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

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

#include "containers.h"

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

-- [Note: INLINE bit fiddling]
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- It is essential that the bit fiddling functions like mask, zero, branchMask
-- etc are inlined. If they do not, the memory allocation skyrockets. The GHC
-- usually gets it right, but it is disastrous if it does not. Therefore we
-- explicitly mark these functions INLINE.


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


-- [Note: Order of constructors]
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- The order of constructors of IntMap matters when considering performance.
-- Currently in GHC 7.0, when type has 3 constructors, they are matched from
-- the first to the last -- the best performance is achieved when the
-- constructors are ordered by frequency.
-- On GHC 7.0, reordering constructors from Nil | Tip | Bin to Bin | Tip | Nil
-- improves the benchmark by circa 10%.

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

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

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

    -- * Construction
    , empty
    , singleton

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

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

    -- * Combine

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

    -- ** Difference
    , difference
    , differenceWith
    , differenceWithKey

    -- ** Intersection
    , intersection
    , intersectionWith
    , intersectionWithKey

    -- ** Compose
    , compose

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

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

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

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

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

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

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

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

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

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

    , mapMaybe
    , mapMaybeWithKey
    , mapEither
    , mapEitherWithKey

    , split
    , splitLookup
    , splitRoot

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

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

    -- * Debugging
    , showTree
    , showTreeWith

    -- * Internal types
    , Mask, Prefix, Nat

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

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

import Data.Functor.Identity (Identity (..))
import Control.Applicative (liftA2)
import Data.Semigroup (Semigroup(stimes))
#if !(MIN_VERSION_base(4,11,0))
import Data.Semigroup (Semigroup((<>)))
#endif
import Data.Semigroup (stimesIdempotentMonoid)
import Data.Functor.Classes

import Control.DeepSeq (NFData(rnf))
import Data.Bits
import qualified Data.Foldable as Foldable
import Data.Maybe (fromMaybe)
import 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

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


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

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

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

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


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

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

type Prefix = Int
type Mask   = Int


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

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

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

{--------------------------------------------------------------------
  Operators
--------------------------------------------------------------------}

-- | \(O(\min(n,W))\). Find the value at a key.
-- Calls 'error' when the element can not be found.
--
-- > fromList [(5,'a'), (3,'b')] ! 1    Error: element not in the map
-- > fromList [(5,'a'), (3,'b')] ! 5 == 'a'

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

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

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

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

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

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

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

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

-- | Folds in order of increasing key.
instance Foldable.Foldable IntMap where
  fold :: forall m. Monoid m => IntMap m -> m
fold = IntMap m -> m
forall m. Monoid m => IntMap m -> m
go
    where go :: IntMap a -> a
go IntMap a
Nil = a
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 Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0     = IntMap a -> a
go IntMap a
r a -> a -> a
forall a. Monoid a => a -> a -> a
`mappend` IntMap a -> a
go IntMap a
l
            | Bool
otherwise = IntMap a -> a
go IntMap a
l a -> a -> a
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 = (a -> b -> b) -> b -> IntMap a -> b
forall a b. (a -> b -> b) -> b -> IntMap a -> b
foldr
  {-# INLINE foldr #-}
  foldl :: forall b a. (b -> a -> b) -> b -> IntMap a -> b
foldl = (b -> a -> b) -> b -> IntMap a -> b
forall b a. (b -> a -> b) -> b -> IntMap a -> b
foldl
  {-# INLINE foldl #-}
  foldMap :: forall m a. Monoid m => (a -> m) -> IntMap a -> m
foldMap a -> m
f IntMap a
t = IntMap a -> m
go IntMap a
t
    where go :: IntMap a -> m
go IntMap a
Nil = m
forall a. Monoid a => a
mempty
          go (Tip Int
_ a
v) = a -> m
f a
v
          go (Bin Int
_ Int
m IntMap a
l IntMap a
r)
            | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0     = IntMap a -> m
go IntMap a
r m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` IntMap a -> m
go IntMap a
l
            | Bool
otherwise = IntMap a -> m
go IntMap a
l m -> m -> m
forall a. Monoid a => a -> a -> a
`mappend` IntMap a -> m
go IntMap a
r
  {-# INLINE foldMap #-}
  foldl' :: forall b a. (b -> a -> b) -> b -> IntMap a -> b
foldl' = (b -> a -> b) -> b -> IntMap a -> b
forall b a. (b -> a -> b) -> b -> IntMap a -> b
foldl'
  {-# INLINE foldl' #-}
  foldr' :: forall a b. (a -> b -> b) -> b -> IntMap a -> b
foldr' = (a -> b -> b) -> b -> IntMap a -> b
forall a b. (a -> b -> b) -> b -> IntMap a -> b
foldr'
  {-# INLINE foldr' #-}
  length :: forall a. IntMap a -> Int
length = IntMap a -> Int
forall a. IntMap a -> Int
size
  {-# INLINE length #-}
  null :: forall a. IntMap a -> Bool
null   = IntMap a -> Bool
forall a. IntMap a -> Bool
null
  {-# INLINE null #-}
  toList :: forall a. IntMap a -> [a]
toList = IntMap a -> [a]
forall a. IntMap a -> [a]
elems -- NB: Foldable.toList /= IntMap.toList
  {-# INLINE toList #-}
  elem :: forall a. Eq a => a -> IntMap a -> Bool
elem = a -> IntMap a -> Bool
forall a. Eq a => a -> IntMap a -> Bool
go
    where go :: t -> IntMap t -> Bool
go !t
_ IntMap t
Nil = Bool
False
          go t
x (Tip Int
_ t
y) = t
x t -> t -> Bool
forall a. Eq a => a -> a -> Bool
== t
y
          go t
x (Bin Int
_ Int
_ IntMap t
l IntMap t
r) = t -> IntMap t -> Bool
go t
x IntMap t
l Bool -> Bool -> Bool
|| t -> IntMap t -> Bool
go t
x IntMap t
r
  {-# INLINABLE elem #-}
  maximum :: forall a. Ord a => IntMap a -> a
maximum = IntMap a -> a
forall a. Ord a => IntMap a -> a
start
    where start :: IntMap a -> a
start IntMap a
Nil = [Char] -> a
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 Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0     = a -> IntMap a -> a
forall {t}. Ord t => t -> IntMap t -> t
go (IntMap a -> a
start IntMap a
r) IntMap a
l
            | Bool
otherwise = a -> IntMap a -> a
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) = t -> t -> t
forall a. Ord a => a -> a -> a
max t
m t
y
          go t
m (Bin Int
_ Int
_ IntMap t
l IntMap t
r) = t -> IntMap t -> t
go (t -> IntMap t -> t
go t
m IntMap t
l) IntMap t
r
  {-# INLINABLE maximum #-}
  minimum :: forall a. Ord a => IntMap a -> a
minimum = IntMap a -> a
forall a. Ord a => IntMap a -> a
start
    where start :: IntMap a -> a
start IntMap a
Nil = [Char] -> a
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 Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0     = a -> IntMap a -> a
forall {t}. Ord t => t -> IntMap t -> t
go (IntMap a -> a
start IntMap a
r) IntMap a
l
            | Bool
otherwise = a -> IntMap a -> a
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) = t -> t -> t
forall a. Ord a => a -> a -> a
min t
m t
y
          go t
m (Bin Int
_ Int
_ IntMap t
l IntMap t
r) = t -> IntMap t -> t
go (t -> IntMap t -> t
go t
m IntMap t
l) IntMap t
r
  {-# INLINABLE minimum #-}
  sum :: forall a. Num a => IntMap a -> a
sum = (a -> a -> a) -> a -> IntMap a -> a
forall b a. (b -> a -> b) -> b -> IntMap a -> b
foldl' a -> a -> a
forall a. Num a => a -> a -> a
(+) a
0
  {-# INLINABLE sum #-}
  product :: forall a. Num a => IntMap a -> a
product = (a -> a -> a) -> a -> IntMap a -> a
forall b a. (b -> a -> b) -> b -> IntMap a -> b
foldl' a -> a -> a
forall a. Num a => a -> a -> a
(*) a
1
  {-# INLINABLE product #-}

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

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

#if __GLASGOW_HASKELL__

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

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

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

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

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

#endif

{--------------------------------------------------------------------
  Query
--------------------------------------------------------------------}
-- | \(O(1)\). Is the map empty?
--
-- > Data.IntMap.null (empty)           == True
-- > Data.IntMap.null (singleton 1 'a') == False

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

-- | \(O(n)\). Number of elements in the map.
--
-- > size empty                                   == 0
-- > size (singleton 1 'a')                       == 1
-- > size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3
size :: IntMap a -> Int
size :: forall a. IntMap a -> Int
size = Int -> IntMap a -> Int
forall {t} {a}. Num t => t -> IntMap a -> t
go Int
0
  where
    go :: t -> IntMap a -> t
go !t
acc (Bin Int
_ Int
_ IntMap a
l IntMap a
r) = t -> IntMap a -> t
go (t -> IntMap a -> t
go t
acc IntMap a
l) IntMap a
r
    go t
acc (Tip Int
_ a
_) = t
1 t -> t -> t
forall a. Num a => a -> a -> a
+ t
acc
    go t
acc IntMap a
Nil = t
acc

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

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

-- | \(O(\min(n,W))\). Is the key not a member of the map?
--
-- > notMember 5 (fromList [(5,'a'), (3,'b')]) == False
-- > notMember 1 (fromList [(5,'a'), (3,'b')]) == True

notMember :: Key -> IntMap a -> Bool
notMember :: forall a. Int -> IntMap a -> Bool
notMember Int
k IntMap a
m = Bool -> Bool
not (Bool -> Bool) -> Bool -> Bool
forall a b. (a -> b) -> a -> b
$ Int -> IntMap a -> Bool
forall a. Int -> IntMap a -> Bool
member Int
k IntMap a
m

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

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

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

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

-- | \(O(\min(n,W))\). The expression @('findWithDefault' def k map)@
-- returns the value at key @k@ or returns @def@ when the key is not an
-- element of the map.
--
-- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x'
-- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a'

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

-- | \(O(\log n)\). 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 Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> if Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
0 then IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
r IntMap a
l else IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
forall a. IntMap a
Nil IntMap a
r
    IntMap a
_ -> IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
forall a. IntMap a
Nil IntMap a
t
  where
    go :: IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
def (Bin Int
p Int
m IntMap a
l IntMap a
r)
      | Int -> Int -> Int -> Bool
nomatch Int
k Int
p Int
m = if Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
p then IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def else IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
r
      | Int -> Int -> Bool
zero Int
k Int
m  = IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
def IntMap a
l
      | Bool
otherwise = IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
l IntMap a
r
    go IntMap a
def (Tip Int
ky a
y)
      | Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<= Int
ky   = IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def
      | Bool
otherwise = (Int, a) -> Maybe (Int, a)
forall a. a -> Maybe a
Just (Int
ky, a
y)
    go IntMap a
def IntMap a
Nil = IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def

-- | \(O(\log n)\). 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 Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> if Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
0 then IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
forall a. IntMap a
Nil IntMap a
l else IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
l IntMap a
r
    IntMap a
_ -> IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
forall a. IntMap a
Nil IntMap a
t
  where
    go :: IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
def (Bin Int
p Int
m IntMap a
l IntMap a
r)
      | Int -> Int -> Int -> Bool
nomatch Int
k Int
p Int
m = if Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
p then IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
l else IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
def
      | Int -> Int -> Bool
zero Int
k Int
m  = IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
r IntMap a
l
      | Bool
otherwise = IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
def IntMap a
r
    go IntMap a
def (Tip Int
ky a
y)
      | Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
ky   = IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
def
      | Bool
otherwise = (Int, a) -> Maybe (Int, a)
forall a. a -> Maybe a
Just (Int
ky, a
y)
    go IntMap a
def IntMap a
Nil = IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
def

-- | \(O(\log n)\). 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 Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> if Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
0 then IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
r IntMap a
l else IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
forall a. IntMap a
Nil IntMap a
r
    IntMap a
_ -> IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
forall a. IntMap a
Nil IntMap a
t
  where
    go :: IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
def (Bin Int
p Int
m IntMap a
l IntMap a
r)
      | Int -> Int -> Int -> Bool
nomatch Int
k Int
p Int
m = if Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
p then IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def else IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
r
      | Int -> Int -> Bool
zero Int
k Int
m  = IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
def IntMap a
l
      | Bool
otherwise = IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
l IntMap a
r
    go IntMap a
def (Tip Int
ky a
y)
      | Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
ky    = IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def
      | Bool
otherwise = (Int, a) -> Maybe (Int, a)
forall a. a -> Maybe a
Just (Int
ky, a
y)
    go IntMap a
def IntMap a
Nil = IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMax IntMap a
def

-- | \(O(\log n)\). 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 Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> if Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
0 then IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
forall a. IntMap a
Nil IntMap a
l else IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
l IntMap a
r
    IntMap a
_ -> IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
forall a. IntMap a
Nil IntMap a
t
  where
    go :: IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
def (Bin Int
p Int
m IntMap a
l IntMap a
r)
      | Int -> Int -> Int -> Bool
nomatch Int
k Int
p Int
m = if Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
p then IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
l else IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
def
      | Int -> Int -> Bool
zero Int
k Int
m  = IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
r IntMap a
l
      | Bool
otherwise = IntMap a -> IntMap a -> Maybe (Int, a)
go IntMap a
def IntMap a
r
    go IntMap a
def (Tip Int
ky a
y)
      | Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
ky    = IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
def
      | Bool
otherwise = (Int, a) -> Maybe (Int, a)
forall a. a -> Maybe a
Just (Int
ky, a
y)
    go IntMap a
def IntMap a
Nil = IntMap a -> Maybe (Int, a)
forall a. IntMap a -> Maybe (Int, a)
unsafeFindMin IntMap a
def


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

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

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

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

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

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

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

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

{--------------------------------------------------------------------
  Insert
--------------------------------------------------------------------}
-- | \(O(\min(n,W))\). Insert a new key\/value pair in the map.
-- If the key is already present in the map, the associated value is
-- replaced with the supplied value, i.e. 'insert' is equivalent to
-- @'insertWith' 'const'@.
--
-- > insert 5 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'x')]
-- > insert 7 'x' (fromList [(5,'a'), (3,'b')]) == fromList [(3, 'b'), (5, 'a'), (7, 'x')]
-- > insert 5 'x' empty                         == singleton 5 'x'

insert :: Key -> a -> IntMap a -> IntMap a
insert :: forall a. Int -> a -> IntMap a -> IntMap a
insert !Int
k a
x t :: IntMap a
t@(Bin Int
p Int
m IntMap a
l IntMap a
r)
  | Int -> Int -> Int -> Bool
nomatch Int
k Int
p Int
m = Int -> IntMap a -> Int -> IntMap a -> IntMap a
forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
p IntMap a
t
  | Int -> Int -> Bool
zero Int
k Int
m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m (Int -> a -> IntMap a -> IntMap a
forall a. Int -> a -> IntMap a -> IntMap a
insert Int
k a
x IntMap a
l) IntMap a
r
  | Bool
otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m IntMap a
l (Int -> a -> IntMap a -> IntMap a
forall a. Int -> a -> IntMap a -> IntMap a
insert Int
k a
x IntMap a
r)
insert Int
k a
x t :: IntMap a
t@(Tip Int
ky a
_)
  | Int
kInt -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==Int
ky         = Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
x
  | Bool
otherwise     = Int -> IntMap a -> Int -> IntMap a -> IntMap a
forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
ky IntMap a
t
insert Int
k a
x IntMap a
Nil = Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
x

-- right-biased insertion, used by 'union'
-- | \(O(\min(n,W))\). Insert with a combining function.
-- @'insertWith' f key value mp@
-- will insert the pair (key, value) into @mp@ if key does
-- not exist in the map. If the key does exist, the function will
-- insert @f new_value old_value@.
--
-- > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")]
-- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
-- > insertWith (++) 5 "xxx" empty                         == singleton 5 "xxx"

insertWith :: (a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
insertWith :: forall a. (a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
insertWith a -> a -> a
f Int
k a
x IntMap a
t
  = (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
forall a. (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
insertWithKey (\Int
_ a
x' a
y' -> a -> a -> a
f a
x' a
y') Int
k a
x IntMap a
t

-- | \(O(\min(n,W))\). Insert with a combining function.
-- @'insertWithKey' f key value mp@
-- will insert the pair (key, value) into @mp@ if key does
-- not exist in the map. If the key does exist, the function will
-- insert @f key new_value old_value@.
--
-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
-- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")]
-- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
-- > insertWithKey f 5 "xxx" empty                         == singleton 5 "xxx"

insertWithKey :: (Key -> a -> a -> a) -> Key -> a -> IntMap a -> IntMap a
insertWithKey :: forall a. (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
insertWithKey Int -> a -> a -> a
f !Int
k a
x t :: IntMap a
t@(Bin Int
p Int
m IntMap a
l IntMap a
r)
  | Int -> Int -> Int -> Bool
nomatch Int
k Int
p Int
m = Int -> IntMap a -> Int -> IntMap a -> IntMap a
forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
p IntMap a
t
  | Int -> Int -> Bool
zero Int
k Int
m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m ((Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
forall a. (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
insertWithKey Int -> a -> a -> a
f Int
k a
x IntMap a
l) IntMap a
r
  | Bool
otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m IntMap a
l ((Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
forall a. (Int -> a -> a -> a) -> Int -> a -> IntMap a -> IntMap a
insertWithKey Int -> a -> a -> a
f Int
k a
x IntMap a
r)
insertWithKey Int -> a -> a -> a
f Int
k a
x t :: IntMap a
t@(Tip Int
ky a
y)
  | Int
k Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
ky       = Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k (Int -> a -> a -> a
f Int
k a
x a
y)
  | Bool
otherwise     = Int -> IntMap a -> Int -> IntMap a -> IntMap a
forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
ky IntMap a
t
insertWithKey Int -> a -> a -> a
_ Int
k a
x IntMap a
Nil = Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
x

-- | \(O(\min(n,W))\). The expression (@'insertLookupWithKey' f k x map@)
-- is a pair where the first element is equal to (@'lookup' k map@)
-- and the second element equal to (@'insertWithKey' f k x map@).
--
-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
-- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
-- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "xxx")])
-- > insertLookupWithKey f 5 "xxx" empty                         == (Nothing,  singleton 5 "xxx")
--
-- This is how to define @insertLookup@ using @insertLookupWithKey@:
--
-- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t
-- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")])
-- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "x")])

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


{--------------------------------------------------------------------
  Deletion
--------------------------------------------------------------------}
-- | \(O(\min(n,W))\). Delete a key and its value from the map. When the key is not
-- a member of the map, the original map is returned.
--
-- > delete 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
-- > delete 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > delete 5 empty                         == empty

delete :: Key -> IntMap a -> IntMap a
delete :: forall a. Int -> IntMap a -> IntMap a
delete !Int
k t :: IntMap a
t@(Bin Int
p Int
m IntMap a
l IntMap a
r)
  | Int -> Int -> Int -> Bool
nomatch Int
k Int
p Int
m = IntMap a
t
  | Int -> Int -> Bool
zero Int
k Int
m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckLeft Int
p Int
m (Int -> IntMap a -> IntMap a
forall a. Int -> IntMap a -> IntMap a
delete Int
k IntMap a
l) IntMap a
r
  | Bool
otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckRight Int
p Int
m IntMap a
l (Int -> IntMap a -> IntMap a
forall a. Int -> IntMap a -> IntMap a
delete Int
k IntMap a
r)
delete Int
k t :: IntMap a
t@(Tip Int
ky a
_)
  | Int
k Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
ky       = IntMap a
forall a. IntMap a
Nil
  | Bool
otherwise     = IntMap a
t
delete Int
_k IntMap a
Nil = IntMap a
forall a. IntMap a
Nil

-- | \(O(\min(n,W))\). Adjust a value at a specific key. When the key is not
-- a member of the map, the original map is returned.
--
-- > adjust ("new " ++) 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
-- > adjust ("new " ++) 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > adjust ("new " ++) 7 empty                         == empty

adjust ::  (a -> a) -> Key -> IntMap a -> IntMap a
adjust :: forall a. (a -> a) -> Int -> IntMap a -> IntMap a
adjust a -> a
f Int
k IntMap a
m
  = (Int -> a -> a) -> Int -> IntMap a -> IntMap a
forall a. (Int -> a -> a) -> Int -> IntMap a -> IntMap a
adjustWithKey (\Int
_ a
x -> a -> a
f a
x) Int
k IntMap a
m

-- | \(O(\min(n,W))\). Adjust a value at a specific key. When the key is not
-- a member of the map, the original map is returned.
--
-- > let f key x = (show key) ++ ":new " ++ x
-- > adjustWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
-- > adjustWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > adjustWithKey f 7 empty                         == empty

adjustWithKey ::  (Key -> a -> a) -> Key -> IntMap a -> IntMap a
adjustWithKey :: forall a. (Int -> a -> a) -> Int -> IntMap a -> IntMap a
adjustWithKey Int -> a -> a
f !Int
k (Bin Int
p Int
m IntMap a
l IntMap a
r)
  | Int -> Int -> Bool
zero Int
k Int
m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m ((Int -> a -> a) -> Int -> IntMap a -> IntMap a
forall a. (Int -> a -> a) -> Int -> IntMap a -> IntMap a
adjustWithKey Int -> a -> a
f Int
k IntMap a
l) IntMap a
r
  | Bool
otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m IntMap a
l ((Int -> a -> a) -> Int -> IntMap a -> IntMap a
forall a. (Int -> a -> a) -> Int -> IntMap a -> IntMap a
adjustWithKey Int -> a -> a
f Int
k IntMap a
r)
adjustWithKey Int -> a -> a
f Int
k t :: IntMap a
t@(Tip Int
ky a
y)
  | Int
k Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
ky       = Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
ky (Int -> a -> a
f Int
k a
y)
  | Bool
otherwise     = IntMap a
t
adjustWithKey Int -> a -> a
_ Int
_ IntMap a
Nil = IntMap a
forall a. IntMap a
Nil


-- | \(O(\min(n,W))\). The expression (@'update' f k map@) updates the value @x@
-- at @k@ (if it is in the map). If (@f x@) is 'Nothing', the element is
-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
--
-- > let f x = if x == "a" then Just "new a" else Nothing
-- > update f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "new a")]
-- > update f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > update f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

update ::  (a -> Maybe a) -> Key -> IntMap a -> IntMap a
update :: forall a. (a -> Maybe a) -> Int -> IntMap a -> IntMap a
update a -> Maybe a
f
  = (Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
forall a. (Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
updateWithKey (\Int
_ a
x -> a -> Maybe a
f a
x)

-- | \(O(\min(n,W))\). The expression (@'update' f k map@) updates the value @x@
-- at @k@ (if it is in the map). If (@f k x@) is 'Nothing', the element is
-- deleted. If it is (@'Just' y@), the key @k@ is bound to the new value @y@.
--
-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
-- > updateWithKey f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:new a")]
-- > updateWithKey f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > updateWithKey f 3 (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

updateWithKey ::  (Key -> a -> Maybe a) -> Key -> IntMap a -> IntMap a
updateWithKey :: forall a. (Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
updateWithKey Int -> a -> Maybe a
f !Int
k (Bin Int
p Int
m IntMap a
l IntMap a
r)
  | Int -> Int -> Bool
zero Int
k Int
m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckLeft Int
p Int
m ((Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
forall a. (Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
updateWithKey Int -> a -> Maybe a
f Int
k IntMap a
l) IntMap a
r
  | Bool
otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckRight Int
p Int
m IntMap a
l ((Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
forall a. (Int -> a -> Maybe a) -> Int -> IntMap a -> IntMap a
updateWithKey Int -> a -> Maybe a
f Int
k IntMap a
r)
updateWithKey Int -> a -> Maybe a
f Int
k t :: IntMap a
t@(Tip Int
ky a
y)
  | Int
k Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
== Int
ky       = case (Int -> a -> Maybe a
f Int
k a
y) of
                      Just a
y' -> Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
ky a
y'
                      Maybe a
Nothing -> IntMap a
forall a. IntMap a
Nil
  | Bool
otherwise     = IntMap a
t
updateWithKey Int -> a -> Maybe a
_ Int
_ IntMap a
Nil = IntMap a
forall a. IntMap a
Nil

-- | \(O(\min(n,W))\). Lookup and update.
-- The function returns original value, if it is updated.
-- This is different behavior than 'Data.Map.updateLookupWithKey'.
-- Returns the original key value if the map entry is deleted.
--
-- > let f k x = if x == "a" then Just ((show k) ++ ":new a") else Nothing
-- > updateLookupWithKey f 5 (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:new a")])
-- > updateLookupWithKey f 7 (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a")])
-- > updateLookupWithKey f 3 (fromList [(5,"a"), (3,"b")]) == (Just "b", singleton 5 "a")

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



-- | \(O(\min(n,W))\). The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof.
-- 'alter' can be used to insert, delete, or update a value in an 'IntMap'.
-- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@.
alter :: (Maybe a -> Maybe a) -> Key -> IntMap a -> IntMap a
alter :: forall a. (Maybe a -> Maybe a) -> Int -> IntMap a -> IntMap a
alter Maybe a -> Maybe a
f !Int
k t :: IntMap a
t@(Bin Int
p Int
m IntMap a
l IntMap a
r)
  | Int -> Int -> Int -> Bool
nomatch Int
k Int
p Int
m = case Maybe a -> Maybe a
f Maybe a
forall a. Maybe a
Nothing of
                      Maybe a
Nothing -> IntMap a
t
                      Just a
x -> Int -> IntMap a -> Int -> IntMap a -> IntMap a
forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
p IntMap a
t
  | Int -> Int -> Bool
zero Int
k Int
m      = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckLeft Int
p Int
m ((Maybe a -> Maybe a) -> Int -> IntMap a -> IntMap a
forall a. (Maybe a -> Maybe a) -> Int -> IntMap a -> IntMap a
alter Maybe a -> Maybe a
f Int
k IntMap a
l) IntMap a
r
  | Bool
otherwise     = Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
binCheckRight Int
p Int
m IntMap a
l ((Maybe a -> Maybe a) -> Int -> IntMap a -> IntMap a
forall a. (Maybe a -> Maybe a) -> Int -> IntMap a -> IntMap a
alter Maybe a -> Maybe a
f Int
k IntMap a
r)
alter Maybe a -> Maybe a
f Int
k t :: IntMap a
t@(Tip Int
ky a
y)
  | Int
kInt -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==Int
ky         = case Maybe a -> Maybe a
f (a -> Maybe a
forall a. a -> Maybe a
Just a
y) of
                      Just a
x -> Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
ky a
x
                      Maybe a
Nothing -> IntMap a
forall a. IntMap a
Nil
  | Bool
otherwise     = case Maybe a -> Maybe a
f Maybe a
forall a. Maybe a
Nothing of
                      Just a
x -> Int -> IntMap a -> Int -> IntMap a -> IntMap a
forall a. Int -> IntMap a -> Int -> IntMap a -> IntMap a
link Int
k (Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
x) Int
ky IntMap a
t
                      Maybe a
Nothing -> Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
ky a
y
alter Maybe a -> Maybe a
f Int
k IntMap a
Nil     = case Maybe a -> Maybe a
f Maybe a
forall a. Maybe a
Nothing of
                      Just a
x -> Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
x
                      Maybe a
Nothing -> IntMap a
forall a. IntMap a
Nil

-- | \(O(\log n)\). 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 = ((Maybe a -> IntMap a) -> f (Maybe a) -> f (IntMap a)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Maybe a -> f (Maybe a)
f Maybe a
mv) ((Maybe a -> IntMap a) -> f (IntMap a))
-> (Maybe a -> IntMap a) -> f (IntMap a)
forall a b. (a -> b) -> a -> b
$ \Maybe a
fres ->
  case Maybe a
fres of
    Maybe a
Nothing -> IntMap a -> (a -> IntMap a) -> Maybe a -> IntMap a
forall b a. b -> (a -> b) -> Maybe a -> b
maybe IntMap a
m (IntMap a -> a -> IntMap a
forall a b. a -> b -> a
const (Int -> IntMap a -> IntMap a
forall a. Int -> IntMap a -> IntMap a
delete Int
k IntMap a
m)) Maybe a
mv
    Just a
v' -> Int -> a -> IntMap a -> IntMap a
forall a. Int -> a -> IntMap a -> IntMap a
insert Int
k a
v' IntMap a
m
  where mv :: Maybe a
mv = Int -> IntMap a -> Maybe a
forall a. Int -> IntMap a -> Maybe a
lookup Int
k IntMap a
m

{--------------------------------------------------------------------
  Union
--------------------------------------------------------------------}
-- | The union of a list of maps.
--
-- > unions [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
-- >     == fromList [(3, "b"), (5, "a"), (7, "C")]
-- > unions [(fromList [(5, "A3"), (3, "B3")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "a"), (3, "b")])]
-- >     == fromList [(3, "B3"), (5, "A3"), (7, "C")]

unions :: Foldable f => f (IntMap a) -> IntMap a
unions :: forall (f :: * -> *) a. Foldable f => f (IntMap a) -> IntMap a
unions f (IntMap a)
xs
  = (IntMap a -> IntMap a -> IntMap a)
-> IntMap a -> f (IntMap a) -> IntMap a
forall b a. (b -> a -> b) -> b -> f a -> b
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' IntMap a -> IntMap a -> IntMap a
forall a. IntMap a -> IntMap a -> IntMap a
union IntMap a
forall a. IntMap a
empty f (IntMap a)
xs

-- | The union of a list of maps, with a combining operation.
--
-- > unionsWith (++) [(fromList [(5, "a"), (3, "b")]), (fromList [(5, "A"), (7, "C")]), (fromList [(5, "A3"), (3, "B3")])]
-- >     == fromList [(3, "bB3"), (5, "aAA3"), (7, "C")]

unionsWith :: Foldable f => (a->a->a) -> f (IntMap a) -> IntMap a
unionsWith :: forall (f :: * -> *) a.
Foldable f =>
(a -> a -> a) -> f (IntMap a) -> IntMap a
unionsWith a -> a -> a
f f (IntMap a)
ts
  = (IntMap a -> IntMap a -> IntMap a)
-> IntMap a -> f (IntMap a) -> IntMap a
forall b a. (b -> a -> b) -> b -> f a -> b
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' ((a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
forall a. (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
unionWith a -> a -> a
f) IntMap a
forall a. IntMap a
empty f (IntMap a)
ts

-- | \(O(n+m)\). The (left-biased) union of two maps.
-- It prefers the first map when duplicate keys are encountered,
-- i.e. (@'union' == 'unionWith' 'const'@).
--
-- > union (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "a"), (7, "C")]

union :: IntMap a -> IntMap a -> IntMap a
union :: forall a. IntMap a -> IntMap a -> IntMap a
union IntMap a
m1 IntMap a
m2
  = (Int -> Int -> IntMap a -> IntMap a -> IntMap a)
-> (IntMap a -> IntMap a -> IntMap a)
-> (IntMap a -> IntMap a)
-> (IntMap a -> IntMap a)
-> IntMap a
-> IntMap a
-> IntMap a
forall c a b.
(Int -> Int -> IntMap c -> IntMap c -> IntMap c)
-> (IntMap a -> IntMap b -> IntMap c)
-> (IntMap a -> IntMap c)
-> (IntMap b -> IntMap c)
-> IntMap a
-> IntMap b
-> IntMap c
mergeWithKey' Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin IntMap a -> IntMap a -> IntMap a
forall a b. a -> b -> a
const IntMap a -> IntMap a
forall a. a -> a
id IntMap a -> IntMap a
forall a. a -> a
id IntMap a
m1 IntMap a
m2

-- | \(O(n+m)\). The union with a combining function.
--
-- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]

unionWith :: (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
unionWith :: forall a. (a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
unionWith a -> a -> a
f IntMap a
m1 IntMap a
m2
  = (Int -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
forall a. (Int -> a -> a -> a) -> IntMap a -> IntMap a -> IntMap a
unionWithKey (\Int
_ a
x a
y -> a -> a -> a
f a
x a
y) IntMap a
m1 IntMap a
m2

-- | \(O(n+m)\). The union with a combining function.
--
-- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value
-- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")]

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

{--------------------------------------------------------------------
  Difference
--------------------------------------------------------------------}
-- | \(O(n+m)\). Difference between two maps (based on keys).
--
-- > difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b"

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

-- | \(O(n+m)\). Difference with a combining function.
--
-- > let f al ar = if al == "b" then Just (al ++ ":" ++ ar) else Nothing
-- > differenceWith f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (7, "C")])
-- >     == singleton 3 "b:B"

differenceWith :: (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
differenceWith :: forall a b. (a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
differenceWith a -> b -> Maybe a
f IntMap a
m1 IntMap b
m2
  = (Int -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
forall a b.
(Int -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
differenceWithKey (\Int
_ a
x b
y -> a -> b -> Maybe a
f a
x b
y) IntMap a
m1 IntMap b
m2

-- | \(O(n+m)\). Difference with a combining function. When two equal keys are
-- encountered, the combining function is applied to the key and both values.
-- If it returns 'Nothing', the element is discarded (proper set difference).
-- If it returns (@'Just' y@), the element is updated with a new value @y@.
--
-- > let f k al ar = if al == "b" then Just ((show k) ++ ":" ++ al ++ "|" ++ ar) else Nothing
-- > differenceWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (3, "B"), (10, "C")])
-- >     == singleton 3 "3:b|B"

differenceWithKey :: (Key -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
differenceWithKey :: forall a b.
(Int -> a -> b -> Maybe a) -> IntMap a -> IntMap b -> IntMap a
differenceWithKey Int -> a -> b -> Maybe a
f IntMap a
m1 IntMap b
m2
  = (Int -> a -> b -> Maybe a)
-> (IntMap a -> IntMap a)
-> (IntMap b -> IntMap a)
-> IntMap a
-> IntMap b
-> IntMap a
forall a b c.
(Int -> a -> b -> Maybe c)
-> (IntMap a -> IntMap c)
-> (IntMap b -> IntMap c)
-> IntMap a
-> IntMap b
-> IntMap c
mergeWithKey Int -> a -> b -> Maybe a
f IntMap a -> IntMap a
forall a. a -> a
id (IntMap a -> IntMap b -> IntMap a
forall a b. a -> b -> a
const IntMap a
forall a. IntMap a
Nil) IntMap a
m1 IntMap b
m2


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


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


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


{--------------------------------------------------------------------
  Intersection
--------------------------------------------------------------------}
-- | \(O(n+m)\). The (left-biased) intersection of two maps (based on keys).
--
-- > intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a"

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


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


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


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


-- | \(O(n+m)\). The intersection with a combining function.
--
-- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA"

intersectionWith :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
intersectionWith :: forall a b c. (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
intersectionWith a -> b -> c
f IntMap a
m1 IntMap b
m2
  = (Int -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
forall a b c.
(Int -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
intersectionWithKey (\Int
_ a
x b
y -> a -> b -> c
f a
x b
y) IntMap a
m1 IntMap b
m2

-- | \(O(n+m)\). The intersection with a combining function.
--
-- > let f k al ar = (show k) ++ ":" ++ al ++ "|" ++ ar
-- > intersectionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "5:a|A"

intersectionWithKey :: (Key -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
intersectionWithKey :: forall a b c.
(Int -> a -> b -> c) -> IntMap a -> IntMap b -> IntMap c
intersectionWithKey Int -> a -> b -> c
f IntMap a
m1 IntMap b
m2
  = (Int -> Int -> IntMap c -> IntMap c -> IntMap c)
-> (IntMap a -> IntMap b -> IntMap c)
-> (IntMap a -> IntMap c)
-> (IntMap b -> IntMap c)
-> IntMap a
-> IntMap b
-> IntMap c
forall c a b.
(Int -> Int -> IntMap c -> IntMap c -> IntMap c)
-> (IntMap a -> IntMap b -> IntMap c)
-> (IntMap a -> IntMap c)
-> (IntMap b -> IntMap c)
-> IntMap a
-> IntMap b
-> IntMap c
mergeWithKey' Int -> Int -> IntMap c -> IntMap c -> IntMap c
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin (\(Tip Int
k1 a
x1) (Tip Int
_k2 b
x2) -> Int -> c -> IntMap c
forall a. Int -> a -> IntMap a
Tip Int
k1 (Int -> a -> b -> c
f Int
k1 a
x1 b
x2)) (IntMap c -> IntMap a -> IntMap c
forall a b. a -> b -> a
const IntMap c
forall a. IntMap a
Nil) (IntMap c -> IntMap b -> IntMap c
forall a b. a -> b -> a
const IntMap c
forall a. IntMap a
Nil) IntMap a
m1 IntMap b
m2

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

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

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

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

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

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

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

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

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

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


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

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

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

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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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

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


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


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


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


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


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

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

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

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

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

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

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

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

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

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


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

-- | \(O(\min(n,W))\). Update the value at the minimal key.
--
-- > updateMinWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"3:b"), (5,"a")]
-- > updateMinWithKey (\ _ _ -> Nothing)                     (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

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

-- | \(O(\min(n,W))\). Update the value at the maximal key.
--
-- > updateMaxWithKey (\ k a -> Just ((show k) ++ ":" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3,"b"), (5,"5:a")]
-- > updateMaxWithKey (\ _ _ -> Nothing)                     (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"

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


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

-- | \(O(\min(n,W))\). Retrieves the maximal (key,value) pair of the map, and
-- the map stripped of that element, or 'Nothing' if passed an empty map.
--
-- > maxViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((5,"a"), singleton 3 "b")
-- > maxViewWithKey empty == Nothing

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

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

-- | \(O(\min(n,W))\). Retrieves the minimal (key,value) pair of the map, and
-- the map stripped of that element, or 'Nothing' if passed an empty map.
--
-- > minViewWithKey (fromList [(5,"a"), (3,"b")]) == Just ((3,"b"), singleton 5 "a")
-- > minViewWithKey empty == Nothing

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

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

-- | \(O(\min(n,W))\). Update the value at the maximal key.
--
-- > updateMax (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "Xa")]
-- > updateMax (\ _ -> Nothing)         (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"

updateMax :: (a -> Maybe a) -> IntMap a -> IntMap a
updateMax :: forall a. (a -> Maybe a) -> IntMap a -> IntMap a
updateMax a -> Maybe a
f = (Int -> a -> Maybe a) -> IntMap a -> IntMap a
forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
updateMaxWithKey ((a -> Maybe a) -> Int -> a -> Maybe a
forall a b. a -> b -> a
const a -> Maybe a
f)

-- | \(O(\min(n,W))\). Update the value at the minimal key.
--
-- > updateMin (\ a -> Just ("X" ++ a)) (fromList [(5,"a"), (3,"b")]) == fromList [(3, "Xb"), (5, "a")]
-- > updateMin (\ _ -> Nothing)         (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

updateMin :: (a -> Maybe a) -> IntMap a -> IntMap a
updateMin :: forall a. (a -> Maybe a) -> IntMap a -> IntMap a
updateMin a -> Maybe a
f = (Int -> a -> Maybe a) -> IntMap a -> IntMap a
forall a. (Int -> a -> Maybe a) -> IntMap a -> IntMap a
updateMinWithKey ((a -> Maybe a) -> Int -> a -> Maybe a
forall a b. a -> b -> a
const a -> Maybe a
f)

-- | \(O(\min(n,W))\). Retrieves the maximal key of the map, and the map
-- stripped of that element, or 'Nothing' if passed an empty map.
maxView :: IntMap a -> Maybe (a, IntMap a)
maxView :: forall a. IntMap a -> Maybe (a, IntMap a)
maxView IntMap a
t = (((Int, a), IntMap a) -> (a, IntMap a))
-> Maybe ((Int, a), IntMap a) -> Maybe (a, IntMap a)
forall a b. (a -> b) -> Maybe a -> Maybe b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\((Int
_, a
x), IntMap a
t') -> (a
x, IntMap a
t')) (IntMap a -> Maybe ((Int, a), IntMap a)
forall a. IntMap a -> Maybe ((Int, a), IntMap a)
maxViewWithKey IntMap a
t)

-- | \(O(\min(n,W))\). Retrieves the minimal key of the map, and the map
-- stripped of that element, or 'Nothing' if passed an empty map.
minView :: IntMap a -> Maybe (a, IntMap a)
minView :: forall a. IntMap a -> Maybe (a, IntMap a)
minView IntMap a
t = (((Int, a), IntMap a) -> (a, IntMap a))
-> Maybe ((Int, a), IntMap a) -> Maybe (a, IntMap a)
forall a b. (a -> b) -> Maybe a -> Maybe b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (\((Int
_, a
x), IntMap a
t') -> (a
x, IntMap a
t')) (IntMap a -> Maybe ((Int, a), IntMap a)
forall a. IntMap a -> Maybe ((Int, a), IntMap a)
minViewWithKey IntMap a
t)

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

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

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

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

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

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

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

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


{--------------------------------------------------------------------
  Submap
--------------------------------------------------------------------}
-- | \(O(n+m)\). Is this a proper submap? (ie. a submap but not equal).
-- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
isProperSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
isProperSubmapOf :: forall a. Eq a => IntMap a -> IntMap a -> Bool
isProperSubmapOf IntMap a
m1 IntMap a
m2
  = (a -> a -> Bool) -> IntMap a -> IntMap a -> Bool
forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isProperSubmapOfBy a -> a -> Bool
forall a. Eq a => a -> a -> Bool
(==) IntMap a
m1 IntMap a
m2

{- | \(O(n+m)\). Is this a proper submap? (ie. a submap but not equal).
 The expression (@'isProperSubmapOfBy' f m1 m2@) returns 'True' when
 @keys m1@ and @keys m2@ are not equal,
 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
 applied to their respective values. For example, the following
 expressions are all 'True':

  > isProperSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
  > isProperSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])

 But the following are all 'False':

  > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])
  > isProperSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
  > isProperSubmapOfBy (<)  (fromList [(1,1)])       (fromList [(1,1),(2,2)])
-}
isProperSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isProperSubmapOfBy :: forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isProperSubmapOfBy a -> b -> Bool
predicate IntMap a
t1 IntMap b
t2
  = case (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Ordering
submapCmp a -> b -> Bool
predicate IntMap a
t1 IntMap b
t2 of
      Ordering
LT -> Bool
True
      Ordering
_  -> Bool
False

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

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

-- | \(O(n+m)\). Is this a submap?
-- Defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
isSubmapOf :: Eq a => IntMap a -> IntMap a -> Bool
isSubmapOf :: forall a. Eq a => IntMap a -> IntMap a -> Bool
isSubmapOf IntMap a
m1 IntMap a
m2
  = (a -> a -> Bool) -> IntMap a -> IntMap a -> Bool
forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isSubmapOfBy a -> a -> Bool
forall a. Eq a => a -> a -> Bool
(==) IntMap a
m1 IntMap a
m2

{- | \(O(n+m)\).
 The expression (@'isSubmapOfBy' f m1 m2@) returns 'True' if
 all keys in @m1@ are in @m2@, and when @f@ returns 'True' when
 applied to their respective values. For example, the following
 expressions are all 'True':

  > isSubmapOfBy (==) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
  > isSubmapOfBy (<=) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
  > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1),(2,2)])

 But the following are all 'False':

  > isSubmapOfBy (==) (fromList [(1,2)]) (fromList [(1,1),(2,2)])
  > isSubmapOfBy (<) (fromList [(1,1)]) (fromList [(1,1),(2,2)])
  > isSubmapOfBy (==) (fromList [(1,1),(2,2)]) (fromList [(1,1)])
-}
isSubmapOfBy :: (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isSubmapOfBy :: forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isSubmapOfBy a -> b -> Bool
predicate t1 :: IntMap a
t1@(Bin Int
p1 Int
m1 IntMap a
l1 IntMap a
r1) (Bin Int
p2 Int
m2 IntMap b
l2 IntMap b
r2)
  | Int -> Int -> Bool
shorter Int
m1 Int
m2  = Bool
False
  | Int -> Int -> Bool
shorter Int
m2 Int
m1  = Int -> Int -> Int -> Bool
match Int
p1 Int
p2 Int
m2 Bool -> Bool -> Bool
&&
                       if Int -> Int -> Bool
zero Int
p1 Int
m2
                       then (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isSubmapOfBy a -> b -> Bool
predicate IntMap a
t1 IntMap b
l2
                       else (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isSubmapOfBy a -> b -> Bool
predicate IntMap a
t1 IntMap b
r2
  | Bool
otherwise      = (Int
p1Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
==Int
p2) Bool -> Bool -> Bool
&& (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isSubmapOfBy a -> b -> Bool
predicate IntMap a
l1 IntMap b
l2 Bool -> Bool -> Bool
&& (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
forall a b. (a -> b -> Bool) -> IntMap a -> IntMap b -> Bool
isSubmapOfBy a -> b -> Bool
predicate IntMap a
r1 IntMap b
r2
isSubmapOfBy a -> b -> Bool
_         (Bin Int
_ Int
_ IntMap a
_ IntMap a
_) IntMap b
_ = Bool
False
isSubmapOfBy a -> b -> Bool
predicate (Tip Int
k a
x) IntMap b
t     = case Int -> IntMap b -> Maybe b
forall a. Int -> IntMap a -> Maybe a
lookup Int
k IntMap b
t of
                                         Just b
y  -> a -> b -> Bool
predicate a
x b
y
                                         Maybe b
Nothing -> Bool
False
isSubmapOfBy a -> b -> Bool
_         IntMap a
Nil IntMap b
_           = Bool
True

{--------------------------------------------------------------------
  Mapping
--------------------------------------------------------------------}
-- | \(O(n)\). Map a function over all values in the map.
--
-- > map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

map :: (a -> b) -> IntMap a -> IntMap b
map :: forall a b. (a -> b) -> IntMap a -> IntMap b
map a -> b
f = IntMap a -> IntMap b
go
  where
    go :: IntMap a -> IntMap b
go (Bin Int
p Int
m IntMap a
l IntMap a
r) = Int -> Int -> IntMap b -> IntMap b -> IntMap b
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m (IntMap a -> IntMap b
go IntMap a
l) (IntMap a -> IntMap b
go IntMap a
r)
    go (Tip Int
k a
x)     = Int -> b -> IntMap b
forall a. Int -> a -> IntMap a
Tip Int
k (a -> b
f a
x)
    go IntMap a
Nil           = IntMap b
forall a. IntMap a
Nil

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

-- | \(O(n)\). Map a function over all values in the map.
--
-- > let f key x = (show key) ++ ":" ++ x
-- > mapWithKey f (fromList [(5,"a"), (3,"b")]) == fromList [(3, "3:b"), (5, "5:a")]

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

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

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

-- | \(O(n)\). The function @'mapAccum'@ threads an accumulating
-- argument through the map in ascending order of keys.
--
-- > let f a b = (a ++ b, b ++ "X")
-- > mapAccum f "Everything: " (fromList [(5,"a"), (3,"b")]) == ("Everything: ba", fromList [(3, "bX"), (5, "aX")])

mapAccum :: (a -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccum :: forall a b c. (a -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
mapAccum a -> b -> (a, c)
f = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
forall a b c.
(a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
mapAccumWithKey (\a
a' Int
_ b
x -> a -> b -> (a, c)
f a
a' b
x)

-- | \(O(n)\). The function @'mapAccumWithKey'@ threads an accumulating
-- argument through the map in ascending order of keys.
--
-- > let f a k b = (a ++ " " ++ (show k) ++ "-" ++ b, b ++ "X")
-- > mapAccumWithKey f "Everything:" (fromList [(5,"a"), (3,"b")]) == ("Everything: 3-b 5-a", fromList [(3, "bX"), (5, "aX")])

mapAccumWithKey :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccumWithKey :: forall a b c.
(a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
mapAccumWithKey a -> Int -> b -> (a, c)
f a
a IntMap b
t
  = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
forall a b c.
(a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
mapAccumL a -> Int -> b -> (a, c)
f a
a IntMap b
t

-- | \(O(n)\). The function @'mapAccumL'@ threads an accumulating
-- argument through the map in ascending order of keys.
mapAccumL :: (a -> Key -> b -> (a,c)) -> a -> IntMap b -> (a,IntMap c)
mapAccumL :: forall a b c.
(a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
mapAccumL a -> Int -> b -> (a, c)
f a
a IntMap b
t
  = case IntMap b
t of
      Bin Int
p Int
m IntMap b
l IntMap b
r
        | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 ->
            let (a
a1,IntMap c
r') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
forall a b c.
(a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
mapAccumL a -> Int -> b -> (a, c)
f a
a IntMap b
r
                (a
a2,IntMap c
l') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
forall a b c.
(a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
mapAccumL a -> Int -> b -> (a, c)
f a
a1 IntMap b
l
            in (a
a2,Int -> Int -> IntMap c -> IntMap c -> IntMap c
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m IntMap c
l' IntMap c
r')
        | Bool
otherwise  ->
            let (a
a1,IntMap c
l') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
forall a b c.
(a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
mapAccumL a -> Int -> b -> (a, c)
f a
a IntMap b
l
                (a
a2,IntMap c
r') = (a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
forall a b c.
(a -> Int -> b -> (a, c)) -> a -> IntMap b -> (a, IntMap c)
mapAccumL a -> Int -> b -> (a, c)
f a
a1 IntMap b
r
            in (a
a2,Int -> Int -> IntMap c -> IntMap c -> IntMap c
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
Bin Int
p Int
m IntMap c
l' IntMap c
r')
      Tip Int
k b
x     -> let (a
a',c
x') = a -> Int -> b -> (a, c)
f a
a Int
k b
x in (a
a',Int -> c -> IntMap c
forall a. Int -> a -> IntMap a
Tip Int
k c
x')
      IntMap b
Nil         -> (a
a,IntMap c
forall a. IntMap a
Nil)

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

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

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

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

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

-- | \(O(n \min(n,W))\).
-- @'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
  = [(Int, a)] -> IntMap a
forall a. [(Int, a)] -> IntMap a
fromDistinctAscList ([(Int, a)] -> IntMap a)
-> (IntMap a -> [(Int, a)]) -> IntMap a -> IntMap a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Int -> a -> [(Int, a)] -> [(Int, a)])
-> [(Int, a)] -> IntMap a -> [(Int, a)]
forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
foldrWithKey (\Int
k a
x [(Int, a)]
xs -> (Int -> Int
f Int
k, a
x) (Int, a) -> [(Int, a)] -> [(Int, a)]
forall a. a -> [a] -> [a]
: [(Int, a)]
xs) []

{--------------------------------------------------------------------
  Filter
--------------------------------------------------------------------}
-- | \(O(n)\). Filter all values that satisfy some predicate.
--
-- > filter (> "a") (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
-- > filter (> "x") (fromList [(5,"a"), (3,"b")]) == empty
-- > filter (< "a") (fromList [(5,"a"), (3,"b")]) == empty

filter :: (a -> Bool) -> IntMap a -> IntMap a
filter :: forall a. (a -> Bool) -> IntMap a -> IntMap a
filter a -> Bool
p IntMap a
m
  = (Int -> a -> Bool) -> IntMap a -> IntMap a
forall a. (Int -> a -> Bool) -> IntMap a -> IntMap a
filterWithKey (\Int
_ a
x -> a -> Bool
p a
x) IntMap a
m

-- | \(O(n)\). Filter all keys\/values that satisfy some predicate.
--
-- > filterWithKey (\k _ -> k > 4) (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"

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

-- | \(O(n)\). Partition the map according to some predicate. The first
-- map contains all elements that satisfy the predicate, the second all
-- elements that fail the predicate. See also 'split'.
--
-- > partition (> "a") (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
-- > partition (< "x") (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
-- > partition (> "x") (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])

partition :: (a -> Bool) -> IntMap a -> (IntMap a,IntMap a)
partition :: forall a. (a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
partition a -> Bool
p IntMap a
m
  = (Int -> a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
forall a. (Int -> a -> Bool) -> IntMap a -> (IntMap a, IntMap a)
partitionWithKey (\Int
_ a
x -> a -> Bool
p a
x) IntMap a
m

-- | \(O(n)\). Partition the map according to some predicate. The first
-- map contains all elements that satisfy the predicate, the second all
-- elements that fail the predicate. See also 'split'.
--
-- > partitionWithKey (\ k _ -> k > 3) (fromList [(5,"a"), (3,"b")]) == (singleton 5 "a", singleton 3 "b")
-- > partitionWithKey (\ k _ -> k < 7) (fromList [(5,"a"), (3,"b")]) == (fromList [(3, "b"), (5, "a")], empty)
-- > partitionWithKey (\ k _ -> k > 7) (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3, "b"), (5, "a")])

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

-- | \(O(n)\). Map values and collect the 'Just' results.
--
-- > let f x = if x == "a" then Just "new a" else Nothing
-- > mapMaybe f (fromList [(5,"a"), (3,"b")]) == singleton 5 "new a"

mapMaybe :: (a -> Maybe b) -> IntMap a -> IntMap b
mapMaybe :: forall a b. (a -> Maybe b) -> IntMap a -> IntMap b
mapMaybe a -> Maybe b
f = (Int -> a -> Maybe b) -> IntMap a -> IntMap b
forall a b. (Int -> a -> Maybe b) -> IntMap a -> IntMap b
mapMaybeWithKey (\Int
_ a
x -> a -> Maybe b
f a
x)

-- | \(O(n)\). Map keys\/values and collect the 'Just' results.
--
-- > let f k _ = if k < 5 then Just ("key : " ++ (show k)) else Nothing
-- > mapMaybeWithKey f (fromList [(5,"a"), (3,"b")]) == singleton 3 "key : 3"

mapMaybeWithKey :: (Key -> a -> Maybe b) -> IntMap a -> IntMap b
mapMaybeWithKey :: forall a b. (Int -> a -> Maybe b) -> IntMap a -> IntMap b
mapMaybeWithKey Int -> a -> Maybe b
f (Bin Int
p Int
m IntMap a
l IntMap a
r)
  = Int -> Int -> IntMap b -> IntMap b -> IntMap b
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p Int
m ((Int -> a -> Maybe b) -> IntMap a -> IntMap b
forall a b. (Int -> a -> Maybe b) -> IntMap a -> IntMap b
mapMaybeWithKey Int -> a -> Maybe b
f IntMap a
l) ((Int -> a -> Maybe b) -> IntMap a -> IntMap b
forall a b. (Int -> a -> Maybe b) -> IntMap a -> IntMap b
mapMaybeWithKey Int -> a -> Maybe b
f IntMap a
r)
mapMaybeWithKey Int -> a -> Maybe b
f (Tip Int
k a
x) = case Int -> a -> Maybe b
f Int
k a
x of
  Just b
y  -> Int -> b -> IntMap b
forall a. Int -> a -> IntMap a
Tip Int
k b
y
  Maybe b
Nothing -> IntMap b
forall a. IntMap a
Nil
mapMaybeWithKey Int -> a -> Maybe b
_ IntMap a
Nil = IntMap b
forall a. IntMap a
Nil

-- | \(O(n)\). Map values and separate the 'Left' and 'Right' results.
--
-- > let f a = if a < "c" then Left a else Right a
-- > mapEither f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
-- >     == (fromList [(3,"b"), (5,"a")], fromList [(1,"x"), (7,"z")])
-- >
-- > mapEither (\ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
-- >     == (empty, fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])

mapEither :: (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
mapEither :: forall a b c. (a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
mapEither a -> Either b c
f IntMap a
m
  = (Int -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
forall a b c.
(Int -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
mapEitherWithKey (\Int
_ a
x -> a -> Either b c
f a
x) IntMap a
m

-- | \(O(n)\). Map keys\/values and separate the 'Left' and 'Right' results.
--
-- > let f k a = if k < 5 then Left (k * 2) else Right (a ++ a)
-- > mapEitherWithKey f (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
-- >     == (fromList [(1,2), (3,6)], fromList [(5,"aa"), (7,"zz")])
-- >
-- > mapEitherWithKey (\_ a -> Right a) (fromList [(5,"a"), (3,"b"), (1,"x"), (7,"z")])
-- >     == (empty, fromList [(1,"x"), (3,"b"), (5,"a"), (7,"z")])

mapEitherWithKey :: (Key -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
mapEitherWithKey :: forall a b c.
(Int -> a -> Either b c) -> IntMap a -> (IntMap b, IntMap c)
mapEitherWithKey Int -> a -> Either b c
f0 IntMap a
t0 = StrictPair (IntMap b) (IntMap c) -> (IntMap b, IntMap c)
forall a b. StrictPair a b -> (a, b)
toPair (StrictPair (IntMap b) (IntMap c) -> (IntMap b, IntMap c))
-> StrictPair (IntMap b) (IntMap c) -> (IntMap b, IntMap c)
forall a b. (a -> b) -> a -> b
$ (Int -> a -> Either b c)
-> IntMap a -> StrictPair (IntMap b) (IntMap c)
forall {t} {a} {a}.
(Int -> t -> Either a a)
-> IntMap t -> StrictPair (IntMap a) (IntMap a)
go Int -> a -> Either b c
f0 IntMap a
t0
  where
    go :: (Int -> t -> Either a a)
-> IntMap t -> StrictPair (IntMap a) (IntMap a)
go Int -> t -> Either a a
f (Bin Int
p Int
m IntMap t
l IntMap t
r) =
      Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p Int
m IntMap a
l1 IntMap a
r1 IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: Int -> Int -> IntMap a -> IntMap a -> IntMap a
forall a. Int -> Int -> IntMap a -> IntMap a -> IntMap a
bin Int
p Int
m IntMap a
l2 IntMap a
r2
      where
        (IntMap a
l1 :*: IntMap a
l2) = (Int -> t -> Either a a)
-> IntMap t -> StrictPair (IntMap a) (IntMap a)
go Int -> t -> Either a a
f IntMap t
l
        (IntMap a
r1 :*: IntMap a
r2) = (Int -> t -> Either a a)
-> IntMap t -> StrictPair (IntMap a) (IntMap a)
go Int -> t -> Either a a
f IntMap t
r
    go Int -> t -> Either a a
f (Tip Int
k t
x) = case Int -> t -> Either a a
f Int
k t
x of
      Left a
y  -> (Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
y IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: IntMap a
forall a. IntMap a
Nil)
      Right a
z -> (IntMap a
forall a. IntMap a
Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: Int -> a -> IntMap a
forall a. Int -> a -> IntMap a
Tip Int
k a
z)
    go Int -> t -> Either a a
_ IntMap t
Nil = (IntMap a
forall a. IntMap a
Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: IntMap a
forall a. IntMap a
Nil)

-- | \(O(\min(n,W))\). The expression (@'split' k map@) is a pair @(map1,map2)@
-- where all keys in @map1@ are lower than @k@ and all keys in
-- @map2@ larger than @k@. Any key equal to @k@ is found in neither @map1@ nor @map2@.
--
-- > split 2 (fromList [(5,"a"), (3,"b")]) == (empty, fromList [(3,"b"), (5,"a")])
-- > split 3 (fromList [(5,"a"), (3,"b")]) == (empty, singleton 5 "a")
-- > split 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", singleton 5 "a")
-- > split 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", empty)
-- > split 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], empty)

split :: Key -> IntMap a -> (IntMap a, IntMap a)
split :: forall a. Int -> IntMap a -> (IntMap a, IntMap a)
split Int
k IntMap a
t =
  case IntMap a
t of
    Bin Int
_ Int
m IntMap a
l IntMap a
r
      | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 ->
        if Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
0 -- handle negative numbers.
        then
          case Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall {a}. Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
go Int
k IntMap a
l of
            (IntMap a
lt :*: IntMap a
gt) ->
              let !lt' :: IntMap a
lt' = IntMap a -> IntMap a -> IntMap a
forall a. IntMap a -> IntMap a -> IntMap a
union IntMap a
r IntMap a
lt
              in (IntMap a
lt', IntMap a
gt)
        else
          case Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall {a}. Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
go Int
k IntMap a
r of
            (IntMap a
lt :*: IntMap a
gt) ->
              let !gt' :: IntMap a
gt' = IntMap a -> IntMap a -> IntMap a
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 Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall {a}. Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
go Int
k IntMap a
t of
          (IntMap a
lt :*: IntMap a
gt) -> (IntMap a
lt, IntMap a
gt)
  where
    go :: Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
go Int
k' t' :: IntMap a
t'@(Bin Int
p Int
m IntMap a
l IntMap a
r)
      | Int -> Int -> Int -> Bool
nomatch Int
k' Int
p Int
m = if Int
k' Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
p then IntMap a
t' IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: IntMap a
forall a. IntMap a
Nil else IntMap a
forall a. IntMap a
Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: IntMap a
t'
      | Int -> Int -> Bool
zero Int
k' Int
m = case Int -> IntMap a -> StrictPair (IntMap a) (IntMap a)
go Int
k' IntMap a
l of (IntMap a
lt :*: IntMap a
gt) -> IntMap a
lt IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: IntMap a -> IntMap a -> IntMap a
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) -> IntMap a -> IntMap a -> IntMap a
forall a. IntMap a -> IntMap a -> IntMap a
union IntMap a
l IntMap a
lt IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: IntMap a
gt
    go Int
k' t' :: IntMap a
t'@(Tip Int
ky a
_)
      | Int
k' Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
ky   = (IntMap a
t' IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: IntMap a
forall a. IntMap a
Nil)
      | Int
k' Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
ky   = (IntMap a
forall a. IntMap a
Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: IntMap a
t')
      | Bool
otherwise = (IntMap a
forall a. IntMap a
Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: IntMap a
forall a. IntMap a
Nil)
    go Int
_ IntMap a
Nil = (IntMap a
forall a. IntMap a
Nil IntMap a -> IntMap a -> StrictPair (IntMap a) (IntMap a)
forall a b. a -> b -> StrictPair a b
:*: IntMap a
forall a. IntMap a
Nil)


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

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

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

-- | \(O(\min(n,W))\). Performs a 'split' but also returns whether the pivot
-- key was found in the original map.
--
-- > splitLookup 2 (fromList [(5,"a"), (3,"b")]) == (empty, Nothing, fromList [(3,"b"), (5,"a")])
-- > splitLookup 3 (fromList [(5,"a"), (3,"b")]) == (empty, Just "b", singleton 5 "a")
-- > splitLookup 4 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Nothing, singleton 5 "a")
-- > splitLookup 5 (fromList [(5,"a"), (3,"b")]) == (singleton 3 "b", Just "a", empty)
-- > splitLookup 6 (fromList [(5,"a"), (3,"b")]) == (fromList [(3,"b"), (5,"a")], Nothing, empty)

splitLookup :: Key -> IntMap a -> (IntMap a, Maybe a, IntMap a)
splitLookup :: forall a. Int -> IntMap a -> (IntMap a, Maybe a, IntMap a)
splitLookup Int
k IntMap a
t =
  case
    case IntMap a
t of
      Bin Int
_ Int
m IntMap a
l IntMap a
r
        | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 ->
          if Int
k Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
>= Int
0 -- handle negative numbers.
          then (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
mapLT (IntMap a -> IntMap a -> IntMap a
forall a. IntMap a -> IntMap a -> IntMap a
union IntMap a
r) (Int -> IntMap a -> SplitLookup a
forall {a}. Int -> IntMap a -> SplitLookup a
go Int
k IntMap a
l)
          else (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
mapGT (IntMap a -> IntMap a -> IntMap a
forall a. IntMap a -> IntMap a -> IntMap a
`union` IntMap a
l) (Int -> IntMap a -> SplitLookup a
forall {a}. Int -> IntMap a -> SplitLookup a
go Int
k IntMap a
r)
      IntMap a
_ -> Int -> IntMap a -> SplitLookup a
forall {a}. Int -> IntMap a -> SplitLookup a
go Int
k IntMap a
t
  of SplitLookup IntMap a
lt Maybe a
fnd IntMap a
gt -> (IntMap a
lt, Maybe a
fnd, IntMap a
gt)
  where
    go :: Int -> IntMap a -> SplitLookup a
go Int
k' t' :: IntMap a
t'@(Bin Int
p Int
m IntMap a
l IntMap a
r)
      | Int -> Int -> Int -> Bool
nomatch Int
k' Int
p Int
m =
          if Int
k' Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
p
          then IntMap a -> Maybe a -> IntMap a -> SplitLookup a
forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup IntMap a
t' Maybe a
forall a. Maybe a
Nothing IntMap a
forall a. IntMap a
Nil
          else IntMap a -> Maybe a -> IntMap a -> SplitLookup a
forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup IntMap a
forall a. IntMap a
Nil Maybe a
forall a. Maybe a
Nothing IntMap a
t'
      | Int -> Int -> Bool
zero Int
k' Int
m = (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
mapGT (IntMap a -> IntMap a -> IntMap a
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 = (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
forall a. (IntMap a -> IntMap a) -> SplitLookup a -> SplitLookup a
mapLT (IntMap a -> IntMap a -> IntMap a
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' Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
ky   = IntMap a -> Maybe a -> IntMap a -> SplitLookup a
forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup IntMap a
t'  Maybe a
forall a. Maybe a
Nothing  IntMap a
forall a. IntMap a
Nil
      | Int
k' Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
ky   = IntMap a -> Maybe a -> IntMap a -> SplitLookup a
forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup IntMap a
forall a. IntMap a
Nil Maybe a
forall a. Maybe a
Nothing  IntMap a
t'
      | Bool
otherwise = IntMap a -> Maybe a -> IntMap a -> SplitLookup a
forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup IntMap a
forall a. IntMap a
Nil (a -> Maybe a
forall a. a -> Maybe a
Just a
y) IntMap a
forall a. IntMap a
Nil
    go Int
_ IntMap a
Nil      = IntMap a -> Maybe a -> IntMap a -> SplitLookup a
forall a. IntMap a -> Maybe a -> IntMap a -> SplitLookup a
SplitLookup IntMap a
forall a. IntMap a
Nil Maybe a
forall a. Maybe a
Nothing  IntMap a
forall a. IntMap a
Nil

{--------------------------------------------------------------------
  Fold
--------------------------------------------------------------------}
-- | \(O(n)\). Fold the values in the map using the given right-associative
-- binary operator, such that @'foldr' f z == 'Prelude.foldr' f z . 'elems'@.
--
-- For example,
--
-- > elems map = foldr (:) [] map
--
-- > let f a len = len + (length a)
-- > foldr f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
foldr :: (a -> b -> b) -> b -> IntMap a -> b
foldr :: forall a b. (a -> b -> b) -> b -> IntMap a -> b
foldr a -> b -> b
f b
z = \IntMap a
t ->      -- Use lambda t to be inlinable with two arguments only.
  case IntMap a
t of
    Bin Int
_ Int
m IntMap a
l IntMap a
r
      | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z IntMap a
l) IntMap a
r -- put negative numbers before
      | Bool
otherwise -> b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z IntMap a
r) IntMap a
l
    IntMap a
_ -> b -> IntMap a -> b
go b
z IntMap a
t
  where
    go :: b -> IntMap a -> b
go b
z' IntMap a
Nil           = b
z'
    go b
z' (Tip Int
_ a
x)     = a -> b -> b
f a
x b
z'
    go b
z' (Bin Int
_ Int
_ IntMap a
l IntMap a
r) = b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z' IntMap a
r) IntMap a
l
{-# INLINE foldr #-}

-- | \(O(n)\). A strict version of 'foldr'. Each application of the operator is
-- evaluated before using the result in the next application. This
-- function is strict in the starting value.
foldr' :: (a -> b -> b) -> b -> IntMap a -> b
foldr' :: forall a b. (a -> b -> b) -> b -> IntMap a -> b
foldr' a -> b -> b
f b
z = \IntMap a
t ->      -- Use lambda t to be inlinable with two arguments only.
  case IntMap a
t of
    Bin Int
_ Int
m IntMap a
l IntMap a
r
      | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z IntMap a
l) IntMap a
r -- put negative numbers before
      | Bool
otherwise -> b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z IntMap a
r) IntMap a
l
    IntMap a
_ -> b -> IntMap a -> b
go b
z IntMap a
t
  where
    go :: b -> IntMap a -> b
go !b
z' IntMap a
Nil          = b
z'
    go b
z' (Tip Int
_ a
x)     = a -> b -> b
f a
x b
z'
    go b
z' (Bin Int
_ Int
_ IntMap a
l IntMap a
r) = b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z' IntMap a
r) IntMap a
l
{-# INLINE foldr' #-}

-- | \(O(n)\). Fold the values in the map using the given left-associative
-- binary operator, such that @'foldl' f z == 'Prelude.foldl' f z . 'elems'@.
--
-- For example,
--
-- > elems = reverse . foldl (flip (:)) []
--
-- > let f len a = len + (length a)
-- > foldl f 0 (fromList [(5,"a"), (3,"bbb")]) == 4
foldl :: (a -> b -> a) -> a -> IntMap b -> a
foldl :: forall b a. (b -> a -> b) -> b -> IntMap a -> b
foldl a -> b -> a
f a
z = \IntMap b
t ->      -- Use lambda t to be inlinable with two arguments only.
  case IntMap b
t of
    Bin Int
_ Int
m IntMap b
l IntMap b
r
      | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z IntMap b
r) IntMap b
l -- put negative numbers before
      | Bool
otherwise -> a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z IntMap b
l) IntMap b
r
    IntMap b
_ -> a -> IntMap b -> a
go a
z IntMap b
t
  where
    go :: a -> IntMap b -> a
go a
z' IntMap b
Nil           = a
z'
    go a
z' (Tip Int
_ b
x)     = a -> b -> a
f a
z' b
x
    go a
z' (Bin Int
_ Int
_ IntMap b
l IntMap b
r) = a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z' IntMap b
l) IntMap b
r
{-# INLINE foldl #-}

-- | \(O(n)\). A strict version of 'foldl'. Each application of the operator is
-- evaluated before using the result in the next application. This
-- function is strict in the starting value.
foldl' :: (a -> b -> a) -> a -> IntMap b -> a
foldl' :: forall b a. (b -> a -> b) -> b -> IntMap a -> b
foldl' a -> b -> a
f a
z = \IntMap b
t ->      -- Use lambda t to be inlinable with two arguments only.
  case IntMap b
t of
    Bin Int
_ Int
m IntMap b
l IntMap b
r
      | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z IntMap b
r) IntMap b
l -- put negative numbers before
      | Bool
otherwise -> a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z IntMap b
l) IntMap b
r
    IntMap b
_ -> a -> IntMap b -> a
go a
z IntMap b
t
  where
    go :: a -> IntMap b -> a
go !a
z' IntMap b
Nil          = a
z'
    go a
z' (Tip Int
_ b
x)     = a -> b -> a
f a
z' b
x
    go a
z' (Bin Int
_ Int
_ IntMap b
l IntMap b
r) = a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z' IntMap b
l) IntMap b
r
{-# INLINE foldl' #-}

-- | \(O(n)\). Fold the keys and values in the map using the given right-associative
-- binary operator, such that
-- @'foldrWithKey' f z == 'Prelude.foldr' ('uncurry' f) z . 'toAscList'@.
--
-- For example,
--
-- > keys map = foldrWithKey (\k x ks -> k:ks) [] map
--
-- > let f k a result = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
-- > foldrWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (5:a)(3:b)"
foldrWithKey :: (Key -> a -> b -> b) -> b -> IntMap a -> b
foldrWithKey :: forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
foldrWithKey Int -> a -> b -> b
f b
z = \IntMap a
t ->      -- Use lambda t to be inlinable with two arguments only.
  case IntMap a
t of
    Bin Int
_ Int
m IntMap a
l IntMap a
r
      | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z IntMap a
l) IntMap a
r -- put negative numbers before
      | Bool
otherwise -> b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z IntMap a
r) IntMap a
l
    IntMap a
_ -> b -> IntMap a -> b
go b
z IntMap a
t
  where
    go :: b -> IntMap a -> b
go b
z' IntMap a
Nil           = b
z'
    go b
z' (Tip Int
kx a
x)    = Int -> a -> b -> b
f Int
kx a
x b
z'
    go b
z' (Bin Int
_ Int
_ IntMap a
l IntMap a
r) = b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z' IntMap a
r) IntMap a
l
{-# INLINE foldrWithKey #-}

-- | \(O(n)\). A strict version of 'foldrWithKey'. Each application of the operator is
-- evaluated before using the result in the next application. This
-- function is strict in the starting value.
foldrWithKey' :: (Key -> a -> b -> b) -> b -> IntMap a -> b
foldrWithKey' :: forall a b. (Int -> a -> b -> b) -> b -> IntMap a -> b
foldrWithKey' Int -> a -> b -> b
f b
z = \IntMap a
t ->      -- Use lambda t to be inlinable with two arguments only.
  case IntMap a
t of
    Bin Int
_ Int
m IntMap a
l IntMap a
r
      | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z IntMap a
l) IntMap a
r -- put negative numbers before
      | Bool
otherwise -> b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z IntMap a
r) IntMap a
l
    IntMap a
_ -> b -> IntMap a -> b
go b
z IntMap a
t
  where
    go :: b -> IntMap a -> b
go !b
z' IntMap a
Nil          = b
z'
    go b
z' (Tip Int
kx a
x)    = Int -> a -> b -> b
f Int
kx a
x b
z'
    go b
z' (Bin Int
_ Int
_ IntMap a
l IntMap a
r) = b -> IntMap a -> b
go (b -> IntMap a -> b
go b
z' IntMap a
r) IntMap a
l
{-# INLINE foldrWithKey' #-}

-- | \(O(n)\). Fold the keys and values in the map using the given left-associative
-- binary operator, such that
-- @'foldlWithKey' f z == 'Prelude.foldl' (\\z' (kx, x) -> f z' kx x) z . 'toAscList'@.
--
-- For example,
--
-- > keys = reverse . foldlWithKey (\ks k x -> k:ks) []
--
-- > let f result k a = result ++ "(" ++ (show k) ++ ":" ++ a ++ ")"
-- > foldlWithKey f "Map: " (fromList [(5,"a"), (3,"b")]) == "Map: (3:b)(5:a)"
foldlWithKey :: (a -> Key -> b -> a) -> a -> IntMap b -> a
foldlWithKey :: forall a b. (a -> Int -> b -> a) -> a -> IntMap b -> a
foldlWithKey a -> Int -> b -> a
f a
z = \IntMap b
t ->      -- Use lambda t to be inlinable with two arguments only.
  case IntMap b
t of
    Bin Int
_ Int
m IntMap b
l IntMap b
r
      | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z IntMap b
r) IntMap b
l -- put negative numbers before
      | Bool
otherwise -> a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z IntMap b
l) IntMap b
r
    IntMap b
_ -> a -> IntMap b -> a
go a
z IntMap b
t
  where
    go :: a -> IntMap b -> a
go a
z' IntMap b
Nil           = a
z'
    go a
z' (Tip Int
kx b
x)    = a -> Int -> b -> a
f a
z' Int
kx b
x
    go a
z' (Bin Int
_ Int
_ IntMap b
l IntMap b
r) = a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z' IntMap b
l) IntMap b
r
{-# INLINE foldlWithKey #-}

-- | \(O(n)\). A strict version of 'foldlWithKey'. Each application of the operator is
-- evaluated before using the result in the next application. This
-- function is strict in the starting value.
foldlWithKey' :: (a -> Key -> b -> a) -> a -> IntMap b -> a
foldlWithKey' :: forall a b. (a -> Int -> b -> a) -> a -> IntMap b -> a
foldlWithKey' a -> Int -> b -> a
f a
z = \IntMap b
t ->      -- Use lambda t to be inlinable with two arguments only.
  case IntMap b
t of
    Bin Int
_ Int
m IntMap b
l IntMap b
r
      | Int
m Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
0 -> a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z IntMap b
r) IntMap b
l -- put negative numbers before
      | Bool
otherwise -> a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z IntMap b
l) IntMap b
r
    IntMap b
_ -> a -> IntMap b -> a
go a
z IntMap b
t
  where
    go :: a -> IntMap b -> a
go !a
z' IntMap b
Nil          = a
z'
    go a
z' (Tip Int
kx b
x)    = a -> Int -> b -> a
f a
z' Int
kx b
x
    go a
z' (Bin Int
_ Int
_ IntMap b
l IntMap b
r) = a -> IntMap b -> a
go (a -> IntMap b -> a
go a
z' IntMap b
l) IntMap b
r
{-# INLINE foldlWithKey' #-}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


-- | \(O(n \min(n,W))\). Create a map from a list of key\/value pairs.
--
-- > fromList [] == empty
-- > fromList [(5,"a"), (3,"b"), (5, "c")] == fromList [(5,"c"), (3,"b")]
-- > fromList [(5,"c"), (3,"b"), (5, "a")] == fromList [(5,"a"), (3,"b")]

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

-- | \(O(n \min(n,W))\). 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
  = (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
forall a. (Int -> a -> a -> a) -> [(Int, a)] -> IntMap a
fromListWithKey (\Int
_ a
x a
y -> a -> a -> a
f a
x a
y) [(Int, a)]
xs

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

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

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

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

-- | \(O(n)\). Build a map from a list of key\/value pairs where
-- the keys are in ascending order, with a combining function on equal keys.
-- /The precondition (input list is ascending) is not checked./
--
-- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]

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

-- | \(O(n)\). Build a map from a list of key\/value pairs where
-- the keys are in ascending order, with a combining function on equal keys.
-- /The precondition (input list is ascending) is not checked./
--
-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
-- > fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "5:b|a")]

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

-- | \(O(n)\). Build a map from a list of key\/value pairs where
-- the keys are in ascending order and all distinct.
-- /The precondition (input list is strictly ascending) is not checked./
--
-- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]

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

-- | \(O(n)\). Build a map from a list of key\/value pairs with monotonic keys
-- and a combining function.
--
-- The precise conditions under which this function works are subtle:
-- For any branch mask, keys with the same prefix w.r.t. the branch
-- mask must occur consecutively in the list.

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

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

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

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

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

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

data Distinct = Distinct | Nondistinct

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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


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

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

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

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

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

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


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

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


{- | \(O(n)\). The expression (@'showTreeWith' hang wide map@) shows
 the tree that implements the map. If @hang@ is
 'True', a /hanging/ tree is shown otherwise a rotated tree is shown. If
 @wide@ is 'True', an extra wide version is shown.
-}
showTreeWith :: Show a => Bool -> Bool -> IntMap a -> String
showTreeWith :: forall a. Show a => Bool -> Bool -> IntMap a -> [Char]
showTreeWith Bool
hang Bool
wide IntMap a
t
  | Bool
hang      = (Bool -> [[Char]] -> IntMap a -> [Char] -> [Char]
forall a.
Show a =>
Bool -> [[Char]] -> IntMap a -> [Char] -> [Char]
showsTreeHang Bool
wide [] IntMap a
t) [Char]
""
  | Bool
otherwise = (Bool -> [[Char]] -> [[Char]] -> IntMap a -> [Char] -> [Char]
forall a.
Show a =>
Bool -> [[Char]] -> [[Char]] -> IntMap a -> [Char] -> [Char]
showsTree Bool
wide [] [] IntMap a
t) [Char]
""

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

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

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

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

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

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

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