0)
  return = pure
#endif
  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 =
    forall (f :: * -> *) x y.
Applicative f =>
(Int -> x -> f (Maybe y)) -> WhenMissing f x y
traverseMaybeMissing forall a b. (a -> b) -> a -> b
$ \Int
k x
x -> do
      Maybe a
res1 <- forall (f :: * -> *) x y.
WhenMissing f x y -> Int -> x -> f (Maybe y)
missingKey WhenMissing f x a
m Int
k x
x
      case Maybe a
res1 of
        Maybe a
Nothing -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. Maybe a
Nothing
        Just a
r  -> 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 -> forall (f :: * -> *) x y.
WhenMissing f x y -> IntMap x -> f (IntMap y)
missingSubtree WhenMissing f x a
t IntMap x
m forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= \IntMap a
m' -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> 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 -> forall (f :: * -> *) x y.
WhenMissing f x y -> Int -> x -> f (Maybe y)
missingKey WhenMissing f x a
t Int
k x
x forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= \Maybe a
q -> (forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> 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 -> forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall (f :: * -> *) x y.
WhenMissing f x y -> IntMap x -> f (IntMap y)
missingSubtree WhenMissing f x a
t IntMap x
m
  , missingKey :: Int -> x -> f (Maybe b)
missingKey     = \Int
k x
x -> forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> 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 =
  forall x y (f :: * -> *) z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
zipWithMaybeAMatched forall a b. (a -> b) -> a -> b
$ \Int
k x
x y
y -> forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> 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 -> forall (f :: * -> *) x y.
WhenMissing f x y -> IntMap x -> f (IntMap y)
missingSubtree WhenMissing f a x
t (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 -> 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 =
  forall (f :: * -> *) x y z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
WhenMatched forall a b. (a -> b) -> a -> b
$ \Int
k b
x y
y -> 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 =
  forall (f :: * -> *) x y z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
WhenMatched forall a b. (a -> b) -> a -> b
$ \Int
k x
x b
y -> 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 #-}


#if !MIN_VERSION_base(4,8,0)
newtype Identity a = Identity {runIdentity :: a}

instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

instance Applicative Identity where
    pure = Identity
    Identity f <*> Identity x = Identity (f x)
#endif

-- | 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 = 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 = 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 = 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 = 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 =
      forall x y (f :: * -> *) z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
zipWithMaybeAMatched forall a b. (a -> b) -> a -> b
$ \Int
k x
x a
y -> do
        Maybe b
res <- 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 Maybe b
res of
          Maybe b
Nothing -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. Maybe a
Nothing
          Just b
r  -> 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 = 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 =
    forall x y (f :: * -> *) z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
zipWithMaybeAMatched forall a b. (a -> b) -> a -> b
$ \Int
k x
x y
y -> do
      Maybe (a -> b)
res <- 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 Maybe (a -> b)
res of
        Maybe (a -> b)
Nothing -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. Maybe a
Nothing
        Just a -> b
r  -> (forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$!) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
r forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< 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
#if !MIN_VERSION_base(4,8,0)
  return = pure
#endif
  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 =
    forall x y (f :: * -> *) z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
zipWithMaybeAMatched forall a b. (a -> b) -> a -> b
$ \Int
k x
x y
y -> do
      Maybe a
res <- 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 Maybe a
res of
        Maybe a
Nothing -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. Maybe a
Nothing
        Just a
r  -> 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) =
  forall (f :: * -> *) x y z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
WhenMatched forall a b. (a -> b) -> a -> b
$ \Int
k x
x y
y -> forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (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 = forall (f :: * -> *) x y z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
WhenMatched forall a b. (a -> b) -> a -> b
$ \ Int
k x
x y
y -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. a -> Maybe a
Just 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 = forall (f :: * -> *) x y z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
WhenMatched forall a b. (a -> b) -> a -> b
$ \ Int
k x
x y
y -> forall a. a -> Maybe a
Just 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 = forall (f :: * -> *) x y z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
WhenMatched forall a b. (a -> b) -> a -> b
$ \ Int
k x
x y
y -> forall (f :: * -> *) a. Applicative f => a -> f a
pure 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 = forall (f :: * -> *) x y z.
(Int -> x -> y -> f (Maybe z)) -> WhenMatched f x y z
WhenMatched 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 = forall a b. a -> b -> a
const (forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. IntMap a
Nil)
  , missingKey :: Int -> x -> f (Maybe y)
missingKey     = \Int
_ x
_ -> forall (f :: * -> *) a. Applicative f => a -> f a
pure 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 = forall (f :: * -> *) a. Applicative f => a -> f a
pure
  , missingKey :: Int -> x -> f (Maybe x)
missingKey     = \Int
_ x
v -> forall (f :: * -> *) a. Applicative f => a -> f a
pure (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 -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$! 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 -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$ 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 -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$! 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 -> forall (f :: * -> *) a. Applicative f => a -> f a
pure 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 -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$! 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 -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$! if Int -> x -> Bool
f Int
k x
x then forall a. a -> Maybe a
Just x
x else 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) <$> f k x
--
-- but this should be a little faster.
--
-- @since 0.5.9
filterAMissing
  :: Applicative f => (Key -> x -> f Bool) -> WhenMissing f x x
filterAMissing :: forall (f :: * -> *) x.
Applicative f =>
(Int -> x -> f Bool) -> WhenMissing f x x
filterAMissing Int -> x -> f Bool
f = WhenMissing
  { missingSubtree :: IntMap x -> f (IntMap x)
missingSubtree = \IntMap x
m -> forall (f :: * -> *) a.
Applicative f =>
(Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
filterWithKeyA Int -> x -> f Bool
f IntMap x
m
  , missingKey :: Int -> x -> f (Maybe x)
missingKey     = \Int
k x
x -> forall a. a -> a -> Bool -> a
bool forall a. Maybe a
Nothing (forall a. a -> Maybe a
Just x
x) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> 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           = forall (f :: * -> *) a. Applicative f => a -> f a
pure 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 forall a. IntMap a
Nil) 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 forall a. Ord a => a -> a -> Bool
< Int
0     = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (forall a b c. (a -> b -> c) -> b -> a -> c
flip (forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p Int
m)) (forall (f :: * -> *) a.
Applicative f =>
(Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
filterWithKeyA Int -> a -> f Bool
f IntMap a
r) (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 = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p Int
m) (forall (f :: * -> *) a.
Applicative f =>
(Int -> a -> f Bool) -> IntMap a -> f (IntMap a)
filterWithKeyA Int -> a -> f Bool
f IntMap a
l) (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 = 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 -> forall a. a -> Maybe a
Just 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 = 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           = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. IntMap a
Nil
    go (Tip Int
k a
x)     = forall b a. b -> (a -> b) -> Maybe a -> b
maybe forall a. IntMap a
Nil (forall a. Int -> a -> IntMap a
Tip Int
k) 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 forall a. Ord a => a -> a -> Bool
< Int
0     = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (forall a b c. (a -> b -> c) -> b -> a -> c
flip (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 = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (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 =
  forall a. Identity a -> a
runIdentity forall a b. (a -> b) -> a -> b
$ 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 = forall (f :: * -> *) a.
Applicative f =>
Int -> f (IntMap a) -> Int -> f (IntMap a) -> f (IntMap a)
linkA Int
k1 (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       = 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        = 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           = 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 = 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 (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       = 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        = 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           = 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 forall a. Eq a => a -> a -> Bool
== Int
p2       = 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      = 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  = 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        = 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         = 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  = 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        = 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         = 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 = forall b a. b -> (a -> b) -> Maybe a -> b
maybe forall a. IntMap a
Nil (forall a. Int -> a -> IntMap a
Tip Int
k) 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 forall a. Eq a => a -> a -> Bool
== Int
k2  = forall b a. b -> (a -> b) -> Maybe a -> b
maybe forall a. IntMap a
Nil (forall a. Int -> a -> IntMap a
Tip Int
k1) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Int -> a -> b -> f (Maybe c)
f Int
k1 a
x1 b
x2
      | Int
k1 forall a. Ord a => a -> a -> Bool
<  Int
k2  = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (forall {a}. Int -> Int -> Maybe a -> Maybe a -> IntMap a
subdoubleton Int
k1 Int
k2) (Int -> a -> f (Maybe c)
g1k Int
k1 a
x1) (Int -> b -> f (Maybe c)
g2k Int
k2 b
x2)
        {-
        = link_ k1 k2 <$> subsingletonBy g1k k1 x1 <*> subsingletonBy g2k k2 x2
        -}
      | Bool
otherwise = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (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     = forall a. IntMap a
Nil
    subdoubleton Int
_ Int
k2  Maybe a
Nothing (Just a
y2)   = forall a. Int -> a -> IntMap a
Tip Int
k2 a
y2
    subdoubleton Int
k1 Int
_  (Just a
y1) Maybe a
Nothing   = forall a. Int -> a -> IntMap a
Tip Int
k1 a
y1
    subdoubleton Int
k1 Int
k2 (Just a
y1) (Just a
y2) = forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k1 (forall a. Int -> a -> IntMap a
Tip Int
k1 a
y1) Int
k2 (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 = 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 = 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 forall a. Ord a => a -> a -> Bool
< Int
0     = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (forall a b c. (a -> b -> c) -> b -> a -> c
flip (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 = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2       (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 forall a. Ord a => a -> a -> Bool
< Int
0 -> forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckRight Int
p Int
m IntMap a
l (forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
go Int -> a -> Maybe a
f IntMap a
r)
            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) = 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' -> forall a. Int -> a -> IntMap a
Tip Int
k t
y'
                        Maybe t
Nothing -> forall a. IntMap a
Nil
    go Int -> t -> Maybe t
_ IntMap t
Nil = 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 forall a. Ord a => a -> a -> Bool
< Int
0 -> forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckLeft Int
p Int
m (forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
go Int -> a -> Maybe a
f IntMap a
l) IntMap a
r
            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) = 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' -> forall a. Int -> a -> IntMap a
Tip Int
k t
y'
                        Maybe t
Nothing -> forall a. IntMap a
Nil
    go Int -> t -> Maybe t
_ IntMap t
Nil = 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 -> forall a. Maybe a
Nothing
  IntMap a
_ -> forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$ case 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 -> forall a. HasCallStack => [Char] -> a
error [Char]
"maxViewWithKeySure Nil"
    Bin Int
p Int
m IntMap a
l IntMap a
r | Int
m forall a. Ord a => a -> a -> Bool
< Int
0 ->
      case forall a. IntMap a -> View a
go IntMap a
l of View Int
k a
a IntMap a
l' -> forall a. Int -> a -> IntMap a -> View a
View Int
k a
a (forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckLeft Int
p Int
m IntMap a
l' IntMap a
r)
    IntMap 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' -> forall a. Int -> a -> IntMap a -> View a
View Int
k a
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) = forall a. Int -> a -> IntMap a -> View a
View Int
k a
y forall a. IntMap a
Nil
    go IntMap a
Nil = 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 -> forall a. Maybe a
Nothing
    IntMap a
_ -> forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$ case 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 -> forall a. HasCallStack => [Char] -> a
error [Char]
"minViewWithKeySure Nil"
    Bin Int
p Int
m IntMap a
l IntMap a
r | Int
m forall a. Ord a => a -> a -> Bool
< Int
0 ->
      case forall a. IntMap a -> View a
go IntMap a
r of
        View Int
k a
a IntMap a
r' -> forall a. Int -> a -> IntMap a -> View a
View Int
k a
a (forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckRight Int
p Int
m IntMap a
l IntMap a
r')
    IntMap 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' -> forall a. Int -> a -> IntMap a -> View a
View Int
k a
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) = forall a. Int -> a -> IntMap a -> View a
View Int
k a
y forall a. IntMap a
Nil
    go IntMap a
Nil = 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 = forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
updateMaxWithKey (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 = forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
updateMinWithKey (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 = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\((Int
_, a
x), IntMap a
t') -> (a
x, IntMap a
t')) (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 = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\((Int
_, a
x), IntMap a
t') -> (a
x, IntMap a
t')) (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 = forall a. a -> Maybe a -> a
fromMaybe (forall a. HasCallStack => [Char] -> a
error [Char]
"deleteFindMax: empty map has no maximal element") forall b c a. (b -> c) -> (a -> b) -> a -> c
. 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 = forall a. a -> Maybe a -> a
fromMaybe (forall a. HasCallStack => [Char] -> a
error [Char]
"deleteFindMin: empty map has no minimal element") forall b c a. (b -> c) -> (a -> b) -> a -> c
. 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 = forall a. Maybe a
Nothing
lookupMin (Tip Int
k a
v) = forall a. a -> Maybe a
Just (Int
k,a
v)
lookupMin (Bin Int
_ Int
m IntMap a
l IntMap a
r)
  | Int
m forall a. Ord a => a -> a -> Bool
< Int
0     = forall a. IntMap a -> Maybe (Int, a)
go IntMap a
r
  | Bool
otherwise = forall a. IntMap a -> Maybe (Int, a)
go IntMap a
l
    where go :: IntMap b -> Maybe (Int, b)
go (Tip Int
k b
v)      = 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            = 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 <- forall a. IntMap a -> Maybe (Int, a)
lookupMin IntMap a
t = (Int, a)
r
  | Bool
otherwise = 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 = forall a. Maybe a
Nothing
lookupMax (Tip Int
k a
v) = forall a. a -> Maybe a
Just (Int
k,a
v)
lookupMax (Bin Int
_ Int
m IntMap a
l IntMap a
r)
  | Int
m forall a. Ord a => a -> a -> Bool
< Int
0     = forall a. IntMap a -> Maybe (Int, a)
go IntMap a
l
  | Bool
otherwise = forall a. IntMap a -> Maybe (Int, a)
go IntMap a
r
    where go :: IntMap b -> Maybe (Int, b)
go (Tip Int
k b
v)      = 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            = 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 <- forall a. IntMap a -> Maybe (Int, a)
lookupMax IntMap a
t = (Int, a)
r
  | Bool
otherwise = 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 = forall b a. b -> (a -> b) -> Maybe a -> b
maybe forall a. IntMap a
Nil forall a b. (a, b) -> b
snd forall b c a. (b -> c) -> (a -> b) -> a -> c
. 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 = forall b a. b -> (a -> b) -> Maybe a -> b
maybe forall a. IntMap a
Nil forall a b. (a, b) -> b
snd forall b c a. (b -> c) -> (a -> b) -> a -> c
. 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
  = forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isProperSubmapOfBy 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 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 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        = forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
submapCmp a -> b -> Bool
predicate IntMap a
t1 IntMap b
l2
                | Bool
otherwise         = 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 (forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
submapCmp a -> b -> Bool
predicate IntMap a
l1 IntMap b
l2, 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 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 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
  = forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isSubmapOfBy 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 forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isSubmapOfBy a -> b -> Bool
predicate IntMap a
t1 IntMap b
l2
                       else 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
p1forall a. Eq a => a -> a -> Bool
==Int
p2) Bool -> Bool -> 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
&& 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 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) = 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)     = forall a. Int -> a -> IntMap a
Tip Int
k (a -> b
f a
x)
    go IntMap a
Nil           = 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
 #-}
#endif
#if __GLASGOW_HASKELL__ >= 709
-- Safe coercions were introduced in 7.8, but did not play well with RULES yet.
{-# RULES
"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 -> forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m (forall a b. (Int -> a -> b) -> IntMap a -> IntMap b
mapWithKey Int -> a -> b
f IntMap a
l) (forall a b. (Int -> a -> b) -> IntMap a -> IntMap b
mapWithKey Int -> a -> b
f IntMap a
r)
      Tip Int
k a
x     -> forall a. Int -> a -> IntMap a
Tip Int
k (Int -> a -> b
f Int
k a
x)
      IntMap a
Nil         -> 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 <$> f k v) ('toList' m)@
-- That is, behaves exactly like a regular 'traverse' except that the traversing
-- function also has access to the key associated with a value.
--
-- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(1, 'a'), (5, 'e')]) == Just (fromList [(1, 'b'), (5, 'f')])
-- > traverseWithKey (\k v -> if odd k then Just (succ v) else Nothing) (fromList [(2, 'c')])           == Nothing
traverseWithKey :: Applicative t => (Key -> a -> t b) -> IntMap a -> t (IntMap b)
traverseWithKey :: forall (t :: * -> *) a b.
Applicative t =>
(Int -> a -> t b) -> IntMap a -> t (IntMap b)
traverseWithKey Int -> a -> t b
f = IntMap a -> t (IntMap b)
go
  where
    go :: IntMap a -> t (IntMap b)
go IntMap a
Nil = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. IntMap a
Nil
    go (Tip Int
k a
v) = forall a. Int -> a -> IntMap a
Tip Int
k forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Int -> a -> t b
f Int
k a
v
    go (Bin Int
p Int
m IntMap a
l IntMap a
r)
      | Int
m forall a. Ord a => a -> a -> Bool
< Int
0     = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (forall a b c. (a -> b -> c) -> b -> a -> c
flip (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 = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 (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 = 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
  = 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 forall a. Ord a => a -> a -> Bool
< Int
0 ->
            let (a
a1,IntMap c
r') = 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') = 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,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') = 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') = 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,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',forall a. Int -> a -> IntMap a
Tip Int
k c
x')
      IntMap b
Nil         -> (a
a,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 forall a. Ord a => a -> a -> Bool
< Int
0 ->
            let (a
a1,IntMap c
l') = 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') = 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,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') = 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') = 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,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',forall a. Int -> a -> IntMap a
Tip Int
k c
x')
      IntMap b
Nil         -> (a
a,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 = forall a. [(Int, a)] -> IntMap a
fromList forall b c a. (b -> c) -> (a -> b) -> a -> c
. 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) 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"

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
  = forall a. (a -> a -> a) -> [(Int, a)] -> IntMap a
fromListWith a -> a -> a
c forall b c a. (b -> c) -> (a -> b) -> a -> c
. 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) forall a. a -> [a] -> [a]
: [(Int, a)]
xs) []

-- | /O(n*min(n,W))/.
-- @'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
  = forall a. [(Int, a)] -> IntMap a
fromDistinctAscList forall b c a. (b -> c) -> (a -> b) -> a -> c
. 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) 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
  = 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           = 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 forall a. IntMap a
Nil
    go (Bin Int
p Int
m IntMap a
l IntMap a
r) = 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
  = 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 = forall a b. StrictPair a b -> (a, b)
toPair forall a b. (a -> b) -> a -> b
$ 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 forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p Int
m IntMap a
l1 IntMap a
r1 forall a b. a -> b -> StrictPair a b
:*: 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 forall a b. a -> b -> StrictPair a b
:*: forall a. IntMap a
Nil)
          | Bool
otherwise     -> (forall a. IntMap a
Nil forall a b. a -> b -> StrictPair a b
:*: IntMap a
t)
        IntMap a
Nil -> (forall a. IntMap a
Nil forall a b. a -> b -> StrictPair a b
:*: 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 = 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)
  = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p Int
m (forall a b. (Int -> a -> Maybe b) -> IntMap a -> IntMap b
mapMaybeWithKey Int -> a -> Maybe b
f IntMap a
l) (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  -> forall a. Int -> a -> IntMap a
Tip Int
k b
y
  Maybe b
Nothing -> forall a. IntMap a
Nil
mapMaybeWithKey Int -> a -> Maybe b
_ IntMap a
Nil = 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
  = 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 = forall a b. StrictPair a b -> (a, b)
toPair forall a b. (a -> b) -> a -> b
$ 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) =
      forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p Int
m IntMap a
l1 IntMap a
r1 forall a b. a -> b -> StrictPair a b
:*: 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  -> (forall a. Int -> a -> IntMap a
Tip Int
k a
y forall a b. a -> b -> StrictPair a b
:*: forall a. IntMap a
Nil)
      Right a
z -> (forall a. IntMap a
Nil forall a b. a -> b -> StrictPair a b
:*: forall a. Int -> a -> IntMap a
Tip Int
k a
z)
    go Int -> t -> Either a a
_ IntMap t
Nil = (forall a. IntMap a
Nil forall a b. a -> b -> StrictPair a b
:*: 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
_ Int
m IntMap a
l IntMap a
r
      | Int
m forall a. Ord a => a -> a -> Bool
< Int
0 ->
        if Int
k forall a. Ord a => a -> a -> Bool
>= Int
0 -- handle negative numbers.
        then
          case 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' = forall a. IntMap a -> IntMap a -> IntMap a
union IntMap a
r IntMap a
lt
              in (IntMap a
lt', IntMap a
gt)
        else
          case 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' = forall a. IntMap a -> IntMap a -> IntMap a
union IntMap a
gt IntMap a
l
              in (IntMap a
lt, IntMap a
gt')
    IntMap a
_ -> case 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' forall a. Ord a => a -> a -> Bool
> Int
p then IntMap a
t' forall a b. a -> b -> StrictPair a b
:*: forall a. IntMap a
Nil else forall a. IntMap a
Nil 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 forall a b. a -> b -> StrictPair a b
:*: forall a. IntMap a -> IntMap a -> IntMap a
union 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) -> forall a. IntMap a -> IntMap a -> IntMap a
union IntMap a
l IntMap a
lt forall a b. a -> b -> StrictPair a b
:*: IntMap a
gt
    go Int
k' t' :: IntMap a
t'@(Tip Int
ky a
_)
      | Int
k' forall a. Ord a => a -> a -> Bool
> Int
ky   = (IntMap a
t' forall a b. a -> b -> StrictPair a b
:*: forall a. IntMap a
Nil)
      | Int
k' forall a. Ord a => a -> a -> Bool
< Int
ky   = (forall a. IntMap a
Nil forall a b. a -> b -> StrictPair a b
:*: IntMap a
t')
      | Bool
otherwise = (forall a. IntMap a
Nil forall a b. a -> b -> StrictPair a b
:*: forall a. IntMap a
Nil)
    go Int
_ IntMap a
Nil = (forall a. IntMap a
Nil forall a b. a -> b -> StrictPair a b
:*: 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) = 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) = 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
_ Int
m IntMap a
l IntMap a
r
        | Int
m forall a. Ord a => a -> a -> Bool
< Int
0 ->
          if Int
k forall a. Ord a => a -> a -> Bool
>= Int
0 -- handle negative numbers.
          then forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
mapLT (forall a. IntMap a -> IntMap a -> IntMap a
union IntMap a
r) (forall {a}. Int -> IntMap a -> SplitLookup a
go Int
k IntMap a
l)
          else forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
mapGT (forall a. IntMap a -> IntMap a -> IntMap a
`union` IntMap a
l) (forall {a}. Int -> IntMap a -> SplitLookup a
go Int
k IntMap a
r)
      IntMap 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' forall a. Ord a => a -> a -> Bool
> Int
p
          then forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup IntMap a
t' forall a. Maybe a
Nothing forall a. IntMap a
Nil
          else forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup forall a. IntMap a
Nil forall a. Maybe a
Nothing IntMap a
t'
      | Int -> Int -> Bool
zero Int
k' Int
m = forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
mapGT (forall a. IntMap a -> IntMap a -> IntMap a
`union` IntMap a
r) (Int -> IntMap a -> SplitLookup a
go Int
k' IntMap a
l)
      | Bool
otherwise = forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
mapLT (forall a. IntMap a -> IntMap a -> IntMap a
union 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' forall a. Ord a => a -> a -> Bool
> Int
ky   = forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup IntMap a
t'  forall a. Maybe a
Nothing  forall a. IntMap a
Nil
      | Int
k' forall a. Ord a => a -> a -> Bool
< Int
ky   = forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup forall a. IntMap a
Nil forall a. Maybe a
Nothing  IntMap a
t'
      | Bool
otherwise = forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup forall a. IntMap a
Nil (forall a. a -> Maybe a
Just a
y) forall a. IntMap a
Nil
    go Int
_ IntMap a
Nil      = forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup forall a. IntMap a
Nil forall a. Maybe a
Nothing  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 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 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 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 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 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 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 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 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           = 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 forall a. Ord a => a -> a -> Bool
< Int
0     = IntMap a -> m
go IntMap a
r forall a. Monoid a => a -> a -> a
`mappend` IntMap a -> m
go IntMap a
l
      | Bool
otherwise = IntMap a -> m
go IntMap a
l 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 = 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 = forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
foldrWithKey (\Int
k a
_ [Int]
ks -> Int
k 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 = forall a. IntMap a -> [(Int, a)]
toAscList

-- | /O(n*min(n,W))/. The set of all keys of the map.
--
-- > keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5]
-- > keysSet empty == Data.IntSet.empty

keysSet :: IntMap a -> IntSet.IntSet
keysSet :: 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 forall a. Bits a => a -> a -> a
.&. Int
IntSet.suffixBitMask forall a. Eq a => a -> a -> Bool
== Int
0 = Int -> Int -> IntSet -> IntSet -> IntSet
IntSet.Bin Int
p Int
m (forall a. IntMap a -> IntSet
keysSet IntMap a
l) (forall a. IntMap a -> IntSet
keysSet IntMap a
r)
  | Bool
otherwise = Int -> Nat -> IntSet
IntSet.Tip (Int
p forall a. Bits a => a -> a -> a
.&. Int
IntSet.prefixBitMask) (forall {a}. Nat -> IntMap a -> Nat
computeBm (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 forall a. Bits a => a -> a -> a
.|. Int -> Nat
IntSet.bitmapOf Int
kx
        computeBm Nat
_   IntMap a
Nil = 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 = forall a. IntMap a
Nil
fromSet Int -> a
f (IntSet.Bin Int
p Int
m IntSet
l IntSet
r) = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m (forall a. (Int -> a) -> IntSet -> IntMap a
fromSet Int -> a
f IntSet
l) (forall a. (Int -> a) -> IntSet -> IntMap a
fromSet Int -> a
f IntSet
r)
fromSet Int -> a
f (IntSet.Tip Int
kx Nat
bm) = forall {a}. (Int -> a) -> Int -> Nat -> Int -> IntMap a
buildTree Int -> a
f Int
kx Nat
bm (Int
IntSet.suffixBitMask 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 -> 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 forall a. Bits a => a -> a -> a
.&. ((Nat
1 Nat -> Int -> Nat
`shiftLL` Int
bits2) forall a. Num a => a -> a -> a
- Nat
1) forall a. Eq a => a -> a -> Bool
== Nat
0 ->
              (Int -> a) -> Int -> Nat -> Int -> IntMap a
buildTree Int -> a
g (Int
prefix 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) forall a. Bits a => a -> a -> a
.&. ((Nat
1 Nat -> Int -> Nat
`shiftLL` Int
bits2) forall a. Num a => a -> a -> a
- Nat
1) 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 ->
              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 forall a. Num a => a -> a -> a
+ Int
bits2) (Nat
bmask Nat -> Int -> Nat
`shiftRL` Int
bits2) Int
bits2)

{--------------------------------------------------------------------
  Lists
--------------------------------------------------------------------}
#if __GLASGOW_HASKELL__ >= 708
-- | @since 0.5.6.2
instance GHCExts.IsList (IntMap a) where
  type Item (IntMap a) = (Key,a)
  fromList :: [Item (IntMap a)] -> IntMap a
fromList = forall a. [(Int, a)] -> IntMap a
fromList
  toList :: IntMap a -> [Item (IntMap a)]
toList   = 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 = 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 = forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
foldrWithKey (\Int
k a
x [(Int, a)]
xs -> (Int
k,a
x)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 = forall a b. (a -> Int -> b -> a) -> a -> IntMap b -> a
foldlWithKey (\[(Int, a)]
xs Int
k a
x -> (Int
k,a
x)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 = 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 = 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
  = forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' forall {a}. IntMap a -> (Int, a) -> IntMap a
ins forall a. IntMap a
empty [(Int, a)]
xs
  where
    ins :: IntMap a -> (Int, a) -> IntMap a
ins IntMap a
t (Int
k,a
x)  = forall a. Int -> a -> IntMap a -> IntMap a
insert Int
k a
x IntMap a
t

-- | /O(n*min(n,W))/. Create a map from a list of key\/value pairs with a combining function. See also 'fromAscListWith'.
--
-- > fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")] == fromList [(3, "ab"), (5, "cba")]
-- > fromListWith (++) [] == empty

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
  = 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

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
  = forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' IntMap a -> (Int, a) -> IntMap a
ins forall a. IntMap a
empty [(Int, a)]
xs
  where
    ins :: IntMap a -> (Int, a) -> IntMap a
ins IntMap a
t (Int
k,a
x) = 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 = 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")]

fromAscListWith :: (a -> a -> a) -> [(Key,a)] -> IntMap a
fromAscListWith :: forall a. (a -> a -> a) -> [(Int, a)] -> IntMap a
fromAscListWith a -> a -> a
f = 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")]

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 = 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 = 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.

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 []              = 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 []
        = 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 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 (forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
linkWithMask Int
m Int
ky IntMap a
ty {-kx-} (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 (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 []
        = forall a. IntMap a -> [(Int, a)] -> Inserted a
Inserted (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 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 forall a. Eq a => a -> a -> Bool
/= Int -> Int -> Int
mask Int
ky Int
m
        = forall a. IntMap a -> [(Int, a)] -> Inserted a
Inserted (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 (forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
linkWithMask Int
mxy Int
ky IntMap a
ty {-kx-} (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 []
        = 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 forall a. Eq a => a -> a -> Bool
/= Int -> Int -> Int
mask Int
ky Int
m
        = 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 (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  = 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  = 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 forall a. Eq a => a -> a -> Bool
== Int
m2) Bool -> Bool -> Bool
&& (Int
p1 forall a. Eq a => a -> a -> Bool
== Int
p2) Bool -> Bool -> Bool
&& (forall a. Eq a => IntMap a -> IntMap a -> Bool
equal IntMap a
l1 IntMap a
l2) Bool -> Bool -> 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 forall a. Eq a => a -> a -> Bool
== Int
ky) Bool -> Bool -> Bool
&& (a
xforall 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 forall a. Eq a => a -> a -> Bool
/= Int
m2) Bool -> Bool -> Bool
|| (Int
p1 forall a. Eq a => a -> a -> Bool
/= Int
p2) Bool -> Bool -> Bool
|| (forall a. Eq a => IntMap a -> IntMap a -> Bool
nequal IntMap a
l1 IntMap a
l2) Bool -> Bool -> 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 forall a. Eq a => a -> a -> Bool
/= Int
ky) Bool -> Bool -> Bool
|| (a
xforall a. Eq a => a -> a -> Bool
/=a
y)
nequal IntMap a
Nil IntMap a
Nil = Bool
False
nequal IntMap a
_   IntMap a
_   = Bool
True

#if MIN_VERSION_base(4,9,0)
-- | @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 forall a. Eq a => a -> a -> Bool
== Int
m2) Bool -> Bool -> Bool
&& (Int
p1 forall a. Eq a => a -> a -> Bool
== Int
p2) Bool -> Bool -> 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
&& (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 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
#endif

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

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

#if MIN_VERSION_base(4,9,0)
-- | @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 =
    forall (f :: * -> *) a b.
Ord1 f =>
(a -> b -> Ordering) -> f a -> f b -> Ordering
liftCompare (forall (f :: * -> *) a b.
Ord1 f =>
(a -> b -> Ordering) -> f a -> f b -> Ordering
liftCompare a -> b -> Ordering
cmp) (forall a. IntMap a -> [(Int, a)]
toList IntMap a
m) (forall a. IntMap a -> [(Int, a)]
toList IntMap b
n)
#endif

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

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

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

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

#if MIN_VERSION_base(4,9,0)
-- | @since 0.5.9
instance Show1 IntMap where
    liftShowsPrec :: forall a.
(Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> IntMap a -> ShowS
liftShowsPrec Int -> a -> ShowS
sp [a] -> ShowS
sl Int
d IntMap a
m =
        forall a. (Int -> a -> ShowS) -> [Char] -> Int -> a -> ShowS
showsUnaryWith (forall (f :: * -> *) a.
Show1 f =>
(Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS
liftShowsPrec Int -> (Int, a) -> ShowS
sp' [(Int, a)] -> ShowS
sl') [Char]
"fromList" Int
d (forall a. IntMap a -> [(Int, a)]
toList IntMap a
m)
      where
        sp' :: Int -> (Int, a) -> ShowS
sp' = forall (f :: * -> *) a.
Show1 f =>
(Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS
liftShowsPrec Int -> a -> ShowS
sp [a] -> ShowS
sl
        sl' :: [(Int, a)] -> ShowS
sl' = forall (f :: * -> *) a.
Show1 f =>
(Int -> a -> ShowS) -> ([a] -> ShowS) -> [f a] -> ShowS
liftShowList Int -> a -> ShowS
sp [a] -> ShowS
sl
#endif

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

  readListPrec :: ReadPrec [IntMap e]
readListPrec = 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

#if MIN_VERSION_base(4,9,0)
-- | @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 = forall a. ([Char] -> ReadS a) -> Int -> ReadS a
readsData forall a b. (a -> b) -> a -> b
$
        forall a t.
(Int -> ReadS a) -> [Char] -> (a -> t) -> [Char] -> ReadS t
readsUnaryWith (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" forall a. [(Int, a)] -> IntMap a
fromList
      where
        rp' :: Int -> ReadS (Int, a)
rp' = 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' = forall (f :: * -> *) a.
Read1 f =>
(Int -> ReadS a) -> ReadS [a] -> ReadS [f a]
liftReadList Int -> ReadS a
rp ReadS [a]
rl
#endif

{--------------------------------------------------------------------
  Typeable
--------------------------------------------------------------------}

INSTANCE_TYPEABLE1(IntMap)

{--------------------------------------------------------------------
  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 = 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 = forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m IntMap a
t1 IntMap a
t2
  | Bool
otherwise = 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   = 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   = 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   = 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) forall a. Bits a => a -> a -> a
.&. (Int -> Nat
natFromInt Int
m) 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) 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) 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 forall a. Bits a => a -> a -> a
.&. ((-Nat
m) 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) 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 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 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)/. 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
  = forall a. Show a => Bool -> Bool -> IntMap a -> [Char]
showTreeWith Bool
True Bool
False IntMap a
s


{- | /O(n)/. The expression (@'showTreeWith' hang wide map@) shows
 the tree that implements the map. If @hang@ is
 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
 @wide@ is 'True', an extra wide version is shown.
-}
showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
showTreeWith :: forall a. Show a => Bool -> Bool -> IntMap a -> [Char]
showTreeWith Bool
hang Bool
wide IntMap a
t
  | Bool
hang      = (forall a. Show a => Bool -> [[Char]] -> IntMap a -> ShowS
showsTreeHang Bool
wide [] IntMap a
t) [Char]
""
  | Bool
otherwise = (forall a.
Show a =>
Bool -> [[Char]] -> [[Char]] -> IntMap a -> ShowS
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 -> ShowS
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 ->
    forall a.
Show a =>
Bool -> [[Char]] -> [[Char]] -> IntMap a -> ShowS
showsTree Bool
wide ([[Char]] -> [[Char]]
withBar [[Char]]
rbars) ([[Char]] -> [[Char]]
withEmpty [[Char]]
rbars) IntMap a
r forall b c a. (b -> c) -> (a -> b) -> a -> c
.
    Bool -> [[Char]] -> ShowS
showWide Bool
wide [[Char]]
rbars forall b c a. (b -> c) -> (a -> b) -> a -> c
.
    [[Char]] -> ShowS
showsBars [[Char]]
lbars forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Char] -> ShowS
showString (Int -> Int -> [Char]
showBin Int
p Int
m) forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Char] -> ShowS
showString [Char]
"\n" forall b c a. (b -> c) -> (a -> b) -> a -> c
.
    Bool -> [[Char]] -> ShowS
showWide Bool
wide [[Char]]
lbars forall b c a. (b -> c) -> (a -> b) -> a -> c
.
    forall a.
Show a =>
Bool -> [[Char]] -> [[Char]] -> IntMap a -> ShowS
showsTree Bool
wide ([[Char]] -> [[Char]]
withEmpty [[Char]]
lbars) ([[Char]] -> [[Char]]
withBar [[Char]]
lbars) IntMap a
l
  Tip Int
k a
x ->
    [[Char]] -> ShowS
showsBars [[Char]]
lbars forall b c a. (b -> c) -> (a -> b) -> a -> c
.
    [Char] -> ShowS
showString [Char]
" " forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Show a => a -> ShowS
shows Int
k forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Char] -> ShowS
showString [Char]
":=" forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Show a => a -> ShowS
shows a
x forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Char] -> ShowS
showString [Char]
"\n"
  IntMap a
Nil -> [[Char]] -> ShowS
showsBars [[Char]]
lbars forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Char] -> ShowS
showString [Char]
"|\n"

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

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

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

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