{-# LANGUAGE CPP #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE PatternGuards #-}
#if defined(__GLASGOW_HASKELL__)
{-# LANGUAGE DeriveLift #-}
{-# LANGUAGE RoleAnnotations #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE TypeFamilies #-}
#endif
#define USE_MAGIC_PROXY 1

#ifdef USE_MAGIC_PROXY
{-# LANGUAGE MagicHash #-}
#endif

{-# OPTIONS_HADDOCK not-home #-}

#include "containers.h"

#if !(WORD_SIZE_IN_BITS >= 61)
#define DEFINE_ALTERF_FALLBACK 1
#endif

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Map.Internal
-- Copyright   :  (c) Daan Leijen 2002
--                (c) Andriy Palamarchuk 2008
-- 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
--
-- An efficient implementation of maps from keys to values (dictionaries).
--
-- Since many function names (but not the type name) clash with
-- "Prelude" names, this module is usually imported @qualified@, e.g.
--
-- >  import Data.Map (Map)
-- >  import qualified Data.Map as Map
--
-- The implementation of 'Map' is based on /size balanced/ binary trees (or
-- trees of /bounded balance/) as described by:
--
--    * Stephen Adams, \"/Efficient sets: a balancing act/\",
--     Journal of Functional Programming 3(4):553-562, October 1993,
--     <http://www.swiss.ai.mit.edu/~adams/BB/>.
--    * J. Nievergelt and E.M. Reingold,
--      \"/Binary search trees of bounded balance/\",
--      SIAM journal of computing 2(1), March 1973.
--
--  Bounds for 'union', 'intersection', and 'difference' are as given
--  by
--
--    * Guy Blelloch, Daniel Ferizovic, and Yihan Sun,
--      \"/Just Join for Parallel Ordered Sets/\",
--      <https://arxiv.org/abs/1602.02120v3>.
--
-- Note that the implementation is /left-biased/ -- the elements of a
-- first argument are always preferred to the second, for example in
-- 'union' or 'insert'.
--
-- Operation comments contain the operation time complexity in
-- the Big-O notation <http://en.wikipedia.org/wiki/Big_O_notation>.
--
-- @since 0.5.9
-----------------------------------------------------------------------------

-- [Note: Using INLINABLE]
-- ~~~~~~~~~~~~~~~~~~~~~~~
-- It is crucial to the performance that the functions specialize on the Ord
-- type when possible. GHC 7.0 and higher does this by itself when it sees th
-- unfolding of a function -- that is why all public functions are marked
-- INLINABLE (that exposes the unfolding).


-- [Note: Using INLINE]
-- ~~~~~~~~~~~~~~~~~~~~
-- For other compilers and GHC pre 7.0, we mark some of the functions INLINE.
-- We mark the functions that just navigate down the tree (lookup, insert,
-- delete and similar). That navigation code gets inlined and thus specialized
-- when possible. There is a price to pay -- code growth. The code INLINED is
-- therefore only the tree navigation, all the real work (rebalancing) is not
-- INLINED by using a NOINLINE.
--
-- All methods marked INLINE have to be nonrecursive -- a 'go' function doing
-- the real work is provided.


-- [Note: Type of local 'go' function]
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- If the local 'go' function uses an Ord class, it sometimes heap-allocates
-- the Ord dictionary when the 'go' function does not have explicit type.
-- In that case we give 'go' explicit type. But this slightly decrease
-- performance, as the resulting 'go' function can float out to top level.


-- [Note: Local 'go' functions and capturing]
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- As opposed to Map, when 'go' function captures an argument, increased
-- heap-allocation can occur: sometimes in a polymorphic function, the 'go'
-- floats out of its enclosing function and then it heap-allocates the
-- dictionary and the argument. Maybe it floats out too late and strictness
-- analyzer cannot see that these could be passed on stack.
--

-- [Note: Order of constructors]
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- The order of constructors of Map matters when considering performance.
-- Currently in GHC 7.0, when type has 2 constructors, a forward conditional
-- jump is made when successfully matching second constructor. Successful match
-- of first constructor results in the forward jump not taken.
-- On GHC 7.0, reordering constructors from Tip | Bin to Bin | Tip
-- improves the benchmark by up to 10% on x86.

module Data.Map.Internal (
    -- * Map type
      Map(..)          -- instance Eq,Show,Read
    , Size

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

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

    -- * 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

    -- ** Disjoint
    , disjoint

    -- ** Compose
    , compose

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

    -- * 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
    , argSet
    , fromSet
    , fromArgSet

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

    -- ** Ordered lists
    , toAscList
    , toDescList
    , fromAscList
    , fromAscListWith
    , fromAscListWithKey
    , fromDistinctAscList
    , fromDescList
    , fromDescListWith
    , fromDescListWithKey
    , fromDistinctDescList

    -- * Filter
    , filter
    , filterWithKey

    , takeWhileAntitone
    , dropWhileAntitone
    , spanAntitone

    , restrictKeys
    , withoutKeys
    , partition
    , partitionWithKey

    , mapMaybe
    , mapMaybeWithKey
    , mapEither
    , mapEitherWithKey

    , split
    , splitLookup
    , splitRoot

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

    -- * Indexed
    , lookupIndex
    , findIndex
    , elemAt
    , updateAt
    , deleteAt
    , take
    , drop
    , splitAt

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

    -- Used by the strict version
    , AreWeStrict (..)
    , atKeyImpl
#ifdef __GLASGOW_HASKELL__
    , atKeyPlain
#endif
    , bin
    , balance
    , balanceL
    , balanceR
    , delta
    , insertMax
    , link
    , link2
    , glue
    , fromDistinctAscList_linkTop
    , fromDistinctAscList_linkAll
    , fromDistinctDescList_linkTop
    , fromDistinctDescList_linkAll
    , MaybeS(..)
    , Identity(..)
    , FromDistinctMonoState(..)
    , Stack(..)
    , foldl'Stack

    -- Used by Map.Merge.Lazy
    , mapWhenMissing
    , mapWhenMatched
    , lmapWhenMissing
    , contramapFirstWhenMatched
    , contramapSecondWhenMatched
    , mapGentlyWhenMissing
    , mapGentlyWhenMatched
    ) where

import Data.Functor.Identity (Identity (..))
import Control.Applicative (liftA3)
import Data.Functor.Classes
import Data.Semigroup (stimesIdempotentMonoid)
import Data.Semigroup (Arg(..), Semigroup(stimes))
#if !(MIN_VERSION_base(4,11,0))
import Data.Semigroup (Semigroup((<>)))
#endif
import Control.Applicative (Const (..))
import Control.DeepSeq (NFData(rnf))
import Data.Bits (shiftL, shiftR)
import qualified Data.Foldable as Foldable
import Data.Bifoldable
import Utils.Containers.Internal.Prelude hiding
  (lookup, map, filter, foldr, foldl, foldl', null, splitAt, take, drop)
import Prelude ()

import qualified Data.Set.Internal as Set
import Data.Set.Internal (Set)
import Utils.Containers.Internal.PtrEquality (ptrEq)
import Utils.Containers.Internal.StrictPair
import Utils.Containers.Internal.StrictMaybe
import Utils.Containers.Internal.BitQueue
#ifdef DEFINE_ALTERF_FALLBACK
import Utils.Containers.Internal.BitUtil (wordSize)
#endif

#if __GLASGOW_HASKELL__
import GHC.Exts (build, lazy)
import Language.Haskell.TH.Syntax (Lift)
-- See Note [ Template Haskell Dependencies ]
import Language.Haskell.TH ()
#  ifdef USE_MAGIC_PROXY
import GHC.Exts (Proxy#, proxy# )
#  endif
import qualified GHC.Exts as GHCExts
import Text.Read hiding (lift)
import Data.Data
import qualified Control.Category as Category
import Data.Coerce
#endif


{--------------------------------------------------------------------
  Operators
--------------------------------------------------------------------}
infixl 9 !,!?,\\ --

-- | \(O(\log n)\). 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'

(!) :: Ord k => Map k a -> k -> a
! :: forall k a. Ord k => Map k a -> k -> a
(!) Map k a
m k
k = forall k a. Ord k => k -> Map k a -> a
find k
k Map k a
m
#if __GLASGOW_HASKELL__
{-# INLINE (!) #-}
#endif

-- | \(O(\log n)\). Find the value at a key.
-- Returns 'Nothing' when the element can not be found.
--
-- prop> fromList [(5, 'a'), (3, 'b')] !? 1 == Nothing
-- prop> fromList [(5, 'a'), (3, 'b')] !? 5 == Just 'a'
--
-- @since 0.5.9

(!?) :: Ord k => Map k a -> k -> Maybe a
!? :: forall k a. Ord k => Map k a -> k -> Maybe a
(!?) Map k a
m k
k = forall k a. Ord k => k -> Map k a -> Maybe a
lookup k
k Map k a
m
#if __GLASGOW_HASKELL__
{-# INLINE (!?) #-}
#endif

-- | Same as 'difference'.
(\\) :: Ord k => Map k a -> Map k b -> Map k a
Map k a
m1 \\ :: forall k a b. Ord k => Map k a -> Map k b -> Map k a
\\ Map k b
m2 = forall k a b. Ord k => Map k a -> Map k b -> Map k a
difference Map k a
m1 Map k b
m2
#if __GLASGOW_HASKELL__
{-# INLINE (\\) #-}
#endif

{--------------------------------------------------------------------
  Size balanced trees.
--------------------------------------------------------------------}
-- | A Map from keys @k@ to values @a@.
--
-- The 'Semigroup' operation for 'Map' is 'union', which prefers
-- values from the left operand. If @m1@ maps a key @k@ to a value
-- @a1@, and @m2@ maps the same key to a different value @a2@, then
-- their union @m1 <> m2@ maps @k@ to @a1@.

-- See Note: Order of constructors
data Map k a  = Bin {-# UNPACK #-} !Size !k a !(Map k a) !(Map k a)
              | Tip

type Size     = Int

#ifdef __GLASGOW_HASKELL__
type role Map nominal representational
#endif

#ifdef __GLASGOW_HASKELL__
-- | @since 0.6.6
deriving instance (Lift k, Lift a) => Lift (Map k a)
#endif

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

instance (Ord k) => Semigroup (Map k v) where
    <> :: Map k v -> Map k v -> Map k v
(<>)    = forall k v. Ord k => Map k v -> Map k v -> Map k v
union
    stimes :: forall b. Integral b => b -> Map k v -> Map k v
stimes  = forall b a. (Integral b, Monoid a) => b -> a -> a
stimesIdempotentMonoid

#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 k, Data a, Ord k) => Data (Map k a) where
  gfoldl :: forall (c :: * -> *).
(forall d b. Data d => c (d -> b) -> d -> c b)
-> (forall g. g -> c g) -> Map k a -> c (Map k a)
gfoldl forall d b. Data d => c (d -> b) -> d -> c b
f forall g. g -> c g
z Map k a
m   = forall g. g -> c g
z forall k a. Ord k => [(k, a)] -> Map k a
fromList forall d b. Data d => c (d -> b) -> d -> c b
`f` forall k a. Map k a -> [(k, a)]
toList Map k a
m
  toConstr :: Map k a -> Constr
toConstr Map k a
_     = Constr
fromListConstr
  gunfold :: forall (c :: * -> *).
(forall b r. Data b => c (b -> r) -> c r)
-> (forall r. r -> c r) -> Constr -> c (Map k a)
gunfold forall b r. Data b => c (b -> r) -> c r
k forall r. r -> c r
z Constr
c  = case Constr -> Size
constrIndex Constr
c of
    Size
1 -> forall b r. Data b => c (b -> r) -> c r
k (forall r. r -> c r
z forall k a. Ord k => [(k, a)] -> Map k a
fromList)
    Size
_ -> forall a. HasCallStack => [Char] -> a
error [Char]
"gunfold"
  dataTypeOf :: Map k a -> DataType
dataTypeOf Map k a
_   = DataType
mapDataType
  dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *).
Typeable t =>
(forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Map k a))
dataCast2 forall d e. (Data d, Data e) => c (t d e)
f    = forall {k1} {k2} {k3} (c :: k1 -> *) (t :: k2 -> k3 -> k1)
       (t' :: k2 -> k3 -> k1) (a :: k2) (b :: k3).
(Typeable t, Typeable t') =>
c (t a b) -> Maybe (c (t' a b))
gcast2 forall d e. (Data d, Data e) => c (t d e)
f

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

mapDataType :: DataType
mapDataType :: DataType
mapDataType = [Char] -> [Constr] -> DataType
mkDataType [Char]
"Data.Map.Internal.Map" [Constr
fromListConstr]

#endif

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

null :: Map k a -> Bool
null :: forall k a. Map k a -> Bool
null Map k a
Tip      = Bool
True
null (Bin {}) = Bool
False
{-# INLINE null #-}

-- | \(O(1)\). The number of elements in the map.
--
-- > size empty                                   == 0
-- > size (singleton 1 'a')                       == 1
-- > size (fromList([(1,'a'), (2,'c'), (3,'b')])) == 3

size :: Map k a -> Int
size :: forall k a. Map k a -> Size
size Map k a
Tip              = Size
0
size (Bin Size
sz k
_ a
_ Map k a
_ Map k a
_) = Size
sz
{-# INLINE size #-}


-- | \(O(\log n)\). Lookup the value at a key in the map.
--
-- The function will return the corresponding value as @('Just' value)@,
-- or 'Nothing' if the key isn't in the map.
--
-- An example of using @lookup@:
--
-- > import Prelude hiding (lookup)
-- > import Data.Map
-- >
-- > employeeDept = fromList([("John","Sales"), ("Bob","IT")])
-- > deptCountry = fromList([("IT","USA"), ("Sales","France")])
-- > countryCurrency = fromList([("USA", "Dollar"), ("France", "Euro")])
-- >
-- > employeeCurrency :: String -> Maybe String
-- > employeeCurrency name = do
-- >     dept <- lookup name employeeDept
-- >     country <- lookup dept deptCountry
-- >     lookup country countryCurrency
-- >
-- > main = do
-- >     putStrLn $ "John's currency: " ++ (show (employeeCurrency "John"))
-- >     putStrLn $ "Pete's currency: " ++ (show (employeeCurrency "Pete"))
--
-- The output of this program:
--
-- >   John's currency: Just "Euro"
-- >   Pete's currency: Nothing
lookup :: Ord k => k -> Map k a -> Maybe a
lookup :: forall k a. Ord k => k -> Map k a -> Maybe a
lookup = forall k a. Ord k => k -> Map k a -> Maybe a
go
  where
    go :: t -> Map t a -> Maybe a
go !t
_ Map t a
Tip = forall a. Maybe a
Nothing
    go t
k (Bin Size
_ t
kx a
x Map t a
l Map t a
r) = case forall a. Ord a => a -> a -> Ordering
compare t
k t
kx of
      Ordering
LT -> t -> Map t a -> Maybe a
go t
k Map t a
l
      Ordering
GT -> t -> Map t a -> Maybe a
go t
k Map t a
r
      Ordering
EQ -> forall a. a -> Maybe a
Just a
x
#if __GLASGOW_HASKELL__
{-# INLINABLE lookup #-}
#else
{-# INLINE lookup #-}
#endif

-- | \(O(\log n)\). Is the key a member of the map? See also 'notMember'.
--
-- > member 5 (fromList [(5,'a'), (3,'b')]) == True
-- > member 1 (fromList [(5,'a'), (3,'b')]) == False
member :: Ord k => k -> Map k a -> Bool
member :: forall k a. Ord k => k -> Map k a -> Bool
member = forall k a. Ord k => k -> Map k a -> Bool
go
  where
    go :: t -> Map t a -> Bool
go !t
_ Map t a
Tip = Bool
False
    go t
k (Bin Size
_ t
kx a
_ Map t a
l Map t a
r) = case forall a. Ord a => a -> a -> Ordering
compare t
k t
kx of
      Ordering
LT -> t -> Map t a -> Bool
go t
k Map t a
l
      Ordering
GT -> t -> Map t a -> Bool
go t
k Map t a
r
      Ordering
EQ -> Bool
True
#if __GLASGOW_HASKELL__
{-# INLINABLE member #-}
#else
{-# INLINE member #-}
#endif

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

notMember :: Ord k => k -> Map k a -> Bool
notMember :: forall k a. Ord k => k -> Map k a -> Bool
notMember k
k Map k a
m = Bool -> Bool
not forall a b. (a -> b) -> a -> b
$ forall k a. Ord k => k -> Map k a -> Bool
member k
k Map k a
m
#if __GLASGOW_HASKELL__
{-# INLINABLE notMember #-}
#else
{-# INLINE notMember #-}
#endif

-- | \(O(\log n)\). Find the value at a key.
-- Calls 'error' when the element can not be found.
find :: Ord k => k -> Map k a -> a
find :: forall k a. Ord k => k -> Map k a -> a
find = forall k a. Ord k => k -> Map k a -> a
go
  where
    go :: t -> Map t a -> a
go !t
_ Map t a
Tip = forall a. HasCallStack => [Char] -> a
error [Char]
"Map.!: given key is not an element in the map"
    go t
k (Bin Size
_ t
kx a
x Map t a
l Map t a
r) = case forall a. Ord a => a -> a -> Ordering
compare t
k t
kx of
      Ordering
LT -> t -> Map t a -> a
go t
k Map t a
l
      Ordering
GT -> t -> Map t a -> a
go t
k Map t a
r
      Ordering
EQ -> a
x
#if __GLASGOW_HASKELL__
{-# INLINABLE find #-}
#else
{-# INLINE find #-}
#endif

-- | \(O(\log n)\). The expression @('findWithDefault' def k map)@ returns
-- the value at key @k@ or returns default value @def@
-- when the key is not in the map.
--
-- > findWithDefault 'x' 1 (fromList [(5,'a'), (3,'b')]) == 'x'
-- > findWithDefault 'x' 5 (fromList [(5,'a'), (3,'b')]) == 'a'
findWithDefault :: Ord k => a -> k -> Map k a -> a
findWithDefault :: forall k a. Ord k => a -> k -> Map k a -> a
findWithDefault = forall k a. Ord k => a -> k -> Map k a -> a
go
  where
    go :: t -> t -> Map t t -> t
go t
def !t
_ Map t t
Tip = t
def
    go t
def t
k (Bin Size
_ t
kx t
x Map t t
l Map t t
r) = case forall a. Ord a => a -> a -> Ordering
compare t
k t
kx of
      Ordering
LT -> t -> t -> Map t t -> t
go t
def t
k Map t t
l
      Ordering
GT -> t -> t -> Map t t -> t
go t
def t
k Map t t
r
      Ordering
EQ -> t
x
#if __GLASGOW_HASKELL__
{-# INLINABLE findWithDefault #-}
#else
{-# INLINE findWithDefault #-}
#endif

-- | \(O(\log n)\). 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')
lookupLT :: Ord k => k -> Map k v -> Maybe (k, v)
lookupLT :: forall k v. Ord k => k -> Map k v -> Maybe (k, v)
lookupLT = forall k v. Ord k => k -> Map k v -> Maybe (k, v)
goNothing
  where
    goNothing :: t -> Map t t -> Maybe (t, t)
goNothing !t
_ Map t t
Tip = forall a. Maybe a
Nothing
    goNothing t
k (Bin Size
_ t
kx t
x Map t t
l Map t t
r) | t
k forall a. Ord a => a -> a -> Bool
<= t
kx = t -> Map t t -> Maybe (t, t)
goNothing t
k Map t t
l
                                 | Bool
otherwise = forall {t} {t}. Ord t => t -> t -> t -> Map t t -> Maybe (t, t)
goJust t
k t
kx t
x Map t t
r

    goJust :: t -> t -> t -> Map t t -> Maybe (t, t)
goJust !t
_ t
kx' t
x' Map t t
Tip = forall a. a -> Maybe a
Just (t
kx', t
x')
    goJust t
k t
kx' t
x' (Bin Size
_ t
kx t
x Map t t
l Map t t
r) | t
k forall a. Ord a => a -> a -> Bool
<= t
kx = t -> t -> t -> Map t t -> Maybe (t, t)
goJust t
k t
kx' t
x' Map t t
l
                                     | Bool
otherwise = t -> t -> t -> Map t t -> Maybe (t, t)
goJust t
k t
kx t
x Map t t
r
#if __GLASGOW_HASKELL__
{-# INLINABLE lookupLT #-}
#else
{-# INLINE lookupLT #-}
#endif

-- | \(O(\log n)\). 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
lookupGT :: Ord k => k -> Map k v -> Maybe (k, v)
lookupGT :: forall k v. Ord k => k -> Map k v -> Maybe (k, v)
lookupGT = forall k v. Ord k => k -> Map k v -> Maybe (k, v)
goNothing
  where
    goNothing :: t -> Map t t -> Maybe (t, t)
goNothing !t
_ Map t t
Tip = forall a. Maybe a
Nothing
    goNothing t
k (Bin Size
_ t
kx t
x Map t t
l Map t t
r) | t
k forall a. Ord a => a -> a -> Bool
< t
kx = forall {t} {t}. Ord t => t -> t -> t -> Map t t -> Maybe (t, t)
goJust t
k t
kx t
x Map t t
l
                                 | Bool
otherwise = t -> Map t t -> Maybe (t, t)
goNothing t
k Map t t
r

    goJust :: t -> t -> t -> Map t t -> Maybe (t, t)
goJust !t
_ t
kx' t
x' Map t t
Tip = forall a. a -> Maybe a
Just (t
kx', t
x')
    goJust t
k t
kx' t
x' (Bin Size
_ t
kx t
x Map t t
l Map t t
r) | t
k forall a. Ord a => a -> a -> Bool
< t
kx = t -> t -> t -> Map t t -> Maybe (t, t)
goJust t
k t
kx t
x Map t t
l
                                     | Bool
otherwise = t -> t -> t -> Map t t -> Maybe (t, t)
goJust t
k t
kx' t
x' Map t t
r
#if __GLASGOW_HASKELL__
{-# INLINABLE lookupGT #-}
#else
{-# INLINE lookupGT #-}
#endif

-- | \(O(\log n)\). 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')
lookupLE :: Ord k => k -> Map k v -> Maybe (k, v)
lookupLE :: forall k v. Ord k => k -> Map k v -> Maybe (k, v)
lookupLE = forall k v. Ord k => k -> Map k v -> Maybe (k, v)
goNothing
  where
    goNothing :: a -> Map a b -> Maybe (a, b)
goNothing !a
_ Map a b
Tip = forall a. Maybe a
Nothing
    goNothing a
k (Bin Size
_ a
kx b
x Map a b
l Map a b
r) = case forall a. Ord a => a -> a -> Ordering
compare a
k a
kx of Ordering
LT -> a -> Map a b -> Maybe (a, b)
goNothing a
k Map a b
l
                                                        Ordering
EQ -> forall a. a -> Maybe a
Just (a
kx, b
x)
                                                        Ordering
GT -> forall {t} {t}. Ord t => t -> t -> t -> Map t t -> Maybe (t, t)
goJust a
k a
kx b
x Map a b
r

    goJust :: t -> t -> t -> Map t t -> Maybe (t, t)
goJust !t
_ t
kx' t
x' Map t t
Tip = forall a. a -> Maybe a
Just (t
kx', t
x')
    goJust t
k t
kx' t
x' (Bin Size
_ t
kx t
x Map t t
l Map t t
r) = case forall a. Ord a => a -> a -> Ordering
compare t
k t
kx of Ordering
LT -> t -> t -> t -> Map t t -> Maybe (t, t)
goJust t
k t
kx' t
x' Map t t
l
                                                            Ordering
EQ -> forall a. a -> Maybe a
Just (t
kx, t
x)
                                                            Ordering
GT -> t -> t -> t -> Map t t -> Maybe (t, t)
goJust t
k t
kx t
x Map t t
r
#if __GLASGOW_HASKELL__
{-# INLINABLE lookupLE #-}
#else
{-# INLINE lookupLE #-}
#endif

-- | \(O(\log n)\). 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
lookupGE :: Ord k => k -> Map k v -> Maybe (k, v)
lookupGE :: forall k v. Ord k => k -> Map k v -> Maybe (k, v)
lookupGE = forall k v. Ord k => k -> Map k v -> Maybe (k, v)
goNothing
  where
    goNothing :: t -> Map t b -> Maybe (t, b)
goNothing !t
_ Map t b
Tip = forall a. Maybe a
Nothing
    goNothing t
k (Bin Size
_ t
kx b
x Map t b
l Map t b
r) = case forall a. Ord a => a -> a -> Ordering
compare t
k t
kx of Ordering
LT -> forall {t} {t}. Ord t => t -> t -> t -> Map t t -> Maybe (t, t)
goJust t
k t
kx b
x Map t b
l
                                                        Ordering
EQ -> forall a. a -> Maybe a
Just (t
kx, b
x)
                                                        Ordering
GT -> t -> Map t b -> Maybe (t, b)
goNothing t
k Map t b
r

    goJust :: a -> a -> b -> Map a b -> Maybe (a, b)
goJust !a
_ a
kx' b
x' Map a b
Tip = forall a. a -> Maybe a
Just (a
kx', b
x')
    goJust a
k a
kx' b
x' (Bin Size
_ a
kx b
x Map a b
l Map a b
r) = case forall a. Ord a => a -> a -> Ordering
compare a
k a
kx of Ordering
LT -> a -> a -> b -> Map a b -> Maybe (a, b)
goJust a
k a
kx b
x Map a b
l
                                                            Ordering
EQ -> forall a. a -> Maybe a
Just (a
kx, b
x)
                                                            Ordering
GT -> a -> a -> b -> Map a b -> Maybe (a, b)
goJust a
k a
kx' b
x' Map a b
r
#if __GLASGOW_HASKELL__
{-# INLINABLE lookupGE #-}
#else
{-# INLINE lookupGE #-}
#endif

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

empty :: Map k a
empty :: forall k a. Map k a
empty = forall k a. Map k a
Tip
{-# INLINE empty #-}

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

singleton :: k -> a -> Map k a
singleton :: forall k a. k -> a -> Map k a
singleton k
k a
x = forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip
{-# INLINE singleton #-}

{--------------------------------------------------------------------
  Insertion
--------------------------------------------------------------------}
-- | \(O(\log n)\). Insert a new key and value in the map.
-- If the key is already present in the map, the associated value is
-- replaced with the supplied value. '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'

-- See Note: Type of local 'go' function
-- See Note: Avoiding worker/wrapper
insert :: Ord k => k -> a -> Map k a -> Map k a
insert :: forall k a. Ord k => k -> a -> Map k a -> Map k a
insert k
kx0 = forall k a. Ord k => k -> k -> a -> Map k a -> Map k a
go k
kx0 k
kx0
  where
    -- Unlike insertR, we only get sharing here
    -- when the inserted value is at the same address
    -- as the present value. We try anyway; this condition
    -- seems particularly likely to occur in 'union'.
    go :: Ord k => k -> k -> a -> Map k a -> Map k a
    go :: forall k a. Ord k => k -> k -> a -> Map k a -> Map k a
go k
orig !k
_  a
x Map k a
Tip = forall k a. k -> a -> Map k a
singleton (forall a. a -> a
lazy k
orig) a
x
    go k
orig !k
kx a
x t :: Map k a
t@(Bin Size
sz k
ky a
y Map k a
l Map k a
r) =
        case forall a. Ord a => a -> a -> Ordering
compare k
kx k
ky of
            Ordering
LT | Map k a
l' forall a. a -> a -> Bool
`ptrEq` Map k a
l -> Map k a
t
               | Bool
otherwise -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y Map k a
l' Map k a
r
               where !l' :: Map k a
l' = forall k a. Ord k => k -> k -> a -> Map k a -> Map k a
go k
orig k
kx a
x Map k a
l
            Ordering
GT | Map k a
r' forall a. a -> a -> Bool
`ptrEq` Map k a
r -> Map k a
t
               | Bool
otherwise -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y Map k a
l Map k a
r'
               where !r' :: Map k a
r' = forall k a. Ord k => k -> k -> a -> Map k a -> Map k a
go k
orig k
kx a
x Map k a
r
            Ordering
EQ | a
x forall a. a -> a -> Bool
`ptrEq` a
y Bool -> Bool -> Bool
&& (forall a. a -> a
lazy k
orig seq :: forall a b. a -> b -> b
`seq` (k
orig forall a. a -> a -> Bool
`ptrEq` k
ky)) -> Map k a
t
               | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sz (forall a. a -> a
lazy k
orig) a
x Map k a
l Map k a
r
#if __GLASGOW_HASKELL__
{-# INLINABLE insert #-}
#else
{-# INLINE insert #-}
#endif

#ifndef __GLASGOW_HASKELL__
lazy :: a -> a
lazy a = a
#endif

-- [Note: Avoiding worker/wrapper]
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-- 'insert' has to go to great lengths to get pointer equality right and
-- to prevent unnecessary allocation. The trouble is that GHC *really* wants
-- to unbox the key and throw away the boxed one. This is bad for us, because
-- we want to compare the pointer of the box we are given to the one already
-- present if they compare EQ. It's also bad for us because it leads to the
-- key being *reboxed* if it's actually stored in the map. Ugh! So we pass the
-- 'go' function *two copies* of the key we're given. One of them we use for
-- comparisons; the other we keep in our pocket. To prevent worker/wrapper from
-- messing with the copy in our pocket, we sprinkle about calls to the magical
-- function 'lazy'. This is all horrible, but it seems to work okay.


-- Insert a new key and value in the map if it is not already present.
-- Used by `union`.

-- See Note: Type of local 'go' function
-- See Note: Avoiding worker/wrapper
insertR :: Ord k => k -> a -> Map k a -> Map k a
insertR :: forall k a. Ord k => k -> a -> Map k a -> Map k a
insertR k
kx0 = forall k a. Ord k => k -> k -> a -> Map k a -> Map k a
go k
kx0 k
kx0
  where
    go :: Ord k => k -> k -> a -> Map k a -> Map k a
    go :: forall k a. Ord k => k -> k -> a -> Map k a -> Map k a
go k
orig !k
_  a
x Map k a
Tip = forall k a. k -> a -> Map k a
singleton (forall a. a -> a
lazy k
orig) a
x
    go k
orig !k
kx a
x t :: Map k a
t@(Bin Size
_ k
ky a
y Map k a
l Map k a
r) =
        case forall a. Ord a => a -> a -> Ordering
compare k
kx k
ky of
            Ordering
LT | Map k a
l' forall a. a -> a -> Bool
`ptrEq` Map k a
l -> Map k a
t
               | Bool
otherwise -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y Map k a
l' Map k a
r
               where !l' :: Map k a
l' = forall k a. Ord k => k -> k -> a -> Map k a -> Map k a
go k
orig k
kx a
x Map k a
l
            Ordering
GT | Map k a
r' forall a. a -> a -> Bool
`ptrEq` Map k a
r -> Map k a
t
               | Bool
otherwise -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y Map k a
l Map k a
r'
               where !r' :: Map k a
r' = forall k a. Ord k => k -> k -> a -> Map k a -> Map k a
go k
orig k
kx a
x Map k a
r
            Ordering
EQ -> Map k a
t
#if __GLASGOW_HASKELL__
{-# INLINABLE insertR #-}
#else
{-# INLINE insertR #-}
#endif

-- | \(O(\log n)\). Insert with a function, combining new value and old value.
-- @'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 the pair @(key, f new_value old_value)@.
--
-- > insertWith (++) 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "xxxa")]
-- > insertWith (++) 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
-- > insertWith (++) 5 "xxx" empty                         == singleton 5 "xxx"
--
-- Also see the performance note on 'fromListWith'.

insertWith :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWith :: forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWith = forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
go
  where
    -- We have no hope of making pointer equality tricks work
    -- here, because lazy insertWith *always* changes the tree,
    -- either adding a new entry or replacing an element with a
    -- thunk.
    go :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
    go :: forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
go a -> a -> a
_ !k
kx a
x Map k a
Tip = forall k a. k -> a -> Map k a
singleton k
kx a
x
    go a -> a -> a
f !k
kx a
x (Bin Size
sy k
ky a
y Map k a
l Map k a
r) =
        case forall a. Ord a => a -> a -> Ordering
compare k
kx k
ky of
            Ordering
LT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y (forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
go a -> a -> a
f k
kx a
x Map k a
l) Map k a
r
            Ordering
GT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y Map k a
l (forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
go a -> a -> a
f k
kx a
x Map k a
r)
            Ordering
EQ -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sy k
kx (a -> a -> a
f a
x a
y) Map k a
l Map k a
r

#if __GLASGOW_HASKELL__
{-# INLINABLE insertWith #-}
#else
{-# INLINE insertWith #-}
#endif

-- | A helper function for 'unionWith'. When the key is already in
-- the map, the key is left alone, not replaced. The combining
-- function is flipped--it is applied to the old value and then the
-- new value.
--
-- Also see the performance note on 'fromListWith'.

insertWithR :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithR :: forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithR = forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
go
  where
    go :: Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
    go :: forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
go a -> a -> a
_ !k
kx a
x Map k a
Tip = forall k a. k -> a -> Map k a
singleton k
kx a
x
    go a -> a -> a
f !k
kx a
x (Bin Size
sy k
ky a
y Map k a
l Map k a
r) =
        case forall a. Ord a => a -> a -> Ordering
compare k
kx k
ky of
            Ordering
LT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y (forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
go a -> a -> a
f k
kx a
x Map k a
l) Map k a
r
            Ordering
GT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y Map k a
l (forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
go a -> a -> a
f k
kx a
x Map k a
r)
            Ordering
EQ -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sy k
ky (a -> a -> a
f a
y a
x) Map k a
l Map k a
r
#if __GLASGOW_HASKELL__
{-# INLINABLE insertWithR #-}
#else
{-# INLINE insertWithR #-}
#endif

-- | \(O(\log n)\). Insert with a function, combining key, new value and old value.
-- @'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 the pair @(key,f key new_value old_value)@.
-- Note that the key passed to f is the same key passed to 'insertWithKey'.
--
-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
-- > insertWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "5:xxx|a")]
-- > insertWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "xxx")]
-- > insertWithKey f 5 "xxx" empty                         == singleton 5 "xxx"
--
-- Also see the performance note on 'fromListWith'.

-- See Note: Type of local 'go' function
insertWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKey :: forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKey = forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
go
  where
    go :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
    go :: forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
go k -> a -> a -> a
_ !k
kx a
x Map k a
Tip = forall k a. k -> a -> Map k a
singleton k
kx a
x
    go k -> a -> a -> a
f k
kx a
x (Bin Size
sy k
ky a
y Map k a
l Map k a
r) =
        case forall a. Ord a => a -> a -> Ordering
compare k
kx k
ky of
            Ordering
LT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y (forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
go k -> a -> a -> a
f k
kx a
x Map k a
l) Map k a
r
            Ordering
GT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y Map k a
l (forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
go k -> a -> a -> a
f k
kx a
x Map k a
r)
            Ordering
EQ -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sy k
kx (k -> a -> a -> a
f k
kx a
x a
y) Map k a
l Map k a
r
#if __GLASGOW_HASKELL__
{-# INLINABLE insertWithKey #-}
#else
{-# INLINE insertWithKey #-}
#endif

-- | A helper function for 'unionWithKey'. When the key is already in
-- the map, the key is left alone, not replaced. The combining
-- function is flipped--it is applied to the old value and then the
-- new value.
--
-- Also see the performance note on 'fromListWith'.

insertWithKeyR :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKeyR :: forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKeyR = forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
go
  where
    go :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
    go :: forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
go k -> a -> a -> a
_ !k
kx a
x Map k a
Tip = forall k a. k -> a -> Map k a
singleton k
kx a
x
    go k -> a -> a -> a
f k
kx a
x (Bin Size
sy k
ky a
y Map k a
l Map k a
r) =
        case forall a. Ord a => a -> a -> Ordering
compare k
kx k
ky of
            Ordering
LT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y (forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
go k -> a -> a -> a
f k
kx a
x Map k a
l) Map k a
r
            Ordering
GT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y Map k a
l (forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
go k -> a -> a -> a
f k
kx a
x Map k a
r)
            Ordering
EQ -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sy k
ky (k -> a -> a -> a
f k
ky a
y a
x) Map k a
l Map k a
r
#if __GLASGOW_HASKELL__
{-# INLINABLE insertWithKeyR #-}
#else
{-# INLINE insertWithKeyR #-}
#endif

-- | \(O(\log n)\). Combines insert operation with old value retrieval.
-- The expression (@'insertLookupWithKey' f k x map@)
-- is a pair where the first element is equal to (@'lookup' k map@)
-- and the second element equal to (@'insertWithKey' f k x map@).
--
-- > let f key new_value old_value = (show key) ++ ":" ++ new_value ++ "|" ++ old_value
-- > insertLookupWithKey f 5 "xxx" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "5:xxx|a")])
-- > insertLookupWithKey f 7 "xxx" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "xxx")])
-- > insertLookupWithKey f 5 "xxx" empty                         == (Nothing,  singleton 5 "xxx")
--
-- This is how to define @insertLookup@ using @insertLookupWithKey@:
--
-- > let insertLookup kx x t = insertLookupWithKey (\_ a _ -> a) kx x t
-- > insertLookup 5 "x" (fromList [(5,"a"), (3,"b")]) == (Just "a", fromList [(3, "b"), (5, "x")])
-- > insertLookup 7 "x" (fromList [(5,"a"), (3,"b")]) == (Nothing,  fromList [(3, "b"), (5, "a"), (7, "x")])
--
-- Also see the performance note on 'fromListWith'.

-- See Note: Type of local 'go' function
insertLookupWithKey :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a
                    -> (Maybe a, Map k a)
insertLookupWithKey :: forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> (Maybe a, Map k a)
insertLookupWithKey k -> a -> a -> a
f0 k
k0 a
x0 = forall a b. StrictPair a b -> (a, b)
toPair forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a.
Ord k =>
(k -> a -> a -> a)
-> k -> a -> Map k a -> StrictPair (Maybe a) (Map k a)
go k -> a -> a -> a
f0 k
k0 a
x0
  where
    go :: Ord k => (k -> a -> a -> a) -> k -> a -> Map k a -> StrictPair (Maybe a) (Map k a)
    go :: forall k a.
Ord k =>
(k -> a -> a -> a)
-> k -> a -> Map k a -> StrictPair (Maybe a) (Map k a)
go k -> a -> a -> a
_ !k
kx a
x Map k a
Tip = (forall a. Maybe a
Nothing forall a b. a -> b -> StrictPair a b
:*: forall k a. k -> a -> Map k a
singleton k
kx a
x)
    go k -> a -> a -> a
f k
kx a
x (Bin Size
sy k
ky a
y Map k a
l Map k a
r) =
        case forall a. Ord a => a -> a -> Ordering
compare k
kx k
ky of
            Ordering
LT -> let !(Maybe a
found :*: Map k a
l') = forall k a.
Ord k =>
(k -> a -> a -> a)
-> k -> a -> Map k a -> StrictPair (Maybe a) (Map k a)
go k -> a -> a -> a
f k
kx a
x Map k a
l
                      !t' :: Map k a
t' = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y Map k a
l' Map k a
r
                  in (Maybe a
found forall a b. a -> b -> StrictPair a b
:*: Map k a
t')
            Ordering
GT -> let !(Maybe a
found :*: Map k a
r') = forall k a.
Ord k =>
(k -> a -> a -> a)
-> k -> a -> Map k a -> StrictPair (Maybe a) (Map k a)
go k -> a -> a -> a
f k
kx a
x Map k a
r
                      !t' :: Map k a
t' = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y Map k a
l Map k a
r'
                  in (Maybe a
found forall a b. a -> b -> StrictPair a b
:*: Map k a
t')
            Ordering
EQ -> (forall a. a -> Maybe a
Just a
y forall a b. a -> b -> StrictPair a b
:*: forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sy k
kx (k -> a -> a -> a
f k
kx a
x a
y) Map k a
l Map k a
r)
#if __GLASGOW_HASKELL__
{-# INLINABLE insertLookupWithKey #-}
#else
{-# INLINE insertLookupWithKey #-}
#endif

{--------------------------------------------------------------------
  Deletion
--------------------------------------------------------------------}
-- | \(O(\log n)\). 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

-- See Note: Type of local 'go' function
delete :: Ord k => k -> Map k a -> Map k a
delete :: forall k a. Ord k => k -> Map k a -> Map k a
delete = forall k a. Ord k => k -> Map k a -> Map k a
go
  where
    go :: Ord k => k -> Map k a -> Map k a
    go :: forall k a. Ord k => k -> Map k a -> Map k a
go !k
_ Map k a
Tip = forall k a. Map k a
Tip
    go k
k t :: Map k a
t@(Bin Size
_ k
kx a
x Map k a
l Map k a
r) =
        case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
            Ordering
LT | Map k a
l' forall a. a -> a -> Bool
`ptrEq` Map k a
l -> Map k a
t
               | Bool
otherwise -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
kx a
x Map k a
l' Map k a
r
               where !l' :: Map k a
l' = forall k a. Ord k => k -> Map k a -> Map k a
go k
k Map k a
l
            Ordering
GT | Map k a
r' forall a. a -> a -> Bool
`ptrEq` Map k a
r -> Map k a
t
               | Bool
otherwise -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
kx a
x Map k a
l Map k a
r'
               where !r' :: Map k a
r' = forall k a. Ord k => k -> Map k a -> Map k a
go k
k Map k a
r
            Ordering
EQ -> forall k a. Map k a -> Map k a -> Map k a
glue Map k a
l Map k a
r
#if __GLASGOW_HASKELL__
{-# INLINABLE delete #-}
#else
{-# INLINE delete #-}
#endif

-- | \(O(\log n)\). Update a value at a specific key with the result of the provided function.
-- 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 :: Ord k => (a -> a) -> k -> Map k a -> Map k a
adjust :: forall k a. Ord k => (a -> a) -> k -> Map k a -> Map k a
adjust a -> a
f = forall k a. Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
adjustWithKey (\k
_ a
x -> a -> a
f a
x)
#if __GLASGOW_HASKELL__
{-# INLINABLE adjust #-}
#else
{-# INLINE adjust #-}
#endif

-- | \(O(\log n)\). 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 :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
adjustWithKey :: forall k a. Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
adjustWithKey = forall k a. Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
go
  where
    go :: Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
    go :: forall k a. Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
go k -> a -> a
_ !k
_ Map k a
Tip = forall k a. Map k a
Tip
    go k -> a -> a
f k
k (Bin Size
sx k
kx a
x Map k a
l Map k a
r) =
        case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
           Ordering
LT -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x (forall k a. Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
go k -> a -> a
f k
k Map k a
l) Map k a
r
           Ordering
GT -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x Map k a
l (forall k a. Ord k => (k -> a -> a) -> k -> Map k a -> Map k a
go k -> a -> a
f k
k Map k a
r)
           Ordering
EQ -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx (k -> a -> a
f k
kx a
x) Map k a
l Map k a
r
#if __GLASGOW_HASKELL__
{-# INLINABLE adjustWithKey #-}
#else
{-# INLINE adjustWithKey #-}
#endif

-- | \(O(\log n)\). 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 :: Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a
update :: forall k a. Ord k => (a -> Maybe a) -> k -> Map k a -> Map k a
update a -> Maybe a
f = forall k a. Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
updateWithKey (\k
_ a
x -> a -> Maybe a
f a
x)
#if __GLASGOW_HASKELL__
{-# INLINABLE update #-}
#else
{-# INLINE update #-}
#endif

-- | \(O(\log n)\). The expression (@'updateWithKey' 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"

-- See Note: Type of local 'go' function
updateWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
updateWithKey :: forall k a. Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
updateWithKey = forall k a. Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
go
  where
    go :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
    go :: forall k a. Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
go k -> a -> Maybe a
_ !k
_ Map k a
Tip = forall k a. Map k a
Tip
    go k -> a -> Maybe a
f k
k(Bin Size
sx k
kx a
x Map k a
l Map k a
r) =
        case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
           Ordering
LT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
kx a
x (forall k a. Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
go k -> a -> Maybe a
f k
k Map k a
l) Map k a
r
           Ordering
GT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
kx a
x Map k a
l (forall k a. Ord k => (k -> a -> Maybe a) -> k -> Map k a -> Map k a
go k -> a -> Maybe a
f k
k Map k a
r)
           Ordering
EQ -> case k -> a -> Maybe a
f k
kx a
x of
                   Just a
x' -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x' Map k a
l Map k a
r
                   Maybe a
Nothing -> forall k a. Map k a -> Map k a -> Map k a
glue Map k a
l Map k a
r
#if __GLASGOW_HASKELL__
{-# INLINABLE updateWithKey #-}
#else
{-# INLINE updateWithKey #-}
#endif

-- | \(O(\log n)\). Lookup and update. See also 'updateWithKey'.
-- The function returns changed value, if it is updated.
-- 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 "5:new 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")

-- See Note: Type of local 'go' function
updateLookupWithKey :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> (Maybe a,Map k a)
updateLookupWithKey :: forall k a.
Ord k =>
(k -> a -> Maybe a) -> k -> Map k a -> (Maybe a, Map k a)
updateLookupWithKey k -> a -> Maybe a
f0 k
k0 = forall a b. StrictPair a b -> (a, b)
toPair forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a.
Ord k =>
(k -> a -> Maybe a)
-> k -> Map k a -> StrictPair (Maybe a) (Map k a)
go k -> a -> Maybe a
f0 k
k0
 where
   go :: Ord k => (k -> a -> Maybe a) -> k -> Map k a -> StrictPair (Maybe a) (Map k a)
   go :: forall k a.
Ord k =>
(k -> a -> Maybe a)
-> k -> Map k a -> StrictPair (Maybe a) (Map k a)
go k -> a -> Maybe a
_ !k
_ Map k a
Tip = (forall a. Maybe a
Nothing forall a b. a -> b -> StrictPair a b
:*: forall k a. Map k a
Tip)
   go k -> a -> Maybe a
f k
k (Bin Size
sx k
kx a
x Map k a
l Map k a
r) =
          case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
               Ordering
LT -> let !(Maybe a
found :*: Map k a
l') = forall k a.
Ord k =>
(k -> a -> Maybe a)
-> k -> Map k a -> StrictPair (Maybe a) (Map k a)
go k -> a -> Maybe a
f k
k Map k a
l
                         !t' :: Map k a
t' = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
kx a
x Map k a
l' Map k a
r
                     in (Maybe a
found forall a b. a -> b -> StrictPair a b
:*: Map k a
t')
               Ordering
GT -> let !(Maybe a
found :*: Map k a
r') = forall k a.
Ord k =>
(k -> a -> Maybe a)
-> k -> Map k a -> StrictPair (Maybe a) (Map k a)
go k -> a -> Maybe a
f k
k Map k a
r
                         !t' :: Map k a
t' = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
kx a
x Map k a
l Map k a
r'
                     in (Maybe a
found forall a b. a -> b -> StrictPair a b
:*: Map k a
t')
               Ordering
EQ -> case k -> a -> Maybe a
f k
kx a
x of
                       Just a
x' -> (forall a. a -> Maybe a
Just a
x' forall a b. a -> b -> StrictPair a b
:*: forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x' Map k a
l Map k a
r)
                       Maybe a
Nothing -> let !glued :: Map k a
glued = forall k a. Map k a -> Map k a -> Map k a
glue Map k a
l Map k a
r
                                  in (forall a. a -> Maybe a
Just a
x forall a b. a -> b -> StrictPair a b
:*: Map k a
glued)
#if __GLASGOW_HASKELL__
{-# INLINABLE updateLookupWithKey #-}
#else
{-# INLINE updateLookupWithKey #-}
#endif

-- | \(O(\log n)\). The expression (@'alter' f k map@) alters the value @x@ at @k@, or absence thereof.
-- 'alter' can be used to insert, delete, or update a value in a 'Map'.
-- In short : @'lookup' k ('alter' f k m) = f ('lookup' k m)@.
--
-- > let f _ = Nothing
-- > alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a")]
-- > alter f 5 (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
-- >
-- > let f _ = Just "c"
-- > alter f 7 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "a"), (7, "c")]
-- > alter f 5 (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "c")]
--
-- Note that @'adjust' = alter . fmap@.

-- See Note: Type of local 'go' function
alter :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a
alter :: forall k a.
Ord k =>
(Maybe a -> Maybe a) -> k -> Map k a -> Map k a
alter = forall k a.
Ord k =>
(Maybe a -> Maybe a) -> k -> Map k a -> Map k a
go
  where
    go :: Ord k => (Maybe a -> Maybe a) -> k -> Map k a -> Map k a
    go :: forall k a.
Ord k =>
(Maybe a -> Maybe a) -> k -> Map k a -> Map k a
go Maybe a -> Maybe a
f !k
k Map k a
Tip = case Maybe a -> Maybe a
f forall a. Maybe a
Nothing of
               Maybe a
Nothing -> forall k a. Map k a
Tip
               Just a
x  -> forall k a. k -> a -> Map k a
singleton k
k a
x

    go Maybe a -> Maybe a
f k
k (Bin Size
sx k
kx a
x Map k a
l Map k a
r) = case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
               Ordering
LT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balance k
kx a
x (forall k a.
Ord k =>
(Maybe a -> Maybe a) -> k -> Map k a -> Map k a
go Maybe a -> Maybe a
f k
k Map k a
l) Map k a
r
               Ordering
GT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balance k
kx a
x Map k a
l (forall k a.
Ord k =>
(Maybe a -> Maybe a) -> k -> Map k a -> Map k a
go Maybe a -> Maybe a
f k
k Map k a
r)
               Ordering
EQ -> case Maybe a -> Maybe a
f (forall a. a -> Maybe a
Just a
x) of
                       Just a
x' -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x' Map k a
l Map k a
r
                       Maybe a
Nothing -> forall k a. Map k a -> Map k a -> Map k a
glue Map k a
l Map k a
r
#if __GLASGOW_HASKELL__
{-# INLINABLE alter #-}
#else
{-# INLINE alter #-}
#endif

-- Used to choose the appropriate alterF implementation.
data AreWeStrict = Strict | Lazy

-- | \(O(\log n)\). 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 a 'Map'.  In short: @'lookup' k \<$\> 'alterF' f k m = f
-- ('lookup' k m)@.
--
-- Example:
--
-- @
-- interactiveAlter :: Int -> Map Int String -> IO (Map Int 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. When used with trivial
-- functors like 'Identity' and 'Const', it is often slightly slower than
-- more specialized combinators like 'lookup' and 'insert'. However, when
-- the functor is non-trivial and key comparison is not particularly cheap,
-- it is the fastest way.
--
-- Note on rewrite rules:
--
-- This module includes GHC rewrite rules to optimize 'alterF' for
-- the 'Const' and 'Identity' functors. In general, these rules
-- improve performance. The sole exception is that when using
-- 'Identity', deleting a key that is already absent takes longer
-- than it would without the rules. If you expect this to occur
-- a very large fraction of the time, you might consider using a
-- private copy of the 'Identity' type.
--
-- Note: 'alterF' is a flipped version of the @at@ combinator from
-- @Control.Lens.At@.
--
-- @since 0.5.8
alterF :: (Functor f, Ord k)
       => (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)
alterF :: forall (f :: * -> *) k a.
(Functor f, Ord k) =>
(Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)
alterF Maybe a -> f (Maybe a)
f k
k Map k a
m = forall (f :: * -> *) k a.
(Functor f, Ord k) =>
AreWeStrict
-> k -> (Maybe a -> f (Maybe a)) -> Map k a -> f (Map k a)
atKeyImpl AreWeStrict
Lazy k
k Maybe a -> f (Maybe a)
f Map k a
m

#ifndef __GLASGOW_HASKELL__
{-# INLINE alterF #-}
#else
{-# INLINABLE [2] alterF #-}

-- We can save a little time by recognizing the special case of
-- `Control.Applicative.Const` and just doing a lookup.
{-# RULES
"alterF/Const" forall k (f :: Maybe a -> Const b (Maybe a)) . alterF f k = \m -> Const . getConst . f $ lookup k m
 #-}

-- base 4.8 and above include Data.Functor.Identity, so we can
-- save a pretty decent amount of time by handling it specially.
{-# RULES
"alterF/Identity" forall k f . alterF f k = atKeyIdentity k f
 #-}
#endif

atKeyImpl :: (Functor f, Ord k) =>
      AreWeStrict -> k -> (Maybe a -> f (Maybe a)) -> Map k a -> f (Map k a)
#ifdef DEFINE_ALTERF_FALLBACK
atKeyImpl strict !k f m
-- It doesn't seem sensible to worry about overflowing the queue
-- if the word size is 61 or more. If I calculate it correctly,
-- that would take a map with nearly a quadrillion entries.
  | wordSize < 61 && size m >= alterFCutoff = alterFFallback strict k f m
#endif
atKeyImpl :: forall (f :: * -> *) k a.
(Functor f, Ord k) =>
AreWeStrict
-> k -> (Maybe a -> f (Maybe a)) -> Map k a -> f (Map k a)
atKeyImpl AreWeStrict
strict !k
k Maybe a -> f (Maybe a)
f Map k a
m = case forall k a. Ord k => k -> Map k a -> TraceResult a
lookupTrace k
k Map k a
m of
  TraceResult Maybe a
mv BitQueue
q -> (forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Maybe a -> f (Maybe a)
f Maybe a
mv) forall a b. (a -> b) -> a -> b
$ \ Maybe a
fres ->
    case Maybe a
fres of
      Maybe a
Nothing -> case Maybe a
mv of
                   Maybe a
Nothing -> Map k a
m
                   Just a
old -> forall any k a. any -> BitQueue -> Map k a -> Map k a
deleteAlong a
old BitQueue
q Map k a
m
      Just a
new -> case AreWeStrict
strict of
         AreWeStrict
Strict -> a
new seq :: forall a b. a -> b -> b
`seq` case Maybe a
mv of
                      Maybe a
Nothing -> forall k a. BitQueue -> k -> a -> Map k a -> Map k a
insertAlong BitQueue
q k
k a
new Map k a
m
                      Just a
_ -> forall a k. BitQueue -> a -> Map k a -> Map k a
replaceAlong BitQueue
q a
new Map k a
m
         AreWeStrict
Lazy -> case Maybe a
mv of
                      Maybe a
Nothing -> forall k a. BitQueue -> k -> a -> Map k a -> Map k a
insertAlong BitQueue
q k
k a
new Map k a
m
                      Just a
_ -> forall a k. BitQueue -> a -> Map k a -> Map k a
replaceAlong BitQueue
q a
new Map k a
m

{-# INLINE atKeyImpl #-}

#ifdef DEFINE_ALTERF_FALLBACK
alterFCutoff :: Int
#if WORD_SIZE_IN_BITS == 32
alterFCutoff = 55744454
#else
alterFCutoff = case wordSize of
      30 -> 17637893
      31 -> 31356255
      32 -> 55744454
      x -> (4^(x*2-2)) `quot` (3^(x*2-2))  -- Unlikely
#endif
#endif

data TraceResult a = TraceResult (Maybe a) {-# UNPACK #-} !BitQueue

-- Look up a key and return a result indicating whether it was found
-- and what path was taken.
lookupTrace :: Ord k => k -> Map k a -> TraceResult a
lookupTrace :: forall k a. Ord k => k -> Map k a -> TraceResult a
lookupTrace = forall k a. Ord k => BitQueueB -> k -> Map k a -> TraceResult a
go BitQueueB
emptyQB
  where
    go :: Ord k => BitQueueB -> k -> Map k a -> TraceResult a
    go :: forall k a. Ord k => BitQueueB -> k -> Map k a -> TraceResult a
go !BitQueueB
q !k
_ Map k a
Tip = forall a. Maybe a -> BitQueue -> TraceResult a
TraceResult forall a. Maybe a
Nothing (BitQueueB -> BitQueue
buildQ BitQueueB
q)
    go BitQueueB
q k
k (Bin Size
_ k
kx a
x Map k a
l Map k a
r) = case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
      Ordering
LT -> (forall k a. Ord k => BitQueueB -> k -> Map k a -> TraceResult a
go forall a b. (a -> b) -> a -> b
$! BitQueueB
q BitQueueB -> Bool -> BitQueueB
`snocQB` Bool
False) k
k Map k a
l
      Ordering
GT -> (forall k a. Ord k => BitQueueB -> k -> Map k a -> TraceResult a
go forall a b. (a -> b) -> a -> b
$! BitQueueB
q BitQueueB -> Bool -> BitQueueB
`snocQB` Bool
True) k
k Map k a
r
      Ordering
EQ -> forall a. Maybe a -> BitQueue -> TraceResult a
TraceResult (forall a. a -> Maybe a
Just a
x) (BitQueueB -> BitQueue
buildQ BitQueueB
q)

#ifdef __GLASGOW_HASKELL__
{-# INLINABLE lookupTrace #-}
#else
{-# INLINE lookupTrace #-}
#endif

-- Insert at a location (which will always be a leaf)
-- described by the path passed in.
insertAlong :: BitQueue -> k -> a -> Map k a -> Map k a
insertAlong :: forall k a. BitQueue -> k -> a -> Map k a -> Map k a
insertAlong !BitQueue
_ k
kx a
x Map k a
Tip = forall k a. k -> a -> Map k a
singleton k
kx a
x
insertAlong BitQueue
q k
kx a
x (Bin Size
sz k
ky a
y Map k a
l Map k a
r) =
  case BitQueue -> Maybe (Bool, BitQueue)
unconsQ BitQueue
q of
        Just (Bool
False, BitQueue
tl) -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y (forall k a. BitQueue -> k -> a -> Map k a -> Map k a
insertAlong BitQueue
tl k
kx a
x Map k a
l) Map k a
r
        Just (Bool
True,BitQueue
tl) -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y Map k a
l (forall k a. BitQueue -> k -> a -> Map k a -> Map k a
insertAlong BitQueue
tl k
kx a
x Map k a
r)
        Maybe (Bool, BitQueue)
Nothing -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sz k
kx a
x Map k a
l Map k a
r  -- Shouldn't happen

-- Delete from a location (which will always be a node)
-- described by the path passed in.
--
-- This is fairly horrifying! We don't actually have any
-- use for the old value we're deleting. But if GHC sees
-- that, then it will allocate a thunk representing the
-- Map with the key deleted before we have any reason to
-- believe we'll actually want that. This transformation
-- enhances sharing, but we don't care enough about that.
-- So deleteAlong needs to take the old value, and we need
-- to convince GHC somehow that it actually uses it. We
-- can't NOINLINE deleteAlong, because that would prevent
-- the BitQueue from being unboxed. So instead we pass the
-- old value to a NOINLINE constant function and then
-- convince GHC that we use the result throughout the
-- computation. Doing the obvious thing and just passing
-- the value itself through the recursion costs 3-4% time,
-- so instead we convert the value to a magical zero-width
-- proxy that's ultimately erased.
deleteAlong :: any -> BitQueue -> Map k a -> Map k a
deleteAlong :: forall any k a. any -> BitQueue -> Map k a -> Map k a
deleteAlong any
old !BitQueue
q0 !Map k a
m = forall k a. Proxy# () -> BitQueue -> Map k a -> Map k a
go (forall a. a -> Proxy# ()
bogus any
old) BitQueue
q0 Map k a
m where
#ifdef USE_MAGIC_PROXY
  go :: Proxy# () -> BitQueue -> Map k a -> Map k a
#else
  go :: any -> BitQueue -> Map k a -> Map k a
#endif
  go :: forall k a. Proxy# () -> BitQueue -> Map k a -> Map k a
go !Proxy# ()
_ !BitQueue
_ Map k a
Tip = forall k a. Map k a
Tip
  go Proxy# ()
foom BitQueue
q (Bin Size
_ k
ky a
y Map k a
l Map k a
r) =
      case BitQueue -> Maybe (Bool, BitQueue)
unconsQ BitQueue
q of
        Just (Bool
False, BitQueue
tl) -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y (forall k a. Proxy# () -> BitQueue -> Map k a -> Map k a
go Proxy# ()
foom BitQueue
tl Map k a
l) Map k a
r
        Just (Bool
True, BitQueue
tl) -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y Map k a
l (forall k a. Proxy# () -> BitQueue -> Map k a -> Map k a
go Proxy# ()
foom BitQueue
tl Map k a
r)
        Maybe (Bool, BitQueue)
Nothing -> forall k a. Map k a -> Map k a -> Map k a
glue Map k a
l Map k a
r

#ifdef USE_MAGIC_PROXY
{-# NOINLINE bogus #-}
bogus :: a -> Proxy# ()
bogus :: forall a. a -> Proxy# ()
bogus a
_ = forall {k} (a :: k). Proxy# a
proxy#
#else
-- No point hiding in this case.
{-# INLINE bogus #-}
bogus :: a -> a
bogus a = a
#endif

-- Replace the value found in the node described
-- by the given path with a new one.
replaceAlong :: BitQueue -> a -> Map k a -> Map k a
replaceAlong :: forall a k. BitQueue -> a -> Map k a -> Map k a
replaceAlong !BitQueue
_ a
_ Map k a
Tip = forall k a. Map k a
Tip -- Should not happen
replaceAlong BitQueue
q  a
x (Bin Size
sz k
ky a
y Map k a
l Map k a
r) =
      case BitQueue -> Maybe (Bool, BitQueue)
unconsQ BitQueue
q of
        Just (Bool
False, BitQueue
tl) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sz k
ky a
y (forall a k. BitQueue -> a -> Map k a -> Map k a
replaceAlong BitQueue
tl a
x Map k a
l) Map k a
r
        Just (Bool
True,BitQueue
tl) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sz k
ky a
y Map k a
l (forall a k. BitQueue -> a -> Map k a -> Map k a
replaceAlong BitQueue
tl a
x Map k a
r)
        Maybe (Bool, BitQueue)
Nothing -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sz k
ky a
x Map k a
l Map k a
r

#ifdef __GLASGOW_HASKELL__
atKeyIdentity :: Ord k => k -> (Maybe a -> Identity (Maybe a)) -> Map k a -> Identity (Map k a)
atKeyIdentity :: forall k a.
Ord k =>
k
-> (Maybe a -> Identity (Maybe a)) -> Map k a -> Identity (Map k a)
atKeyIdentity k
k Maybe a -> Identity (Maybe a)
f Map k a
t = forall a. a -> Identity a
Identity forall a b. (a -> b) -> a -> b
$ forall k a.
Ord k =>
AreWeStrict -> k -> (Maybe a -> Maybe a) -> Map k a -> Map k a
atKeyPlain AreWeStrict
Lazy k
k (coerce :: forall a b. Coercible a b => a -> b
coerce Maybe a -> Identity (Maybe a)
f) Map k a
t
{-# INLINABLE atKeyIdentity #-}

atKeyPlain :: Ord k => AreWeStrict -> k -> (Maybe a -> Maybe a) -> Map k a -> Map k a
atKeyPlain :: forall k a.
Ord k =>
AreWeStrict -> k -> (Maybe a -> Maybe a) -> Map k a -> Map k a
atKeyPlain AreWeStrict
strict k
k0 Maybe a -> Maybe a
f0 Map k a
t = case forall k a.
Ord k =>
k -> (Maybe a -> Maybe a) -> Map k a -> Altered k a
go k
k0 Maybe a -> Maybe a
f0 Map k a
t of
    AltSmaller Map k a
t' -> Map k a
t'
    AltBigger Map k a
t' -> Map k a
t'
    AltAdj Map k a
t' -> Map k a
t'
    Altered k a
AltSame -> Map k a
t
  where
    go :: Ord k => k -> (Maybe a -> Maybe a) -> Map k a -> Altered k a
    go :: forall k a.
Ord k =>
k -> (Maybe a -> Maybe a) -> Map k a -> Altered k a
go !k
k Maybe a -> Maybe a
f Map k a
Tip = case Maybe a -> Maybe a
f forall a. Maybe a
Nothing of
                   Maybe a
Nothing -> forall k a. Altered k a
AltSame
                   Just a
x  -> case AreWeStrict
strict of
                     AreWeStrict
Lazy -> forall k a. Map k a -> Altered k a
AltBigger forall a b. (a -> b) -> a -> b
$ forall k a. k -> a -> Map k a
singleton k
k a
x
                     AreWeStrict
Strict -> a
x seq :: forall a b. a -> b -> b
`seq` (forall k a. Map k a -> Altered k a
AltBigger forall a b. (a -> b) -> a -> b
$ forall k a. k -> a -> Map k a
singleton k
k a
x)

    go k
k Maybe a -> Maybe a
f (Bin Size
sx k
kx a
x Map k a
l Map k a
r) = case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
                   Ordering
LT -> case forall k a.
Ord k =>
k -> (Maybe a -> Maybe a) -> Map k a -> Altered k a
go k
k Maybe a -> Maybe a
f Map k a
l of
                           AltSmaller Map k a
l' -> forall k a. Map k a -> Altered k a
AltSmaller forall a b. (a -> b) -> a -> b
$ forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
kx a
x Map k a
l' Map k a
r
                           AltBigger Map k a
l' -> forall k a. Map k a -> Altered k a
AltBigger forall a b. (a -> b) -> a -> b
$ forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
kx a
x Map k a
l' Map k a
r
                           AltAdj Map k a
l' -> forall k a. Map k a -> Altered k a
AltAdj forall a b. (a -> b) -> a -> b
$ forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x Map k a
l' Map k a
r
                           Altered k a
AltSame -> forall k a. Altered k a
AltSame
                   Ordering
GT -> case forall k a.
Ord k =>
k -> (Maybe a -> Maybe a) -> Map k a -> Altered k a
go k
k Maybe a -> Maybe a
f Map k a
r of
                           AltSmaller Map k a
r' -> forall k a. Map k a -> Altered k a
AltSmaller forall a b. (a -> b) -> a -> b
$ forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
kx a
x Map k a
l Map k a
r'
                           AltBigger Map k a
r' -> forall k a. Map k a -> Altered k a
AltBigger forall a b. (a -> b) -> a -> b
$ forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
kx a
x Map k a
l Map k a
r'
                           AltAdj Map k a
r' -> forall k a. Map k a -> Altered k a
AltAdj forall a b. (a -> b) -> a -> b
$ forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x Map k a
l Map k a
r'
                           Altered k a
AltSame -> forall k a. Altered k a
AltSame
                   Ordering
EQ -> case Maybe a -> Maybe a
f (forall a. a -> Maybe a
Just a
x) of
                           Just a
x' -> case AreWeStrict
strict of
                             AreWeStrict
Lazy -> forall k a. Map k a -> Altered k a
AltAdj forall a b. (a -> b) -> a -> b
$ forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x' Map k a
l Map k a
r
                             AreWeStrict
Strict -> a
x' seq :: forall a b. a -> b -> b
`seq` (forall k a. Map k a -> Altered k a
AltAdj forall a b. (a -> b) -> a -> b
$ forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x' Map k a
l Map k a
r)
                           Maybe a
Nothing -> forall k a. Map k a -> Altered k a
AltSmaller forall a b. (a -> b) -> a -> b
$ forall k a. Map k a -> Map k a -> Map k a
glue Map k a
l Map k a
r
{-# INLINE atKeyPlain #-}

data Altered k a = AltSmaller !(Map k a) | AltBigger !(Map k a) | AltAdj !(Map k a) | AltSame
#endif

#ifdef DEFINE_ALTERF_FALLBACK
-- When the map is too large to use a bit queue, we fall back to
-- this much slower version which uses a more "natural" implementation
-- improved with Yoneda to avoid repeated fmaps. This works okayish for
-- some operations, but it's pretty lousy for lookups.
alterFFallback :: (Functor f, Ord k)
   => AreWeStrict -> k -> (Maybe a -> f (Maybe a)) -> Map k a -> f (Map k a)
alterFFallback Lazy k f t = alterFYoneda k (\m q -> q <$> f m) t id
alterFFallback Strict k f t = alterFYoneda k (\m q -> q . forceMaybe <$> f m) t id
  where
    forceMaybe Nothing = Nothing
    forceMaybe may@(Just !_) = may
{-# NOINLINE alterFFallback #-}

alterFYoneda :: Ord k =>
      k -> (Maybe a -> (Maybe a -> b) -> f b) -> Map k a -> (Map k a -> b) -> f b
alterFYoneda = go
  where
    go :: Ord k =>
      k -> (Maybe a -> (Maybe a -> b) -> f b) -> Map k a -> (Map k a -> b) -> f b
    go !k f Tip g = f Nothing $ \ mx -> case mx of
      Nothing -> g Tip
      Just x -> g (singleton k x)
    go k f (Bin sx kx x l r) g = case compare k kx of
               LT -> go k f l (\m -> g (balance kx x m r))
               GT -> go k f r (\m -> g (balance kx x l m))
               EQ -> f (Just x) $ \ mx' -> case mx' of
                       Just x' -> g (Bin sx kx x' l r)
                       Nothing -> g (glue l r)
{-# INLINE alterFYoneda #-}
#endif

{--------------------------------------------------------------------
  Indexing
--------------------------------------------------------------------}
-- | \(O(\log n)\). Return the /index/ of a key, which is its zero-based index in
-- the sequence sorted by keys. The index is a number from /0/ up to, but not
-- including, the 'size' of the map. Calls 'error' when the key is not
-- a 'member' of the map.
--
-- > findIndex 2 (fromList [(5,"a"), (3,"b")])    Error: element is not in the map
-- > findIndex 3 (fromList [(5,"a"), (3,"b")]) == 0
-- > findIndex 5 (fromList [(5,"a"), (3,"b")]) == 1
-- > findIndex 6 (fromList [(5,"a"), (3,"b")])    Error: element is not in the map

-- See Note: Type of local 'go' function
findIndex :: Ord k => k -> Map k a -> Int
findIndex :: forall k a. Ord k => k -> Map k a -> Size
findIndex = forall k a. Ord k => Size -> k -> Map k a -> Size
go Size
0
  where
    go :: Ord k => Int -> k -> Map k a -> Int
    go :: forall k a. Ord k => Size -> k -> Map k a -> Size
go !Size
_   !k
_ Map k a
Tip  = forall a. HasCallStack => [Char] -> a
error [Char]
"Map.findIndex: element is not in the map"
    go Size
idx k
k (Bin Size
_ k
kx a
_ Map k a
l Map k a
r) = case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
      Ordering
LT -> forall k a. Ord k => Size -> k -> Map k a -> Size
go Size
idx k
k Map k a
l
      Ordering
GT -> forall k a. Ord k => Size -> k -> Map k a -> Size
go (Size
idx forall a. Num a => a -> a -> a
+ forall k a. Map k a -> Size
size Map k a
l forall a. Num a => a -> a -> a
+ Size
1) k
k Map k a
r
      Ordering
EQ -> Size
idx forall a. Num a => a -> a -> a
+ forall k a. Map k a -> Size
size Map k a
l
#if __GLASGOW_HASKELL__
{-# INLINABLE findIndex #-}
#endif

-- | \(O(\log n)\). Lookup the /index/ of a key, which is its zero-based index in
-- the sequence sorted by keys. The index is a number from /0/ up to, but not
-- including, the 'size' of the map.
--
-- > isJust (lookupIndex 2 (fromList [(5,"a"), (3,"b")]))   == False
-- > fromJust (lookupIndex 3 (fromList [(5,"a"), (3,"b")])) == 0
-- > fromJust (lookupIndex 5 (fromList [(5,"a"), (3,"b")])) == 1
-- > isJust (lookupIndex 6 (fromList [(5,"a"), (3,"b")]))   == False

-- See Note: Type of local 'go' function
lookupIndex :: Ord k => k -> Map k a -> Maybe Int
lookupIndex :: forall k a. Ord k => k -> Map k a -> Maybe Size
lookupIndex = forall k a. Ord k => Size -> k -> Map k a -> Maybe Size
go Size
0
  where
    go :: Ord k => Int -> k -> Map k a -> Maybe Int
    go :: forall k a. Ord k => Size -> k -> Map k a -> Maybe Size
go !Size
_  !k
_ Map k a
Tip  = forall a. Maybe a
Nothing
    go Size
idx k
k (Bin Size
_ k
kx a
_ Map k a
l Map k a
r) = case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
      Ordering
LT -> forall k a. Ord k => Size -> k -> Map k a -> Maybe Size
go Size
idx k
k Map k a
l
      Ordering
GT -> forall k a. Ord k => Size -> k -> Map k a -> Maybe Size
go (Size
idx forall a. Num a => a -> a -> a
+ forall k a. Map k a -> Size
size Map k a
l forall a. Num a => a -> a -> a
+ Size
1) k
k Map k a
r
      Ordering
EQ -> forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$! Size
idx forall a. Num a => a -> a -> a
+ forall k a. Map k a -> Size
size Map k a
l
#if __GLASGOW_HASKELL__
{-# INLINABLE lookupIndex #-}
#endif

-- | \(O(\log n)\). Retrieve an element by its /index/, i.e. by its zero-based
-- index in the sequence sorted by keys. If the /index/ is out of range (less
-- than zero, greater or equal to 'size' of the map), 'error' is called.
--
-- > elemAt 0 (fromList [(5,"a"), (3,"b")]) == (3,"b")
-- > elemAt 1 (fromList [(5,"a"), (3,"b")]) == (5, "a")
-- > elemAt 2 (fromList [(5,"a"), (3,"b")])    Error: index out of range

elemAt :: Int -> Map k a -> (k,a)
elemAt :: forall k a. Size -> Map k a -> (k, a)
elemAt !Size
_ Map k a
Tip = forall a. HasCallStack => [Char] -> a
error [Char]
"Map.elemAt: index out of range"
elemAt Size
i (Bin Size
_ k
kx a
x Map k a
l Map k a
r)
  = case forall a. Ord a => a -> a -> Ordering
compare Size
i Size
sizeL of
      Ordering
LT -> forall k a. Size -> Map k a -> (k, a)
elemAt Size
i Map k a
l
      Ordering
GT -> forall k a. Size -> Map k a -> (k, a)
elemAt (Size
iforall a. Num a => a -> a -> a
-Size
sizeLforall a. Num a => a -> a -> a
-Size
1) Map k a
r
      Ordering
EQ -> (k
kx,a
x)
  where
    sizeL :: Size
sizeL = forall k a. Map k a -> Size
size Map k a
l

-- | \(O(\log n)\). Take a given number of entries in key order, beginning
-- with the smallest keys.
--
-- @
-- take n = 'fromDistinctAscList' . 'Prelude.take' n . 'toAscList'
-- @
--
-- @since 0.5.8

take :: Int -> Map k a -> Map k a
take :: forall k a. Size -> Map k a -> Map k a
take Size
i Map k a
m | Size
i forall a. Ord a => a -> a -> Bool
>= forall k a. Map k a -> Size
size Map k a
m = Map k a
m
take Size
i0 Map k a
m0 = forall k a. Size -> Map k a -> Map k a
go Size
i0 Map k a
m0
  where
    go :: Size -> Map k a -> Map k a
go Size
i !Map k a
_ | Size
i forall a. Ord a => a -> a -> Bool
<= Size
0 = forall k a. Map k a
Tip
    go !Size
_ Map k a
Tip = forall k a. Map k a
Tip
    go Size
i (Bin Size
_ k
kx a
x Map k a
l Map k a
r) =
      case forall a. Ord a => a -> a -> Ordering
compare Size
i Size
sizeL of
        Ordering
LT -> Size -> Map k a -> Map k a
go Size
i Map k a
l
        Ordering
GT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l (Size -> Map k a -> Map k a
go (Size
i forall a. Num a => a -> a -> a
- Size
sizeL forall a. Num a => a -> a -> a
- Size
1) Map k a
r)
        Ordering
EQ -> Map k a
l
      where sizeL :: Size
sizeL = forall k a. Map k a -> Size
size Map k a
l

-- | \(O(\log n)\). Drop a given number of entries in key order, beginning
-- with the smallest keys.
--
-- @
-- drop n = 'fromDistinctAscList' . 'Prelude.drop' n . 'toAscList'
-- @
--
-- @since 0.5.8
drop :: Int -> Map k a -> Map k a
drop :: forall k a. Size -> Map k a -> Map k a
drop Size
i Map k a
m | Size
i forall a. Ord a => a -> a -> Bool
>= forall k a. Map k a -> Size
size Map k a
m = forall k a. Map k a
Tip
drop Size
i0 Map k a
m0 = forall k a. Size -> Map k a -> Map k a
go Size
i0 Map k a
m0
  where
    go :: Size -> Map k a -> Map k a
go Size
i Map k a
m | Size
i forall a. Ord a => a -> a -> Bool
<= Size
0 = Map k a
m
    go !Size
_ Map k a
Tip = forall k a. Map k a
Tip
    go Size
i (Bin Size
_ k
kx a
x Map k a
l Map k a
r) =
      case forall a. Ord a => a -> a -> Ordering
compare Size
i Size
sizeL of
        Ordering
LT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x (Size -> Map k a -> Map k a
go Size
i Map k a
l) Map k a
r
        Ordering
GT -> Size -> Map k a -> Map k a
go (Size
i forall a. Num a => a -> a -> a
- Size
sizeL forall a. Num a => a -> a -> a
- Size
1) Map k a
r
        Ordering
EQ -> forall k a. k -> a -> Map k a -> Map k a
insertMin k
kx a
x Map k a
r
      where sizeL :: Size
sizeL = forall k a. Map k a -> Size
size Map k a
l

-- | \(O(\log n)\). Split a map at a particular index.
--
-- @
-- splitAt !n !xs = ('take' n xs, 'drop' n xs)
-- @
--
-- @since 0.5.8
splitAt :: Int -> Map k a -> (Map k a, Map k a)
splitAt :: forall k a. Size -> Map k a -> (Map k a, Map k a)
splitAt Size
i0 Map k a
m0
  | Size
i0 forall a. Ord a => a -> a -> Bool
>= forall k a. Map k a -> Size
size Map k a
m0 = (Map k a
m0, forall k a. Map k a
Tip)
  | Bool
otherwise = forall a b. StrictPair a b -> (a, b)
toPair forall a b. (a -> b) -> a -> b
$ forall {k} {a}. Size -> Map k a -> StrictPair (Map k a) (Map k a)
go Size
i0 Map k a
m0
  where
    go :: Size -> Map k a -> StrictPair (Map k a) (Map k a)
go Size
i Map k a
m | Size
i forall a. Ord a => a -> a -> Bool
<= Size
0 = forall k a. Map k a
Tip forall a b. a -> b -> StrictPair a b
:*: Map k a
m
    go !Size
_ Map k a
Tip = forall k a. Map k a
Tip forall a b. a -> b -> StrictPair a b
:*: forall k a. Map k a
Tip
    go Size
i (Bin Size
_ k
kx a
x Map k a
l Map k a
r)
      = case forall a. Ord a => a -> a -> Ordering
compare Size
i Size
sizeL of
          Ordering
LT -> case Size -> Map k a -> StrictPair (Map k a) (Map k a)
go Size
i Map k a
l of
                  Map k a
ll :*: Map k a
lr -> Map k a
ll forall a b. a -> b -> StrictPair a b
:*: forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
lr Map k a
r
          Ordering
GT -> case Size -> Map k a -> StrictPair (Map k a) (Map k a)
go (Size
i forall a. Num a => a -> a -> a
- Size
sizeL forall a. Num a => a -> a -> a
- Size
1) Map k a
r of
                  Map k a
rl :*: Map k a
rr -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
rl forall a b. a -> b -> StrictPair a b
:*: Map k a
rr
          Ordering
EQ -> Map k a
l forall a b. a -> b -> StrictPair a b
:*: forall k a. k -> a -> Map k a -> Map k a
insertMin k
kx a
x Map k a
r
      where sizeL :: Size
sizeL = forall k a. Map k a -> Size
size Map k a
l

-- | \(O(\log n)\). Update the element at /index/, i.e. by its zero-based index in
-- the sequence sorted by keys. If the /index/ is out of range (less than zero,
-- greater or equal to 'size' of the map), 'error' is called.
--
-- > updateAt (\ _ _ -> Just "x") 0    (fromList [(5,"a"), (3,"b")]) == fromList [(3, "x"), (5, "a")]
-- > updateAt (\ _ _ -> Just "x") 1    (fromList [(5,"a"), (3,"b")]) == fromList [(3, "b"), (5, "x")]
-- > updateAt (\ _ _ -> Just "x") 2    (fromList [(5,"a"), (3,"b")])    Error: index out of range
-- > updateAt (\ _ _ -> Just "x") (-1) (fromList [(5,"a"), (3,"b")])    Error: index out of range
-- > updateAt (\_ _  -> Nothing)  0    (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
-- > updateAt (\_ _  -> Nothing)  1    (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
-- > updateAt (\_ _  -> Nothing)  2    (fromList [(5,"a"), (3,"b")])    Error: index out of range
-- > updateAt (\_ _  -> Nothing)  (-1) (fromList [(5,"a"), (3,"b")])    Error: index out of range

updateAt :: (k -> a -> Maybe a) -> Int -> Map k a -> Map k a
updateAt :: forall k a. (k -> a -> Maybe a) -> Size -> Map k a -> Map k a
updateAt k -> a -> Maybe a
f !Size
i Map k a
t =
  case Map k a
t of
    Map k a
Tip -> forall a. HasCallStack => [Char] -> a
error [Char]
"Map.updateAt: index out of range"
    Bin Size
sx k
kx a
x Map k a
l Map k a
r -> case forall a. Ord a => a -> a -> Ordering
compare Size
i Size
sizeL of
      Ordering
LT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
kx a
x (forall k a. (k -> a -> Maybe a) -> Size -> Map k a -> Map k a
updateAt k -> a -> Maybe a
f Size
i Map k a
l) Map k a
r
      Ordering
GT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
kx a
x Map k a
l (forall k a. (k -> a -> Maybe a) -> Size -> Map k a -> Map k a
updateAt k -> a -> Maybe a
f (Size
iforall a. Num a => a -> a -> a
-Size
sizeLforall a. Num a => a -> a -> a
-Size
1) Map k a
r)
      Ordering
EQ -> case k -> a -> Maybe a
f k
kx a
x of
              Just a
x' -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x' Map k a
l Map k a
r
              Maybe a
Nothing -> forall k a. Map k a -> Map k a -> Map k a
glue Map k a
l Map k a
r
      where
        sizeL :: Size
sizeL = forall k a. Map k a -> Size
size Map k a
l

-- | \(O(\log n)\). Delete the element at /index/, i.e. by its zero-based index in
-- the sequence sorted by keys. If the /index/ is out of range (less than zero,
-- greater or equal to 'size' of the map), 'error' is called.
--
-- > deleteAt 0  (fromList [(5,"a"), (3,"b")]) == singleton 5 "a"
-- > deleteAt 1  (fromList [(5,"a"), (3,"b")]) == singleton 3 "b"
-- > deleteAt 2 (fromList [(5,"a"), (3,"b")])     Error: index out of range
-- > deleteAt (-1) (fromList [(5,"a"), (3,"b")])  Error: index out of range

deleteAt :: Int -> Map k a -> Map k a
deleteAt :: forall k a. Size -> Map k a -> Map k a
deleteAt !Size
i Map k a
t =
  case Map k a
t of
    Map k a
Tip -> forall a. HasCallStack => [Char] -> a
error [Char]
"Map.deleteAt: index out of range"
    Bin Size
_ k
kx a
x Map k a
l Map k a
r -> case forall a. Ord a => a -> a -> Ordering
compare Size
i Size
sizeL of
      Ordering
LT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
kx a
x (forall k a. Size -> Map k a -> Map k a
deleteAt Size
i Map k a
l) Map k a
r
      Ordering
GT -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
kx a
x Map k a
l (forall k a. Size -> Map k a -> Map k a
deleteAt (Size
iforall a. Num a => a -> a -> a
-Size
sizeLforall a. Num a => a -> a -> a
-Size
1) Map k a
r)
      Ordering
EQ -> forall k a. Map k a -> Map k a -> Map k a
glue Map k a
l Map k a
r
      where
        sizeL :: Size
sizeL = forall k a. Map k a -> Size
size Map k a
l


{--------------------------------------------------------------------
  Minimal, Maximal
--------------------------------------------------------------------}

lookupMinSure :: k -> a -> Map k a -> (k, a)
lookupMinSure :: forall k a. k -> a -> Map k a -> (k, a)
lookupMinSure k
k a
a Map k a
Tip = (k
k, a
a)
lookupMinSure k
_ a
_ (Bin Size
_ k
k a
a Map k a
l Map k a
_) = forall k a. k -> a -> Map k a -> (k, a)
lookupMinSure k
k a
a Map k a
l

-- | \(O(\log n)\). The minimal key of the map. Returns 'Nothing' if the map is empty.
--
-- > lookupMin (fromList [(5,"a"), (3,"b")]) == Just (3,"b")
-- > lookupMin empty = Nothing
--
-- @since 0.5.9

lookupMin :: Map k a -> Maybe (k,a)
lookupMin :: forall k a. Map k a -> Maybe (k, a)
lookupMin Map k a
Tip = forall a. Maybe a
Nothing
lookupMin (Bin Size
_ k
k a
x Map k a
l Map k a
_) = forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$! forall k a. k -> a -> Map k a -> (k, a)
lookupMinSure k
k a
x Map k a
l

-- | \(O(\log n)\). The minimal key of the map. Calls 'error' if the map is empty.
--
-- > findMin (fromList [(5,"a"), (3,"b")]) == (3,"b")
-- > findMin empty                            Error: empty map has no minimal element

findMin :: Map k a -> (k,a)
findMin :: forall k a. Map k a -> (k, a)
findMin Map k a
t
  | Just (k, a)
r <- forall k a. Map k a -> Maybe (k, a)
lookupMin Map k a
t = (k, a)
r
  | Bool
otherwise = forall a. HasCallStack => [Char] -> a
error [Char]
"Map.findMin: empty map has no minimal element"

lookupMaxSure :: k -> a -> Map k a -> (k, a)
lookupMaxSure :: forall k a. k -> a -> Map k a -> (k, a)
lookupMaxSure k
k a
a Map k a
Tip = (k
k, a
a)
lookupMaxSure k
_ a
_ (Bin Size
_ k
k a
a Map k a
_ Map k a
r) = forall k a. k -> a -> Map k a -> (k, a)
lookupMaxSure k
k a
a Map k a
r

-- | \(O(\log n)\). The maximal key of the map. Returns 'Nothing' if the map is empty.
--
-- > lookupMax (fromList [(5,"a"), (3,"b")]) == Just (5,"a")
-- > lookupMax empty = Nothing
--
-- @since 0.5.9

lookupMax :: Map k a -> Maybe (k, a)
lookupMax :: forall k a. Map k a -> Maybe (k, a)
lookupMax Map k a
Tip = forall a. Maybe a
Nothing
lookupMax (Bin Size
_ k
k a
x Map k a
_ Map k a
r) = forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$! forall k a. k -> a -> Map k a -> (k, a)
lookupMaxSure k
k a
x Map k a
r

-- | \(O(\log n)\). The maximal key of the map. Calls 'error' if the map is empty.
--
-- > findMax (fromList [(5,"a"), (3,"b")]) == (5,"a")
-- > findMax empty                            Error: empty map has no maximal element

findMax :: Map k a -> (k,a)
findMax :: forall k a. Map k a -> (k, a)
findMax Map k a
t
  | Just (k, a)
r <- forall k a. Map k a -> Maybe (k, a)
lookupMax Map k a
t = (k, a)
r
  | Bool
otherwise = forall a. HasCallStack => [Char] -> a
error [Char]
"Map.findMax: empty map has no maximal element"

-- | \(O(\log n)\). Delete the minimal key. Returns an empty map if the map is empty.
--
-- > deleteMin (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(5,"a"), (7,"c")]
-- > deleteMin empty == empty

deleteMin :: Map k a -> Map k a
deleteMin :: forall k a. Map k a -> Map k a
deleteMin (Bin Size
_ k
_  a
_ Map k a
Tip Map k a
r)  = Map k a
r
deleteMin (Bin Size
_ k
kx a
x Map k a
l Map k a
r)    = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
kx a
x (forall k a. Map k a -> Map k a
deleteMin Map k a
l) Map k a
r
deleteMin Map k a
Tip                 = forall k a. Map k a
Tip

-- | \(O(\log n)\). Delete the maximal key. Returns an empty map if the map is empty.
--
-- > deleteMax (fromList [(5,"a"), (3,"b"), (7,"c")]) == fromList [(3,"b"), (5,"a")]
-- > deleteMax empty == empty

deleteMax :: Map k a -> Map k a
deleteMax :: forall k a. Map k a -> Map k a
deleteMax (Bin Size
_ k
_  a
_ Map k a
l Map k a
Tip)  = Map k a
l
deleteMax (Bin Size
_ k
kx a
x Map k a
l Map k a
r)    = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
kx a
x Map k a
l (forall k a. Map k a -> Map k a
deleteMax Map k a
r)
deleteMax Map k a
Tip                 = forall k a. Map k a
Tip

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

updateMin :: (a -> Maybe a) -> Map k a -> Map k a
updateMin :: forall a k. (a -> Maybe a) -> Map k a -> Map k a
updateMin a -> Maybe a
f Map k a
m
  = forall k a. (k -> a -> Maybe a) -> Map k a -> Map k a
updateMinWithKey (\k
_ a
x -> a -> Maybe a
f a
x) Map k a
m

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

updateMax :: (a -> Maybe a) -> Map k a -> Map k a
updateMax :: forall a k. (a -> Maybe a) -> Map k a -> Map k a
updateMax a -> Maybe a
f Map k a
m
  = forall k a. (k -> a -> Maybe a) -> Map k a -> Map k a
updateMaxWithKey (\k
_ a
x -> a -> Maybe a
f a
x) Map k a
m


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

updateMinWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
updateMinWithKey :: forall k a. (k -> a -> Maybe a) -> Map k a -> Map k a
updateMinWithKey k -> a -> Maybe a
_ Map k a
Tip                 = forall k a. Map k a
Tip
updateMinWithKey k -> a -> Maybe a
f (Bin Size
sx k
kx a
x Map k a
Tip Map k a
r) = case k -> a -> Maybe a
f k
kx a
x of
                                           Maybe a
Nothing -> Map k a
r
                                           Just a
x' -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x' forall k a. Map k a
Tip Map k a
r
updateMinWithKey k -> a -> Maybe a
f (Bin Size
_ k
kx a
x Map k a
l Map k a
r)    = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
kx a
x (forall k a. (k -> a -> Maybe a) -> Map k a -> Map k a
updateMinWithKey k -> a -> Maybe a
f Map k a
l) Map k a
r

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

updateMaxWithKey :: (k -> a -> Maybe a) -> Map k a -> Map k a
updateMaxWithKey :: forall k a. (k -> a -> Maybe a) -> Map k a -> Map k a
updateMaxWithKey k -> a -> Maybe a
_ Map k a
Tip                 = forall k a. Map k a
Tip
updateMaxWithKey k -> a -> Maybe a
f (Bin Size
sx k
kx a
x Map k a
l Map k a
Tip) = case k -> a -> Maybe a
f k
kx a
x of
                                           Maybe a
Nothing -> Map k a
l
                                           Just a
x' -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
x' Map k a
l forall k a. Map k a
Tip
updateMaxWithKey k -> a -> Maybe a
f (Bin Size
_ k
kx a
x Map k a
l Map k a
r)    = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
kx a
x Map k a
l (forall k a. (k -> a -> Maybe a) -> Map k a -> Map k a
updateMaxWithKey k -> a -> Maybe a
f Map k a
r)

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

minViewWithKey :: Map k a -> Maybe ((k,a), Map k a)
minViewWithKey :: forall k a. Map k a -> Maybe ((k, a), Map k a)
minViewWithKey Map k a
Tip = forall a. Maybe a
Nothing
minViewWithKey (Bin Size
_ k
k a
x Map k a
l Map k a
r) = forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$
  case forall k a. k -> a -> Map k a -> Map k a -> MinView k a
minViewSure k
k a
x Map k a
l Map k a
r of
    MinView k
km a
xm Map k a
t -> ((k
km, a
xm), Map k a
t)
-- We inline this to give GHC the best possible chance of getting
-- rid of the Maybe and pair constructors, as well as the thunk under
-- the Just.
{-# INLINE minViewWithKey #-}

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

maxViewWithKey :: Map k a -> Maybe ((k,a), Map k a)
maxViewWithKey :: forall k a. Map k a -> Maybe ((k, a), Map k a)
maxViewWithKey Map k a
Tip = forall a. Maybe a
Nothing
maxViewWithKey (Bin Size
_ k
k a
x Map k a
l Map k a
r) = forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$
  case forall k a. k -> a -> Map k a -> Map k a -> MaxView k a
maxViewSure k
k a
x Map k a
l Map k a
r of
    MaxView k
km a
xm Map k a
t -> ((k
km, a
xm), Map k a
t)
-- See note on inlining at minViewWithKey
{-# INLINE maxViewWithKey #-}

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

minView :: Map k a -> Maybe (a, Map k a)
minView :: forall k a. Map k a -> Maybe (a, Map k a)
minView Map k a
t = case forall k a. Map k a -> Maybe ((k, a), Map k a)
minViewWithKey Map k a
t of
              Maybe ((k, a), Map k a)
Nothing -> forall a. Maybe a
Nothing
              Just ~((k
_, a
x), Map k a
t') -> forall a. a -> Maybe a
Just (a
x, Map k a
t')

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

maxView :: Map k a -> Maybe (a, Map k a)
maxView :: forall k a. Map k a -> Maybe (a, Map k a)
maxView Map k a
t = case forall k a. Map k a -> Maybe ((k, a), Map k a)
maxViewWithKey Map k a
t of
              Maybe ((k, a), Map k a)
Nothing -> forall a. Maybe a
Nothing
              Just ~((k
_, a
x), Map k a
t') -> forall a. a -> Maybe a
Just (a
x, Map k a
t')

{--------------------------------------------------------------------
  Union.
--------------------------------------------------------------------}
-- | The union of a list of maps:
--   (@'unions' == 'Prelude.foldl' 'union' 'empty'@).
--
-- > 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, Ord k) => f (Map k a) -> Map k a
unions :: forall (f :: * -> *) k a.
(Foldable f, Ord k) =>
f (Map k a) -> Map k a
unions f (Map k a)
ts
  = forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' forall k v. Ord k => Map k v -> Map k v -> Map k v
union forall k a. Map k a
empty f (Map k a)
ts
#if __GLASGOW_HASKELL__
{-# INLINABLE unions #-}
#endif

-- | The union of a list of maps, with a combining operation:
--   (@'unionsWith' f == 'Prelude.foldl' ('unionWith' f) 'empty'@).
--
-- > 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, Ord k) => (a->a->a) -> f (Map k a) -> Map k a
unionsWith :: forall (f :: * -> *) k a.
(Foldable f, Ord k) =>
(a -> a -> a) -> f (Map k a) -> Map k a
unionsWith a -> a -> a
f f (Map k a)
ts
  = forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' (forall k a. Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWith a -> a -> a
f) forall k a. Map k a
empty f (Map k a)
ts
#if __GLASGOW_HASKELL__
{-# INLINABLE unionsWith #-}
#endif

-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\).
-- The expression (@'union' t1 t2@) takes the left-biased union of @t1@ and @t2@.
-- It prefers @t1@ 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 :: Ord k => Map k a -> Map k a -> Map k a
union :: forall k v. Ord k => Map k v -> Map k v -> Map k v
union Map k a
t1 Map k a
Tip  = Map k a
t1
union Map k a
t1 (Bin Size
_ k
k a
x Map k a
Tip Map k a
Tip) = forall k a. Ord k => k -> a -> Map k a -> Map k a
insertR k
k a
x Map k a
t1
union (Bin Size
_ k
k a
x Map k a
Tip Map k a
Tip) Map k a
t2 = forall k a. Ord k => k -> a -> Map k a -> Map k a
insert k
k a
x Map k a
t2
union Map k a
Tip Map k a
t2 = Map k a
t2
union t1 :: Map k a
t1@(Bin Size
_ k
k1 a
x1 Map k a
l1 Map k a
r1) Map k a
t2 = case forall k a. Ord k => k -> Map k a -> (Map k a, Map k a)
split k
k1 Map k a
t2 of
  (Map k a
l2, Map k a
r2) | Map k a
l1l2 forall a. a -> a -> Bool
`ptrEq` Map k a
l1 Bool -> Bool -> Bool
&& Map k a
r1r2 forall a. a -> a -> Bool
`ptrEq` Map k a
r1 -> Map k a
t1
           | Bool
otherwise -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
k1 a
x1 Map k a
l1l2 Map k a
r1r2
           where !l1l2 :: Map k a
l1l2 = forall k v. Ord k => Map k v -> Map k v -> Map k v
union Map k a
l1 Map k a
l2
                 !r1r2 :: Map k a
r1r2 = forall k v. Ord k => Map k v -> Map k v -> Map k v
union Map k a
r1 Map k a
r2
#if __GLASGOW_HASKELL__
{-# INLINABLE union #-}
#endif

{--------------------------------------------------------------------
  Union with a combining function
--------------------------------------------------------------------}
-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). Union with a combining function.
--
-- > unionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "aA"), (7, "C")]
--
-- Also see the performance note on 'fromListWith'.

unionWith :: Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a
-- QuickCheck says pointer equality never happens here.
unionWith :: forall k a. Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWith a -> a -> a
_f Map k a
t1 Map k a
Tip = Map k a
t1
unionWith a -> a -> a
f Map k a
t1 (Bin Size
_ k
k a
x Map k a
Tip Map k a
Tip) = forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithR a -> a -> a
f k
k a
x Map k a
t1
unionWith a -> a -> a
f (Bin Size
_ k
k a
x Map k a
Tip Map k a
Tip) Map k a
t2 = forall k a. Ord k => (a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWith a -> a -> a
f k
k a
x Map k a
t2
unionWith a -> a -> a
_f Map k a
Tip Map k a
t2 = Map k a
t2
unionWith a -> a -> a
f (Bin Size
_ k
k1 a
x1 Map k a
l1 Map k a
r1) Map k a
t2 = case forall k a. Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)
splitLookup k
k1 Map k a
t2 of
  (Map k a
l2, Maybe a
mb, Map k a
r2) -> case Maybe a
mb of
      Maybe a
Nothing -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
k1 a
x1 Map k a
l1l2 Map k a
r1r2
      Just a
x2 -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
k1 (a -> a -> a
f a
x1 a
x2) Map k a
l1l2 Map k a
r1r2
    where !l1l2 :: Map k a
l1l2 = forall k a. Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWith a -> a -> a
f Map k a
l1 Map k a
l2
          !r1r2 :: Map k a
r1r2 = forall k a. Ord k => (a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWith a -> a -> a
f Map k a
r1 Map k a
r2
#if __GLASGOW_HASKELL__
{-# INLINABLE unionWith #-}
#endif

-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\).
-- Union with a combining function.
--
-- > let f key left_value right_value = (show key) ++ ":" ++ left_value ++ "|" ++ right_value
-- > unionWithKey f (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == fromList [(3, "b"), (5, "5:a|A"), (7, "C")]
--
-- Also see the performance note on 'fromListWith'.

unionWithKey :: Ord k => (k -> a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWithKey :: forall k a.
Ord k =>
(k -> a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWithKey k -> a -> a -> a
_f Map k a
t1 Map k a
Tip = Map k a
t1
unionWithKey k -> a -> a -> a
f Map k a
t1 (Bin Size
_ k
k a
x Map k a
Tip Map k a
Tip) = forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKeyR k -> a -> a -> a
f k
k a
x Map k a
t1
unionWithKey k -> a -> a -> a
f (Bin Size
_ k
k a
x Map k a
Tip Map k a
Tip) Map k a
t2 = forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKey k -> a -> a -> a
f k
k a
x Map k a
t2
unionWithKey k -> a -> a -> a
_f Map k a
Tip Map k a
t2 = Map k a
t2
unionWithKey k -> a -> a -> a
f (Bin Size
_ k
k1 a
x1 Map k a
l1 Map k a
r1) Map k a
t2 = case forall k a. Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)
splitLookup k
k1 Map k a
t2 of
  (Map k a
l2, Maybe a
mb, Map k a
r2) -> case Maybe a
mb of
      Maybe a
Nothing -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
k1 a
x1 Map k a
l1l2 Map k a
r1r2
      Just a
x2 -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
k1 (k -> a -> a -> a
f k
k1 a
x1 a
x2) Map k a
l1l2 Map k a
r1r2
    where !l1l2 :: Map k a
l1l2 = forall k a.
Ord k =>
(k -> a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWithKey k -> a -> a -> a
f Map k a
l1 Map k a
l2
          !r1r2 :: Map k a
r1r2 = forall k a.
Ord k =>
(k -> a -> a -> a) -> Map k a -> Map k a -> Map k a
unionWithKey k -> a -> a -> a
f Map k a
r1 Map k a
r2
#if __GLASGOW_HASKELL__
{-# INLINABLE unionWithKey #-}
#endif

{--------------------------------------------------------------------
  Difference
--------------------------------------------------------------------}

-- We don't currently attempt to use any pointer equality tricks for
-- 'difference'. To do so, we'd have to match on the first argument
-- and split the second. Unfortunately, the proof of the time bound
-- relies on doing it the way we do, and it's not clear whether that
-- bound holds the other way.

-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). Difference of two maps.
-- Return elements of the first map not existing in the second map.
--
-- > difference (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 3 "b"

difference :: Ord k => Map k a -> Map k b -> Map k a
difference :: forall k a b. Ord k => Map k a -> Map k b -> Map k a
difference Map k a
Tip Map k b
_   = forall k a. Map k a
Tip
difference Map k a
t1 Map k b
Tip  = Map k a
t1
difference Map k a
t1 (Bin Size
_ k
k b
_ Map k b
l2 Map k b
r2) = case forall k a. Ord k => k -> Map k a -> (Map k a, Map k a)
split k
k Map k a
t1 of
  (Map k a
l1, Map k a
r1)
    | forall k a. Map k a -> Size
size Map k a
l1l2 forall a. Num a => a -> a -> a
+ forall k a. Map k a -> Size
size Map k a
r1r2 forall a. Eq a => a -> a -> Bool
== forall k a. Map k a -> Size
size Map k a
t1 -> Map k a
t1
    | Bool
otherwise -> forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
l1l2 Map k a
r1r2
    where
      !l1l2 :: Map k a
l1l2 = forall k a b. Ord k => Map k a -> Map k b -> Map k a
difference Map k a
l1 Map k b
l2
      !r1r2 :: Map k a
r1r2 = forall k a b. Ord k => Map k a -> Map k b -> Map k a
difference Map k a
r1 Map k b
r2
#if __GLASGOW_HASKELL__
{-# INLINABLE difference #-}
#endif

-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). Remove all keys in a 'Set' from a 'Map'.
--
-- @
-- m \`withoutKeys\` s = 'filterWithKey' (\\k _ -> k ``Set.notMember`` s) m
-- m \`withoutKeys\` s = m ``difference`` 'fromSet' (const ()) s
-- @
--
-- @since 0.5.8

withoutKeys :: Ord k => Map k a -> Set k -> Map k a
withoutKeys :: forall k a. Ord k => Map k a -> Set k -> Map k a
withoutKeys Map k a
Tip Set k
_ = forall k a. Map k a
Tip
withoutKeys Map k a
m Set k
Set.Tip = Map k a
m
withoutKeys Map k a
m (Set.Bin Size
_ k
k Set k
ls Set k
rs) = case forall k a. Ord k => k -> Map k a -> (Map k a, Bool, Map k a)
splitMember k
k Map k a
m of
  (Map k a
lm, Bool
b, Map k a
rm)
     | Bool -> Bool
not Bool
b Bool -> Bool -> Bool
&& Map k a
lm' forall a. a -> a -> Bool
`ptrEq` Map k a
lm Bool -> Bool -> Bool
&& Map k a
rm' forall a. a -> a -> Bool
`ptrEq` Map k a
rm -> Map k a
m
     | Bool
otherwise -> forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
lm' Map k a
rm'
     where
       !lm' :: Map k a
lm' = forall k a. Ord k => Map k a -> Set k -> Map k a
withoutKeys Map k a
lm Set k
ls
       !rm' :: Map k a
rm' = forall k a. Ord k => Map k a -> Set k -> Map k a
withoutKeys Map k a
rm Set k
rs
#if __GLASGOW_HASKELL__
{-# INLINABLE withoutKeys #-}
#endif

-- | \(O(n+m)\). Difference with a combining function.
-- When two equal keys are
-- encountered, the combining function is applied to the values of these keys.
-- 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 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 :: Ord k => (a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
differenceWith :: forall k a b.
Ord k =>
(a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
differenceWith a -> b -> Maybe a
f = forall k a c b.
Ord k =>
SimpleWhenMissing k a c
-> SimpleWhenMissing k b c
-> SimpleWhenMatched k a b c
-> Map k a
-> Map k b
-> Map k c
merge forall (f :: * -> *) k x. Applicative f => WhenMissing f k x x
preserveMissing forall (f :: * -> *) k x y. Applicative f => WhenMissing f k x y
dropMissing forall a b. (a -> b) -> a -> b
$
       forall (f :: * -> *) k x y z.
Applicative f =>
(k -> x -> y -> Maybe z) -> WhenMatched f k x y z
zipWithMaybeMatched (\k
_ a
x b
y -> a -> b -> Maybe a
f a
x b
y)
#if __GLASGOW_HASKELL__
{-# INLINABLE differenceWith #-}
#endif

-- | \(O(n+m)\). 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 :: Ord k => (k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
differenceWithKey :: forall k a b.
Ord k =>
(k -> a -> b -> Maybe a) -> Map k a -> Map k b -> Map k a
differenceWithKey k -> a -> b -> Maybe a
f =
  forall k a c b.
Ord k =>
SimpleWhenMissing k a c
-> SimpleWhenMissing k b c
-> SimpleWhenMatched k a b c
-> Map k a
-> Map k b
-> Map k c
merge forall (f :: * -> *) k x. Applicative f => WhenMissing f k x x
preserveMissing forall (f :: * -> *) k x y. Applicative f => WhenMissing f k x y
dropMissing (forall (f :: * -> *) k x y z.
Applicative f =>
(k -> x -> y -> Maybe z) -> WhenMatched f k x y z
zipWithMaybeMatched k -> a -> b -> Maybe a
f)
#if __GLASGOW_HASKELL__
{-# INLINABLE differenceWithKey #-}
#endif


{--------------------------------------------------------------------
  Intersection
--------------------------------------------------------------------}
-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). Intersection of two maps.
-- Return data in the first map for the keys existing in both maps.
-- (@'intersection' m1 m2 == 'intersectionWith' 'const' m1 m2@).
--
-- > intersection (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "a"

intersection :: Ord k => Map k a -> Map k b -> Map k a
intersection :: forall k a b. Ord k => Map k a -> Map k b -> Map k a
intersection Map k a
Tip Map k b
_ = forall k a. Map k a
Tip
intersection Map k a
_ Map k b
Tip = forall k a. Map k a
Tip
intersection t1 :: Map k a
t1@(Bin Size
_ k
k a
x Map k a
l1 Map k a
r1) Map k b
t2
  | Bool
mb = if Map k a
l1l2 forall a. a -> a -> Bool
`ptrEq` Map k a
l1 Bool -> Bool -> Bool
&& Map k a
r1r2 forall a. a -> a -> Bool
`ptrEq` Map k a
r1
         then Map k a
t1
         else forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
k a
x Map k a
l1l2 Map k a
r1r2
  | Bool
otherwise = forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
l1l2 Map k a
r1r2
  where
    !(Map k b
l2, Bool
mb, Map k b
r2) = forall k a. Ord k => k -> Map k a -> (Map k a, Bool, Map k a)
splitMember k
k Map k b
t2
    !l1l2 :: Map k a
l1l2 = forall k a b. Ord k => Map k a -> Map k b -> Map k a
intersection Map k a
l1 Map k b
l2
    !r1r2 :: Map k a
r1r2 = forall k a b. Ord k => Map k a -> Map k b -> Map k a
intersection Map k a
r1 Map k b
r2
#if __GLASGOW_HASKELL__
{-# INLINABLE intersection #-}
#endif

-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). Restrict a 'Map' to only those keys
-- found in a 'Set'.
--
-- @
-- m \`restrictKeys\` s = 'filterWithKey' (\\k _ -> k ``Set.member`` s) m
-- m \`restrictKeys\` s = m ``intersection`` 'fromSet' (const ()) s
-- @
--
-- @since 0.5.8
restrictKeys :: Ord k => Map k a -> Set k -> Map k a
restrictKeys :: forall k a. Ord k => Map k a -> Set k -> Map k a
restrictKeys Map k a
Tip Set k
_ = forall k a. Map k a
Tip
restrictKeys Map k a
_ Set k
Set.Tip = forall k a. Map k a
Tip
restrictKeys m :: Map k a
m@(Bin Size
_ k
k a
x Map k a
l1 Map k a
r1) Set k
s
  | Bool
b = if Map k a
l1l2 forall a. a -> a -> Bool
`ptrEq` Map k a
l1 Bool -> Bool -> Bool
&& Map k a
r1r2 forall a. a -> a -> Bool
`ptrEq` Map k a
r1
        then Map k a
m
        else forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
k a
x Map k a
l1l2 Map k a
r1r2
  | Bool
otherwise = forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
l1l2 Map k a
r1r2
  where
    !(Set k
l2, Bool
b, Set k
r2) = forall a. Ord a => a -> Set a -> (Set a, Bool, Set a)
Set.splitMember k
k Set k
s
    !l1l2 :: Map k a
l1l2 = forall k a. Ord k => Map k a -> Set k -> Map k a
restrictKeys Map k a
l1 Set k
l2
    !r1r2 :: Map k a
r1r2 = forall k a. Ord k => Map k a -> Set k -> Map k a
restrictKeys Map k a
r1 Set k
r2
#if __GLASGOW_HASKELL__
{-# INLINABLE restrictKeys #-}
#endif

-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). Intersection with a combining function.
--
-- > intersectionWith (++) (fromList [(5, "a"), (3, "b")]) (fromList [(5, "A"), (7, "C")]) == singleton 5 "aA"

intersectionWith :: Ord k => (a -> b -> c) -> Map k a -> Map k b -> Map k c
-- We have no hope of pointer equality tricks here because every single
-- element in the result will be a thunk.
intersectionWith :: forall k a b c.
Ord k =>
(a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWith a -> b -> c
_f Map k a
Tip Map k b
_ = forall k a. Map k a
Tip
intersectionWith a -> b -> c
_f Map k a
_ Map k b
Tip = forall k a. Map k a
Tip
intersectionWith a -> b -> c
f (Bin Size
_ k
k a
x1 Map k a
l1 Map k a
r1) Map k b
t2 = case Maybe b
mb of
    Just b
x2 -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
k (a -> b -> c
f a
x1 b
x2) Map k c
l1l2 Map k c
r1r2
    Maybe b
Nothing -> forall k a. Map k a -> Map k a -> Map k a
link2 Map k c
l1l2 Map k c
r1r2
  where
    !(Map k b
l2, Maybe b
mb, Map k b
r2) = forall k a. Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)
splitLookup k
k Map k b
t2
    !l1l2 :: Map k c
l1l2 = forall k a b c.
Ord k =>
(a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWith a -> b -> c
f Map k a
l1 Map k b
l2
    !r1r2 :: Map k c
r1r2 = forall k a b c.
Ord k =>
(a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWith a -> b -> c
f Map k a
r1 Map k b
r2
#if __GLASGOW_HASKELL__
{-# INLINABLE intersectionWith #-}
#endif

-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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 :: Ord k => (k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWithKey :: forall k a b c.
Ord k =>
(k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWithKey k -> a -> b -> c
_f Map k a
Tip Map k b
_ = forall k a. Map k a
Tip
intersectionWithKey k -> a -> b -> c
_f Map k a
_ Map k b
Tip = forall k a. Map k a
Tip
intersectionWithKey k -> a -> b -> c
f (Bin Size
_ k
k a
x1 Map k a
l1 Map k a
r1) Map k b
t2 = case Maybe b
mb of
    Just b
x2 -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
k (k -> a -> b -> c
f k
k a
x1 b
x2) Map k c
l1l2 Map k c
r1r2
    Maybe b
Nothing -> forall k a. Map k a -> Map k a -> Map k a
link2 Map k c
l1l2 Map k c
r1r2
  where
    !(Map k b
l2, Maybe b
mb, Map k b
r2) = forall k a. Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)
splitLookup k
k Map k b
t2
    !l1l2 :: Map k c
l1l2 = forall k a b c.
Ord k =>
(k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWithKey k -> a -> b -> c
f Map k a
l1 Map k b
l2
    !r1r2 :: Map k c
r1r2 = forall k a b c.
Ord k =>
(k -> a -> b -> c) -> Map k a -> Map k b -> Map k c
intersectionWithKey k -> a -> b -> c
f Map k a
r1 Map k b
r2
#if __GLASGOW_HASKELL__
{-# INLINABLE intersectionWithKey #-}
#endif

{--------------------------------------------------------------------
  Disjoint
--------------------------------------------------------------------}
-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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
--
-- @
-- xs ``disjoint`` ys = null (xs ``intersection`` ys)
-- @
--
-- @since 0.6.2.1

-- See 'Data.Set.Internal.isSubsetOfX' for some background
-- on the implementation design.
disjoint :: Ord k => Map k a -> Map k b -> Bool
disjoint :: forall k a b. Ord k => Map k a -> Map k b -> Bool
disjoint Map k a
Tip Map k b
_ = Bool
True
disjoint Map k a
_ Map k b
Tip = Bool
True
disjoint (Bin Size
1 k
k a
_ Map k a
_ Map k a
_) Map k b
t = k
k forall k a. Ord k => k -> Map k a -> Bool
`notMember` Map k b
t
disjoint (Bin Size
_ k
k a
_ Map k a
l Map k a
r) Map k b
t
  = Bool -> Bool
not Bool
found Bool -> Bool -> Bool
&& forall k a b. Ord k => Map k a -> Map k b -> Bool
disjoint Map k a
l Map k b
lt Bool -> Bool -> Bool
&& forall k a b. Ord k => Map k a -> Map k b -> Bool
disjoint Map k a
r Map k b
gt
  where
    (Map k b
lt,Bool
found,Map k b
gt) = forall k a. Ord k => k -> Map k a -> (Map k a, Bool, Map k a)
splitMember k
k Map k b
t

{--------------------------------------------------------------------
  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: \( O (n * \log(m)) \), 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.Map.Strict" exposed a version of
-- 'compose' that forced the values of the output 'Map'. This version does not
-- force these values.
--
-- @since 0.6.3.1
compose :: Ord b => Map b c -> Map a b -> Map a c
compose :: forall b c a. Ord b => Map b c -> Map a b -> Map a c
compose Map b c
bc !Map a b
ab
  | forall k a. Map k a -> Bool
null Map b c
bc = forall k a. Map k a
empty
  | Bool
otherwise = forall a b k. (a -> Maybe b) -> Map k a -> Map k b
mapMaybe (Map b c
bc forall k a. Ord k => Map k a -> k -> Maybe a
!?) Map a b
ab

-- | 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 @ k -> x -> f (Maybe z) @.
--
-- @since 0.5.9

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

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

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

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

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

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

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

-- | Map contravariantly over a @'WhenMatched' f k x _ z@.
--
-- @since 0.5.9
contramapSecondWhenMatched :: (b -> a)
                           -> WhenMatched f k x a z
                           -> WhenMatched f k x b z
contramapSecondWhenMatched :: forall b a (f :: * -> *) k x z.
(b -> a) -> WhenMatched f k x a z -> WhenMatched f k x b z
contramapSecondWhenMatched b -> a
f WhenMatched f k x a z
t = forall (f :: * -> *) k x y z.
(k -> x -> y -> f (Maybe z)) -> WhenMatched f k x y z
WhenMatched forall a b. (a -> b) -> a -> b
$
  \k
k x
x b
y -> forall (f :: * -> *) k x y z.
WhenMatched f k x y z -> k -> x -> y -> f (Maybe z)
runWhenMatched WhenMatched f k x a z
t k
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 k x z @ is an abstract representation
-- of a function of type @ k -> 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 k x y z @ is an abstract representation
-- of a function of type @ k -> x -> y -> f (Maybe z) @.
--
-- @since 0.5.9
newtype WhenMatched f k x y z = WhenMatched
  { forall (f :: * -> *) k x y z.
WhenMatched f k x y z -> k -> x -> y -> f (Maybe z)
matchedKey :: k -> x -> y -> f (Maybe z) }

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

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

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

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

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

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

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

-- | A tactic for dealing with keys present in both maps in 'merge'.
--
-- A tactic of type @ SimpleWhenMatched k x y z @ is an abstract representation
-- of a function of type @ k -> 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 :: (k -> x -> y -> z)
--                -> SimpleWhenMatched k x y z
-- @
--
-- @since 0.5.9
zipWithMatched :: Applicative f
               => (k -> x -> y -> z)
               -> WhenMatched f k x y z
zipWithMatched :: forall (f :: * -> *) k x y z.
Applicative f =>
(k -> x -> y -> z) -> WhenMatched f k x y z
zipWithMatched k -> x -> y -> z
f = forall (f :: * -> *) k x y z.
(k -> x -> y -> f (Maybe z)) -> WhenMatched f k x y z
WhenMatched forall a b. (a -> b) -> a -> b
$ \ k
k x
x y
y -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$ k -> x -> y -> z
f k
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
                => (k -> x -> y -> f z)
                -> WhenMatched f k x y z
zipWithAMatched :: forall (f :: * -> *) k x y z.
Applicative f =>
(k -> x -> y -> f z) -> WhenMatched f k x y z
zipWithAMatched k -> x -> y -> f z
f = forall (f :: * -> *) k x y z.
(k -> x -> y -> f (Maybe z)) -> WhenMatched f k x y z
WhenMatched forall a b. (a -> b) -> a -> b
$ \ k
k x
x y
y -> forall a. a -> Maybe a
Just forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> k -> x -> y -> f z
f k
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 :: (k -> x -> y -> Maybe z)
--                     -> SimpleWhenMatched k x y z
-- @
--
-- @since 0.5.9
zipWithMaybeMatched :: Applicative f
                    => (k -> x -> y -> Maybe z)
                    -> WhenMatched f k x y z
zipWithMaybeMatched :: forall (f :: * -> *) k x y z.
Applicative f =>
(k -> x -> y -> Maybe z) -> WhenMatched f k x y z
zipWithMaybeMatched k -> x -> y -> Maybe z
f = forall (f :: * -> *) k x y z.
(k -> x -> y -> f (Maybe z)) -> WhenMatched f k x y z
WhenMatched forall a b. (a -> b) -> a -> b
$ \ k
k x
x y
y -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$ k -> x -> y -> Maybe z
f k
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 :: (k -> x -> y -> f (Maybe z))
                     -> WhenMatched f k x y z
zipWithMaybeAMatched :: forall k x y (f :: * -> *) z.
(k -> x -> y -> f (Maybe z)) -> WhenMatched f k x y z
zipWithMaybeAMatched k -> x -> y -> f (Maybe z)
f = forall (f :: * -> *) k x y z.
(k -> x -> y -> f (Maybe z)) -> WhenMatched f k x y z
WhenMatched forall a b. (a -> b) -> a -> b
$ \ k
k x
x y
y -> k -> x -> y -> f (Maybe z)
f k
k x
x y
y
{-# INLINE zipWithMaybeAMatched #-}

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

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

-- | Force the entries whose keys are missing from
-- the other map and otherwise preserve them unchanged.
--
-- @
-- preserveMissing' :: SimpleWhenMissing k x x
-- @
--
-- prop> preserveMissing' = Merge.Lazy.mapMaybeMissing (\_ x -> Just $! x)
--
-- but @preserveMissing'@ is quite a bit faster.
--
-- @since 0.5.9
preserveMissing' :: Applicative f => WhenMissing f k x x
preserveMissing' :: forall (f :: * -> *) k x. Applicative f => WhenMissing f k x x
preserveMissing' = WhenMissing
  { missingSubtree :: Map k x -> f (Map k x)
missingSubtree = \Map k x
t -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$! forall k a. Map k a -> ()
forceTree Map k x
t seq :: forall a b. a -> b -> b
`seq` Map k x
t
  , missingKey :: k -> x -> f (Maybe x)
missingKey = \k
_ x
v -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$! forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$! x
v }
{-# INLINE preserveMissing' #-}

-- Force all the values in a tree.
forceTree :: Map k a -> ()
forceTree :: forall k a. Map k a -> ()
forceTree (Bin Size
_ k
_ a
v Map k a
l Map k a
r) = a
v seq :: forall a b. a -> b -> b
`seq` forall k a. Map k a -> ()
forceTree Map k a
l seq :: forall a b. a -> b -> b
`seq` forall k a. Map k a -> ()
forceTree Map k a
r seq :: forall a b. a -> b -> b
`seq` ()
forceTree Map k a
Tip = ()

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

-- | Filter the entries whose keys are missing from the other map.
--
-- @
-- filterMissing :: (k -> x -> Bool) -> SimpleWhenMissing k 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
              => (k -> x -> Bool) -> WhenMissing f k x x
filterMissing :: forall (f :: * -> *) k x.
Applicative f =>
(k -> x -> Bool) -> WhenMissing f k x x
filterMissing k -> x -> Bool
f = WhenMissing
  { missingSubtree :: Map k x -> f (Map k x)
missingSubtree = \Map k x
m -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$! forall k a. (k -> a -> Bool) -> Map k a -> Map k a
filterWithKey k -> x -> Bool
f Map k x
m
  , missingKey :: k -> x -> f (Maybe x)
missingKey = \k
k x
x -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$! if k -> x -> Bool
f k
k x
x then forall a. a -> Maybe a
Just x
x else forall a. Maybe a
Nothing }
{-# INLINE filterMissing #-}

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

-- | 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
                    => (k -> x -> f y) -> WhenMissing f k x y
traverseMissing :: forall (f :: * -> *) k x y.
Applicative f =>
(k -> x -> f y) -> WhenMissing f k x y
traverseMissing k -> x -> f y
f = WhenMissing
  { missingSubtree :: Map k x -> f (Map k y)
missingSubtree = forall (t :: * -> *) k a b.
Applicative t =>
(k -> a -> t b) -> Map k a -> t (Map k b)
traverseWithKey k -> x -> f y
f
  , missingKey :: k -> x -> f (Maybe y)
missingKey = \k
k x
x -> forall a. a -> Maybe a
Just forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> k -> x -> f y
f k
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
                      => (k -> x -> f (Maybe y)) -> WhenMissing f k x y
traverseMaybeMissing :: forall (f :: * -> *) k x y.
Applicative f =>
(k -> x -> f (Maybe y)) -> WhenMissing f k x y
traverseMaybeMissing k -> x -> f (Maybe y)
f = WhenMissing
  { missingSubtree :: Map k x -> f (Map k y)
missingSubtree = forall (f :: * -> *) k a b.
Applicative f =>
(k -> a -> f (Maybe b)) -> Map k a -> f (Map k b)
traverseMaybeWithKey k -> x -> f (Maybe y)
f
  , missingKey :: k -> x -> f (Maybe y)
missingKey = k -> x -> f (Maybe y)
f }
{-# INLINE traverseMaybeMissing #-}

-- | 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 preserveMissing dropMissing (zipWithMatched f)
-- prop> symmetricDifference = merge preserveMissing preserveMissing (zipWithMaybeMatched $ \ _ _ _ -> Nothing)
-- prop> mapEachPiece f g h = merge (mapMissing f) (mapMissing g) (zipWithMatched h)
--
-- @since 0.5.9
merge :: Ord k
             => SimpleWhenMissing k a c -- ^ What to do with keys in @m1@ but not @m2@
             -> SimpleWhenMissing k b c -- ^ What to do with keys in @m2@ but not @m1@
             -> SimpleWhenMatched k a b c -- ^ What to do with keys in both @m1@ and @m2@
             -> Map k a -- ^ Map @m1@
             -> Map k b -- ^ Map @m2@
             -> Map k c
merge :: forall k a c b.
Ord k =>
SimpleWhenMissing k a c
-> SimpleWhenMissing k b c
-> SimpleWhenMatched k a b c
-> Map k a
-> Map k b
-> Map k c
merge SimpleWhenMissing k a c
g1 SimpleWhenMissing k b c
g2 SimpleWhenMatched k a b c
f Map k a
m1 Map k b
m2 = forall a. Identity a -> a
runIdentity forall a b. (a -> b) -> a -> b
$
  forall (f :: * -> *) k a c b.
(Applicative f, Ord k) =>
WhenMissing f k a c
-> WhenMissing f k b c
-> WhenMatched f k a b c
-> Map k a
-> Map k b
-> f (Map k c)
mergeA SimpleWhenMissing k a c
g1 SimpleWhenMissing k b c
g2 SimpleWhenMatched k a b c
f Map k a
m1 Map k 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, Ord k)
  => WhenMissing f k a c -- ^ What to do with keys in @m1@ but not @m2@
  -> WhenMissing f k b c -- ^ What to do with keys in @m2@ but not @m1@
  -> WhenMatched f k a b c -- ^ What to do with keys in both @m1@ and @m2@
  -> Map k a -- ^ Map @m1@
  -> Map k b -- ^ Map @m2@
  -> f (Map k c)
mergeA :: forall (f :: * -> *) k a c b.
(Applicative f, Ord k) =>
WhenMissing f k a c
-> WhenMissing f k b c
-> WhenMatched f k a b c
-> Map k a
-> Map k b
-> f (Map k c)
mergeA
    WhenMissing{missingSubtree :: forall (f :: * -> *) k x y.
WhenMissing f k x y -> Map k x -> f (Map k y)
missingSubtree = Map k a -> f (Map k c)
g1t, missingKey :: forall (f :: * -> *) k x y.
WhenMissing f k x y -> k -> x -> f (Maybe y)
missingKey = k -> a -> f (Maybe c)
g1k}
    WhenMissing{missingSubtree :: forall (f :: * -> *) k x y.
WhenMissing f k x y -> Map k x -> f (Map k y)
missingSubtree = Map k b -> f (Map k c)
g2t}
    (WhenMatched k -> a -> b -> f (Maybe c)
f) = Map k a -> Map k b -> f (Map k c)
go
  where
    go :: Map k a -> Map k b -> f (Map k c)
go Map k a
t1 Map k b
Tip = Map k a -> f (Map k c)
g1t Map k a
t1
    go Map k a
Tip Map k b
t2 = Map k b -> f (Map k c)
g2t Map k b
t2
    go (Bin Size
_ k
kx a
x1 Map k a
l1 Map k a
r1) Map k b
t2 = case forall k a. Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)
splitLookup k
kx Map k b
t2 of
      (Map k b
l2, Maybe b
mx2, Map k b
r2) -> case Maybe b
mx2 of
          Maybe b
Nothing -> forall (f :: * -> *) a b c d.
Applicative f =>
(a -> b -> c -> d) -> f a -> f b -> f c -> f d
liftA3 (\Map k c
l' Maybe c
mx' Map k c
r' -> forall b a. b -> (a -> b) -> Maybe a -> b
maybe forall k a. Map k a -> Map k a -> Map k a
link2 (forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx) Maybe c
mx' Map k c
l' Map k c
r')
                        f (Map k c)
l1l2 (k -> a -> f (Maybe c)
g1k k
kx a
x1) f (Map k c)
r1r2
          Just b
x2 -> forall (f :: * -> *) a b c d.
Applicative f =>
(a -> b -> c -> d) -> f a -> f b -> f c -> f d
liftA3 (\Map k c
l' Maybe c
mx' Map k c
r' -> forall b a. b -> (a -> b) -> Maybe a -> b
maybe forall k a. Map k a -> Map k a -> Map k a
link2 (forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx) Maybe c
mx' Map k c
l' Map k c
r')
                        f (Map k c)
l1l2 (k -> a -> b -> f (Maybe c)
f k
kx a
x1 b
x2) f (Map k c)
r1r2
        where
          !l1l2 :: f (Map k c)
l1l2 = Map k a -> Map k b -> f (Map k c)
go Map k a
l1 Map k b
l2
          !r1r2 :: f (Map k c)
r1r2 = Map k a -> Map k b -> f (Map k c)
go Map k a
r1 Map k b
r2
{-# INLINE mergeA #-}


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

-- | \(O(n+m)\). An unsafe general combining function.
--
-- WARNING: This function can produce corrupt maps and its results
-- may depend on the internal structures of its inputs. Users should
-- prefer 'merge' or 'mergeA'.
--
-- When 'mergeWithKey' is given three arguments, it is inlined to the call
-- site. You should therefore use 'mergeWithKey' only to define 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
-- 'Map'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@,
-- @'filterWithKey' f@, or @'mapMaybeWithKey' f@ could be used for any @f@.

mergeWithKey :: Ord k
             => (k -> a -> b -> Maybe c)
             -> (Map k a -> Map k c)
             -> (Map k b -> Map k c)
             -> Map k a -> Map k b -> Map k c
mergeWithKey :: forall k a b c.
Ord k =>
(k -> a -> b -> Maybe c)
-> (Map k a -> Map k c)
-> (Map k b -> Map k c)
-> Map k a
-> Map k b
-> Map k c
mergeWithKey k -> a -> b -> Maybe c
f Map k a -> Map k c
g1 Map k b -> Map k c
g2 = Map k a -> Map k b -> Map k c
go
  where
    go :: Map k a -> Map k b -> Map k c
go Map k a
Tip Map k b
t2 = Map k b -> Map k c
g2 Map k b
t2
    go Map k a
t1 Map k b
Tip = Map k a -> Map k c
g1 Map k a
t1
    go (Bin Size
_ k
kx a
x Map k a
l1 Map k a
r1) Map k b
t2 =
      case Maybe b
found of
        Maybe b
Nothing -> case Map k a -> Map k c
g1 (forall k a. k -> a -> Map k a
singleton k
kx a
x) of
                     Map k c
Tip -> forall k a. Map k a -> Map k a -> Map k a
link2 Map k c
l' Map k c
r'
                     (Bin Size
_ k
_ c
x' Map k c
Tip Map k c
Tip) -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx c
x' Map k c
l' Map k c
r'
                     Map k c
_ -> forall a. HasCallStack => [Char] -> a
error [Char]
"mergeWithKey: Given function only1 does not fulfill required conditions (see documentation)"
        Just b
x2 -> case k -> a -> b -> Maybe c
f k
kx a
x b
x2 of
                     Maybe c
Nothing -> forall k a. Map k a -> Map k a -> Map k a
link2 Map k c
l' Map k c
r'
                     Just c
x' -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx c
x' Map k c
l' Map k c
r'
      where
        (Map k b
l2, Maybe b
found, Map k b
r2) = forall k a. Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)
splitLookup k
kx Map k b
t2
        l' :: Map k c
l' = Map k a -> Map k b -> Map k c
go Map k a
l1 Map k b
l2
        r' :: Map k c
r' = Map k a -> Map k b -> Map k c
go Map k a
r1 Map k b
r2
{-# INLINE mergeWithKey #-}

{--------------------------------------------------------------------
  Submap
--------------------------------------------------------------------}
-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\).
-- This function is defined as (@'isSubmapOf' = 'isSubmapOfBy' (==)@).
--
isSubmapOf :: (Ord k,Eq a) => Map k a -> Map k a -> Bool
isSubmapOf :: forall k a. (Ord k, Eq a) => Map k a -> Map k a -> Bool
isSubmapOf Map k a
m1 Map k a
m2 = forall k a b.
Ord k =>
(a -> b -> Bool) -> Map k a -> Map k b -> Bool
isSubmapOfBy forall a. Eq a => a -> a -> Bool
(==) Map k a
m1 Map k a
m2
#if __GLASGOW_HASKELL__
{-# INLINABLE isSubmapOf #-}
#endif

{- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\).
 The expression (@'isSubmapOfBy' f t1 t2@) returns 'True' if
 all keys in @t1@ are in tree @t2@, and when @f@ returns 'True' when
 applied to their respective values. For example, the following
 expressions are all 'True':

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

 But the following are all 'False':

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

 Note that @isSubmapOfBy (\_ _ -> True) m1 m2@ tests whether all the keys
 in @m1@ are also keys in @m2@.

-}
isSubmapOfBy :: Ord k => (a->b->Bool) -> Map k a -> Map k b -> Bool
isSubmapOfBy :: forall k a b.
Ord k =>
(a -> b -> Bool) -> Map k a -> Map k b -> Bool
isSubmapOfBy a -> b -> Bool
f Map k a
t1 Map k b
t2
  = forall k a. Map k a -> Size
size Map k a
t1 forall a. Ord a => a -> a -> Bool
<= forall k a. Map k a -> Size
size Map k b
t2 Bool -> Bool -> Bool
&& forall k a b.
Ord k =>
(a -> b -> Bool) -> Map k a -> Map k b -> Bool
submap' a -> b -> Bool
f Map k a
t1 Map k b
t2
#if __GLASGOW_HASKELL__
{-# INLINABLE isSubmapOfBy #-}
#endif

-- Test whether a map is a submap of another without the *initial*
-- size test. See Data.Set.Internal.isSubsetOfX for notes on
-- implementation and analysis.
submap' :: Ord a => (b -> c -> Bool) -> Map a b -> Map a c -> Bool
submap' :: forall k a b.
Ord k =>
(a -> b -> Bool) -> Map k a -> Map k b -> Bool
submap' b -> c -> Bool
_ Map a b
Tip Map a c
_ = Bool
True
submap' b -> c -> Bool
_ Map a b
_ Map a c
Tip = Bool
False
submap' b -> c -> Bool
f (Bin Size
1 a
kx b
x Map a b
_ Map a b
_) Map a c
t
  = case forall k a. Ord k => k -> Map k a -> Maybe a
lookup a
kx Map a c
t of
      Just c
y -> b -> c -> Bool
f b
x c
y
      Maybe c
Nothing -> Bool
False
submap' b -> c -> Bool
f (Bin Size
_ a
kx b
x Map a b
l Map a b
r) Map a c
t
  = case Maybe c
found of
      Maybe c
Nothing -> Bool
False
      Just c
y  -> b -> c -> Bool
f b
x c
y
                 Bool -> Bool -> Bool
&& forall k a. Map k a -> Size
size Map a b
l forall a. Ord a => a -> a -> Bool
<= forall k a. Map k a -> Size
size Map a c
lt Bool -> Bool -> Bool
&& forall k a. Map k a -> Size
size Map a b
r forall a. Ord a => a -> a -> Bool
<= forall k a. Map k a -> Size
size Map a c
gt
                 Bool -> Bool -> Bool
&& forall k a b.
Ord k =>
(a -> b -> Bool) -> Map k a -> Map k b -> Bool
submap' b -> c -> Bool
f Map a b
l Map a c
lt Bool -> Bool -> Bool
&& forall k a b.
Ord k =>
(a -> b -> Bool) -> Map k a -> Map k b -> Bool
submap' b -> c -> Bool
f Map a b
r Map a c
gt
  where
    (Map a c
lt,Maybe c
found,Map a c
gt) = forall k a. Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)
splitLookup a
kx Map a c
t
#if __GLASGOW_HASKELL__
{-# INLINABLE submap' #-}
#endif

-- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). Is this a proper submap? (ie. a submap but not equal).
-- Defined as (@'isProperSubmapOf' = 'isProperSubmapOfBy' (==)@).
isProperSubmapOf :: (Ord k,Eq a) => Map k a -> Map k a -> Bool
isProperSubmapOf :: forall k a. (Ord k, Eq a) => Map k a -> Map k a -> Bool
isProperSubmapOf Map k a
m1 Map k a
m2
  = forall k a b.
Ord k =>
(a -> b -> Bool) -> Map k a -> Map k b -> Bool
isProperSubmapOfBy forall a. Eq a => a -> a -> Bool
(==) Map k a
m1 Map k a
m2
#if __GLASGOW_HASKELL__
{-# INLINABLE isProperSubmapOf #-}
#endif

{- | \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr), \; 0 < m \leq n\). 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 :: Ord k => (a -> b -> Bool) -> Map k a -> Map k b -> Bool
isProperSubmapOfBy :: forall k a b.
Ord k =>
(a -> b -> Bool) -> Map k a -> Map k b -> Bool
isProperSubmapOfBy a -> b -> Bool
f Map k a
t1 Map k b
t2
  = forall k a. Map k a -> Size
size Map k a
t1 forall a. Ord a => a -> a -> Bool
< forall k a. Map k a -> Size
size Map k b
t2 Bool -> Bool -> Bool
&& forall k a b.
Ord k =>
(a -> b -> Bool) -> Map k a -> Map k b -> Bool
submap' a -> b -> Bool
f Map k a
t1 Map k b
t2
#if __GLASGOW_HASKELL__
{-# INLINABLE isProperSubmapOfBy #-}
#endif

{--------------------------------------------------------------------
  Filter and partition
--------------------------------------------------------------------}
-- | \(O(n)\). Filter all values that satisfy the 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) -> Map k a -> Map k a
filter :: forall a k. (a -> Bool) -> Map k a -> Map k a
filter a -> Bool
p Map k a
m
  = forall k a. (k -> a -> Bool) -> Map k a -> Map k a
filterWithKey (\k
_ a
x -> a -> Bool
p a
x) Map k a
m

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

filterWithKey :: (k -> a -> Bool) -> Map k a -> Map k a
filterWithKey :: forall k a. (k -> a -> Bool) -> Map k a -> Map k a
filterWithKey k -> a -> Bool
_ Map k a
Tip = forall k a. Map k a
Tip
filterWithKey k -> a -> Bool
p t :: Map k a
t@(Bin Size
_ k
kx a
x Map k a
l Map k a
r)
  | k -> a -> Bool
p k
kx a
x    = if Map k a
pl forall a. a -> a -> Bool
`ptrEq` Map k a
l Bool -> Bool -> Bool
&& Map k a
pr forall a. a -> a -> Bool
`ptrEq` Map k a
r
                then Map k a
t
                else forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
pl Map k a
pr
  | Bool
otherwise = forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
pl Map k a
pr
  where !pl :: Map k a
pl = forall k a. (k -> a -> Bool) -> Map k a -> Map k a
filterWithKey k -> a -> Bool
p Map k a
l
        !pr :: Map k a
pr = forall k a. (k -> a -> Bool) -> Map k a -> Map k a
filterWithKey k -> a -> Bool
p Map k a
r

-- | \(O(n)\). Filter keys and values using an 'Applicative'
-- predicate.
filterWithKeyA :: Applicative f => (k -> a -> f Bool) -> Map k a -> f (Map k a)
filterWithKeyA :: forall (f :: * -> *) k a.
Applicative f =>
(k -> a -> f Bool) -> Map k a -> f (Map k a)
filterWithKeyA k -> a -> f Bool
_ Map k a
Tip = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall k a. Map k a
Tip
filterWithKeyA k -> a -> f Bool
p t :: Map k a
t@(Bin Size
_ k
kx a
x Map k a
l Map k a
r) =
  forall (f :: * -> *) a b c d.
Applicative f =>
(a -> b -> c -> d) -> f a -> f b -> f c -> f d
liftA3 Bool -> Map k a -> Map k a -> Map k a
combine (k -> a -> f Bool
p k
kx a
x) (forall (f :: * -> *) k a.
Applicative f =>
(k -> a -> f Bool) -> Map k a -> f (Map k a)
filterWithKeyA k -> a -> f Bool
p Map k a
l) (forall (f :: * -> *) k a.
Applicative f =>
(k -> a -> f Bool) -> Map k a -> f (Map k a)
filterWithKeyA k -> a -> f Bool
p Map k a
r)
  where
    combine :: Bool -> Map k a -> Map k a -> Map k a
combine Bool
True Map k a
pl Map k a
pr
      | Map k a
pl forall a. a -> a -> Bool
`ptrEq` Map k a
l Bool -> Bool -> Bool
&& Map k a
pr forall a. a -> a -> Bool
`ptrEq` Map k a
r = Map k a
t
      | Bool
otherwise = forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
pl Map k a
pr
    combine Bool
False Map k a
pl Map k a
pr = forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
pl Map k a
pr

-- | \(O(\log n)\). Take while a predicate on the keys holds.
-- The user is responsible for ensuring that for all keys @j@ and @k@ in the map,
-- @j \< k ==\> p j \>= p k@. See note at 'spanAntitone'.
--
-- @
-- takeWhileAntitone p = 'fromDistinctAscList' . 'Data.List.takeWhile' (p . fst) . 'toList'
-- takeWhileAntitone p = 'filterWithKey' (\k _ -> p k)
-- @
--
-- @since 0.5.8

takeWhileAntitone :: (k -> Bool) -> Map k a -> Map k a
takeWhileAntitone :: forall k a. (k -> Bool) -> Map k a -> Map k a
takeWhileAntitone k -> Bool
_ Map k a
Tip = forall k a. Map k a
Tip
takeWhileAntitone k -> Bool
p (Bin Size
_ k
kx a
x Map k a
l Map k a
r)
  | k -> Bool
p k
kx = forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l (forall k a. (k -> Bool) -> Map k a -> Map k a
takeWhileAntitone k -> Bool
p Map k a
r)
  | Bool
otherwise = forall k a. (k -> Bool) -> Map k a -> Map k a
takeWhileAntitone k -> Bool
p Map k a
l

-- | \(O(\log n)\). Drop while a predicate on the keys holds.
-- The user is responsible for ensuring that for all keys @j@ and @k@ in the map,
-- @j \< k ==\> p j \>= p k@. See note at 'spanAntitone'.
--
-- @
-- dropWhileAntitone p = 'fromDistinctAscList' . 'Data.List.dropWhile' (p . fst) . 'toList'
-- dropWhileAntitone p = 'filterWithKey' (\\k _ -> not (p k))
-- @
--
-- @since 0.5.8

dropWhileAntitone :: (k -> Bool) -> Map k a -> Map k a
dropWhileAntitone :: forall k a. (k -> Bool) -> Map k a -> Map k a
dropWhileAntitone k -> Bool
_ Map k a
Tip = forall k a. Map k a
Tip
dropWhileAntitone k -> Bool
p (Bin Size
_ k
kx a
x Map k a
l Map k a
r)
  | k -> Bool
p k
kx = forall k a. (k -> Bool) -> Map k a -> Map k a
dropWhileAntitone k -> Bool
p Map k a
r
  | Bool
otherwise = forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x (forall k a. (k -> Bool) -> Map k a -> Map k a
dropWhileAntitone k -> Bool
p Map k a
l) Map k a
r

-- | \(O(\log n)\). Divide a map at the point where a predicate on the keys stops holding.
-- The user is responsible for ensuring that for all keys @j@ and @k@ in the map,
-- @j \< k ==\> p j \>= p k@.
--
-- @
-- spanAntitone p xs = ('takeWhileAntitone' p xs, 'dropWhileAntitone' p xs)
-- spanAntitone p xs = partitionWithKey (\\k _ -> p k) xs
-- @
--
-- Note: if @p@ is not actually antitone, then @spanAntitone@ will split the map
-- at some /unspecified/ point where the predicate switches from holding to not
-- holding (where the predicate is seen to hold before the first key and to fail
-- after the last key).
--
-- @since 0.5.8

spanAntitone :: (k -> Bool) -> Map k a -> (Map k a, Map k a)
spanAntitone :: forall k a. (k -> Bool) -> Map k a -> (Map k a, Map k a)
spanAntitone k -> Bool
p0 Map k a
m = forall a b. StrictPair a b -> (a, b)
toPair (forall {k} {a}.
(k -> Bool) -> Map k a -> StrictPair (Map k a) (Map k a)
go k -> Bool
p0 Map k a
m)
  where
    go :: (k -> Bool) -> Map k a -> StrictPair (Map k a) (Map k a)
go k -> Bool
_ Map k a
Tip = forall k a. Map k a
Tip forall a b. a -> b -> StrictPair a b
:*: forall k a. Map k a
Tip
    go k -> Bool
p (Bin Size
_ k
kx a
x Map k a
l Map k a
r)
      | k -> Bool
p k
kx = let Map k a
u :*: Map k a
v = (k -> Bool) -> Map k a -> StrictPair (Map k a) (Map k a)
go k -> Bool
p Map k a
r in forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
u forall a b. a -> b -> StrictPair a b
:*: Map k a
v
      | Bool
otherwise = let Map k a
u :*: Map k a
v = (k -> Bool) -> Map k a -> StrictPair (Map k a) (Map k a)
go k -> Bool
p Map k a
l in Map k a
u forall a b. a -> b -> StrictPair a b
:*: forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
v Map k a
r

-- | \(O(n)\). Partition the map according to a 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) -> Map k a -> (Map k a,Map k a)
partition :: forall a k. (a -> Bool) -> Map k a -> (Map k a, Map k a)
partition a -> Bool
p Map k a
m
  = forall k a. (k -> a -> Bool) -> Map k a -> (Map k a, Map k a)
partitionWithKey (\k
_ a
x -> a -> Bool
p a
x) Map k a
m

-- | \(O(n)\). Partition the map according to a 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 :: (k -> a -> Bool) -> Map k a -> (Map k a,Map k a)
partitionWithKey :: forall k a. (k -> a -> Bool) -> Map k a -> (Map k a, Map k a)
partitionWithKey k -> a -> Bool
p0 Map k a
t0 = forall a b. StrictPair a b -> (a, b)
toPair forall a b. (a -> b) -> a -> b
$ forall {k} {a}.
(k -> a -> Bool) -> Map k a -> StrictPair (Map k a) (Map k a)
go k -> a -> Bool
p0 Map k a
t0
  where
    go :: (k -> a -> Bool) -> Map k a -> StrictPair (Map k a) (Map k a)
go k -> a -> Bool
_ Map k a
Tip = (forall k a. Map k a
Tip forall a b. a -> b -> StrictPair a b
:*: forall k a. Map k a
Tip)
    go k -> a -> Bool
p t :: Map k a
t@(Bin Size
_ k
kx a
x Map k a
l Map k a
r)
      | k -> a -> Bool
p k
kx a
x    = (if Map k a
l1 forall a. a -> a -> Bool
`ptrEq` Map k a
l Bool -> Bool -> Bool
&& Map k a
r1 forall a. a -> a -> Bool
`ptrEq` Map k a
r
                     then Map k a
t
                     else forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l1 Map k a
r1) forall a b. a -> b -> StrictPair a b
:*: forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
l2 Map k a
r2
      | Bool
otherwise = forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
l1 Map k a
r1 forall a b. a -> b -> StrictPair a b
:*:
                    (if Map k a
l2 forall a. a -> a -> Bool
`ptrEq` Map k a
l Bool -> Bool -> Bool
&& Map k a
r2 forall a. a -> a -> Bool
`ptrEq` Map k a
r
                     then Map k a
t
                     else forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l2 Map k a
r2)
      where
        (Map k a
l1 :*: Map k a
l2) = (k -> a -> Bool) -> Map k a -> StrictPair (Map k a) (Map k a)
go k -> a -> Bool
p Map k a
l
        (Map k a
r1 :*: Map k a
r2) = (k -> a -> Bool) -> Map k a -> StrictPair (Map k a) (Map k a)
go k -> a -> Bool
p Map k a
r

-- | \(O(n)\). 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) -> Map k a -> Map k b
mapMaybe :: forall a b k. (a -> Maybe b) -> Map k a -> Map k b
mapMaybe a -> Maybe b
f = forall k a b. (k -> a -> Maybe b) -> Map k a -> Map k b
mapMaybeWithKey (\k
_ 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 :: (k -> a -> Maybe b) -> Map k a -> Map k b
mapMaybeWithKey :: forall k a b. (k -> a -> Maybe b) -> Map k a -> Map k b
mapMaybeWithKey k -> a -> Maybe b
_ Map k a
Tip = forall k a. Map k a
Tip
mapMaybeWithKey k -> a -> Maybe b
f (Bin Size
_ k
kx a
x Map k a
l Map k a
r) = case k -> a -> Maybe b
f k
kx a
x of
  Just b
y  -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx b
y (forall k a b. (k -> a -> Maybe b) -> Map k a -> Map k b
mapMaybeWithKey k -> a -> Maybe b
f Map k a
l) (forall k a b. (k -> a -> Maybe b) -> Map k a -> Map k b
mapMaybeWithKey k -> a -> Maybe b
f Map k a
r)
  Maybe b
Nothing -> forall k a. Map k a -> Map k a -> Map k a
link2 (forall k a b. (k -> a -> Maybe b) -> Map k a -> Map k b
mapMaybeWithKey k -> a -> Maybe b
f Map k a
l) (forall k a b. (k -> a -> Maybe b) -> Map k a -> Map k b
mapMaybeWithKey k -> a -> Maybe b
f Map k a
r)

-- | \(O(n)\). Traverse keys\/values and collect the 'Just' results.
--
-- @since 0.5.8
traverseMaybeWithKey :: Applicative f
                     => (k -> a -> f (Maybe b)) -> Map k a -> f (Map k b)
traverseMaybeWithKey :: forall (f :: * -> *) k a b.
Applicative f =>
(k -> a -> f (Maybe b)) -> Map k a -> f (Map k b)
traverseMaybeWithKey = forall (f :: * -> *) k a b.
Applicative f =>
(k -> a -> f (Maybe b)) -> Map k a -> f (Map k b)
go
  where
    go :: (k -> t -> f (Maybe a)) -> Map k t -> f (Map k a)
go k -> t -> f (Maybe a)
_ Map k t
Tip = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall k a. Map k a
Tip
    go k -> t -> f (Maybe a)
f (Bin Size
_ k
kx t
x Map k t
Tip Map k t
Tip) = forall b a. b -> (a -> b) -> Maybe a -> b
maybe forall k a. Map k a
Tip (\a
x' -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
kx a
x' forall k a. Map k a
Tip forall k a. Map k a
Tip) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> k -> t -> f (Maybe a)
f k
kx t
x
    go k -> t -> f (Maybe a)
f (Bin Size
_ k
kx t
x Map k t
l Map k t
r) = forall (f :: * -> *) a b c d.
Applicative f =>
(a -> b -> c -> d) -> f a -> f b -> f c -> f d
liftA3 Map k a -> Maybe a -> Map k a -> Map k a
combine ((k -> t -> f (Maybe a)) -> Map k t -> f (Map k a)
go k -> t -> f (Maybe a)
f Map k t
l) (k -> t -> f (Maybe a)
f k
kx t
x) ((k -> t -> f (Maybe a)) -> Map k t -> f (Map k a)
go k -> t -> f (Maybe a)
f Map k t
r)
      where
        combine :: Map k a -> Maybe a -> Map k a -> Map k a
combine !Map k a
l' Maybe a
mx !Map k a
r' = case Maybe a
mx of
          Maybe a
Nothing -> forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
l' Map k a
r'
          Just a
x' -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x' Map k a
l' Map k a
r'

-- | \(O(n)\). 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) -> Map k a -> (Map k b, Map k c)
mapEither :: forall a b c k. (a -> Either b c) -> Map k a -> (Map k b, Map k c)
mapEither a -> Either b c
f Map k a
m
  = forall k a b c.
(k -> a -> Either b c) -> Map k a -> (Map k b, Map k c)
mapEitherWithKey (\k
_ a
x -> a -> Either b c
f a
x) Map k 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 :: (k -> a -> Either b c) -> Map k a -> (Map k b, Map k c)
mapEitherWithKey :: forall k a b c.
(k -> a -> Either b c) -> Map k a -> (Map k b, Map k c)
mapEitherWithKey k -> a -> Either b c
f0 Map k a
t0 = forall a b. StrictPair a b -> (a, b)
toPair forall a b. (a -> b) -> a -> b
$ forall {k} {t} {a} {a}.
(k -> t -> Either a a) -> Map k t -> StrictPair (Map k a) (Map k a)
go k -> a -> Either b c
f0 Map k a
t0
  where
    go :: (k -> t -> Either a a) -> Map k t -> StrictPair (Map k a) (Map k a)
go k -> t -> Either a a
_ Map k t
Tip = (forall k a. Map k a
Tip forall a b. a -> b -> StrictPair a b
:*: forall k a. Map k a
Tip)
    go k -> t -> Either a a
f (Bin Size
_ k
kx t
x Map k t
l Map k t
r) = case k -> t -> Either a a
f k
kx t
x of
      Left a
y  -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
y Map k a
l1 Map k a
r1 forall a b. a -> b -> StrictPair a b
:*: forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
l2 Map k a
r2
      Right a
z -> forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
l1 Map k a
r1 forall a b. a -> b -> StrictPair a b
:*: forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
z Map k a
l2 Map k a
r2
     where
        (Map k a
l1 :*: Map k a
l2) = (k -> t -> Either a a) -> Map k t -> StrictPair (Map k a) (Map k a)
go k -> t -> Either a a
f Map k t
l
        (Map k a
r1 :*: Map k a
r2) = (k -> t -> Either a a) -> Map k t -> StrictPair (Map k a) (Map k a)
go k -> t -> Either a a
f Map k t
r

{--------------------------------------------------------------------
  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) -> Map k a -> Map k b
map :: forall a b k. (a -> b) -> Map k a -> Map k b
map a -> b
f = Map k a -> Map k b
go where
  go :: Map k a -> Map k b
go Map k a
Tip = forall k a. Map k a
Tip
  go (Bin Size
sx k
kx a
x Map k a
l Map k a
r) = forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx (a -> b
f a
x) (Map k a -> Map k b
go Map k a
l) (Map k a -> Map k b
go Map k a
r)
-- We use a `go` function to allow `map` to inline. This makes
-- a big difference if someone uses `map (const x) m` instead
-- of `x <$ m`; it doesn't seem to do any harm.

#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 :: (k -> a -> b) -> Map k a -> Map k b
mapWithKey :: forall k a b. (k -> a -> b) -> Map k a -> Map k b
mapWithKey k -> a -> b
_ Map k a
Tip = forall k a. Map k a
Tip
mapWithKey k -> a -> b
f (Bin Size
sx k
kx a
x Map k a
l Map k a
r) = forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx (k -> a -> b
f k
kx a
x) (forall k a b. (k -> a -> b) -> Map k a -> Map k b
mapWithKey k -> a -> b
f Map k a
l) (forall k a b. (k -> a -> b) -> Map k a -> Map k b
mapWithKey k -> a -> b
f Map k a
r)

#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 m == '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 => (k -> a -> t b) -> Map k a -> t (Map k b)
traverseWithKey :: forall (t :: * -> *) k a b.
Applicative t =>
(k -> a -> t b) -> Map k a -> t (Map k b)
traverseWithKey k -> a -> t b
f = Map k a -> t (Map k b)
go
  where
    go :: Map k a -> t (Map k b)
go Map k a
Tip = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall k a. Map k a
Tip
    go (Bin Size
1 k
k a
v Map k a
_ Map k a
_) = (\b
v' -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k b
v' forall k a. Map k a
Tip forall k a. Map k a
Tip) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> k -> a -> t b
f k
k a
v
    go (Bin Size
s k
k a
v Map k a
l Map k a
r) = forall (f :: * -> *) a b c d.
Applicative f =>
(a -> b -> c -> d) -> f a -> f b -> f c -> f d
liftA3 (forall a b c. (a -> b -> c) -> b -> a -> c
flip (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
s k
k)) (Map k a -> t (Map k b)
go Map k a
l) (k -> a -> t b
f k
k a
v) (Map k a -> t (Map k b)
go Map k 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 -> Map k b -> (a,Map k c)
mapAccum :: forall a b c k. (a -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
mapAccum a -> b -> (a, c)
f a
a Map k b
m
  = forall a k b c.
(a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
mapAccumWithKey (\a
a' k
_ b
x' -> a -> b -> (a, c)
f a
a' b
x') a
a Map k b
m

-- | \(O(n)\). 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 -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccumWithKey :: forall a k b c.
(a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
mapAccumWithKey a -> k -> b -> (a, c)
f a
a Map k b
t
  = forall a k b c.
(a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
mapAccumL a -> k -> b -> (a, c)
f a
a Map k b
t

-- | \(O(n)\). The function 'mapAccumL' threads an accumulating
-- argument through the map in ascending order of keys.
mapAccumL :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccumL :: forall a k b c.
(a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
mapAccumL a -> k -> b -> (a, c)
_ a
a Map k b
Tip               = (a
a,forall k a. Map k a
Tip)
mapAccumL a -> k -> b -> (a, c)
f a
a (Bin Size
sx k
kx b
x Map k b
l Map k b
r) =
  let (a
a1,Map k c
l') = forall a k b c.
(a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
mapAccumL a -> k -> b -> (a, c)
f a
a Map k b
l
      (a
a2,c
x') = a -> k -> b -> (a, c)
f a
a1 k
kx b
x
      (a
a3,Map k c
r') = forall a k b c.
(a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
mapAccumL a -> k -> b -> (a, c)
f a
a2 Map k b
r
  in (a
a3,forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx c
x' Map k c
l' Map k c
r')

-- | \(O(n)\). The function 'mapAccumRWithKey' threads an accumulating
-- argument through the map in descending order of keys.
mapAccumRWithKey :: (a -> k -> b -> (a,c)) -> a -> Map k b -> (a,Map k c)
mapAccumRWithKey :: forall a k b c.
(a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
mapAccumRWithKey a -> k -> b -> (a, c)
_ a
a Map k b
Tip = (a
a,forall k a. Map k a
Tip)
mapAccumRWithKey a -> k -> b -> (a, c)
f a
a (Bin Size
sx k
kx b
x Map k b
l Map k b
r) =
  let (a
a1,Map k c
r') = forall a k b c.
(a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
mapAccumRWithKey a -> k -> b -> (a, c)
f a
a Map k b
r
      (a
a2,c
x') = a -> k -> b -> (a, c)
f a
a1 k
kx b
x
      (a
a3,Map k c
l') = forall a k b c.
(a -> k -> b -> (a, c)) -> a -> Map k b -> (a, Map k c)
mapAccumRWithKey a -> k -> b -> (a, c)
f a
a2 Map k b
l
  in (a
a3,forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx c
x' Map k c
l' Map k c
r')

-- | \(O(n \log n)\).
-- @'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 :: Ord k2 => (k1->k2) -> Map k1 a -> Map k2 a
mapKeys :: forall k2 k1 a. Ord k2 => (k1 -> k2) -> Map k1 a -> Map k2 a
mapKeys k1 -> k2
f = forall k a. Ord k => [(k, a)] -> Map k a
fromList forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a b. (k -> a -> b -> b) -> b -> Map k a -> b
foldrWithKey (\k1
k a
x [(k2, a)]
xs -> (k1 -> k2
f k1
k, a
x) forall a. a -> [a] -> [a]
: [(k2, a)]
xs) []
#if __GLASGOW_HASKELL__
{-# INLINABLE mapKeys #-}
#endif

-- | \(O(n \log n)\).
-- @'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@. The value at the greater of the two original keys
-- is used as the first argument to @c@.
--
-- > mapKeysWith (++) (\ _ -> 1) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 1 "cdab"
-- > mapKeysWith (++) (\ _ -> 3) (fromList [(1,"b"), (2,"a"), (3,"d"), (4,"c")]) == singleton 3 "cdab"
--
-- Also see the performance note on 'fromListWith'.

mapKeysWith :: Ord k2 => (a -> a -> a) -> (k1->k2) -> Map k1 a -> Map k2 a
mapKeysWith :: forall k2 a k1.
Ord k2 =>
(a -> a -> a) -> (k1 -> k2) -> Map k1 a -> Map k2 a
mapKeysWith a -> a -> a
c k1 -> k2
f = forall k a. Ord k => (a -> a -> a) -> [(k, a)] -> Map k a
fromListWith a -> a -> a
c forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall k a b. (k -> a -> b -> b) -> b -> Map k a -> b
foldrWithKey (\k1
k a
x [(k2, a)]
xs -> (k1 -> k2
f k1
k, a
x) forall a. a -> [a] -> [a]
: [(k2, a)]
xs) []
#if __GLASGOW_HASKELL__
{-# INLINABLE mapKeysWith #-}
#endif


-- | \(O(n)\).
-- @'mapKeysMonotonic' f s == 'mapKeys' f s@, but works only when @f@
-- is strictly monotonic.
-- That is, for any values @x@ and @y@, if @x@ < @y@ then @f x@ < @f y@.
-- /The precondition is not checked./
-- Semi-formally, we have:
--
-- > and [x < y ==> f x < f y | x <- ls, y <- ls]
-- >                     ==> mapKeysMonotonic f s == mapKeys f s
-- >     where ls = keys s
--
-- This means that @f@ maps distinct original keys to distinct resulting keys.
-- This function has better performance than 'mapKeys'.
--
-- > mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")]) == fromList [(6, "b"), (10, "a")]
-- > valid (mapKeysMonotonic (\ k -> k * 2) (fromList [(5,"a"), (3,"b")])) == True
-- > valid (mapKeysMonotonic (\ _ -> 1)     (fromList [(5,"a"), (3,"b")])) == False

mapKeysMonotonic :: (k1->k2) -> Map k1 a -> Map k2 a
mapKeysMonotonic :: forall k1 k2 a. (k1 -> k2) -> Map k1 a -> Map k2 a
mapKeysMonotonic k1 -> k2
_ Map k1 a
Tip = forall k a. Map k a
Tip
mapKeysMonotonic k1 -> k2
f (Bin Size
sz k1
k a
x Map k1 a
l Map k1 a
r) =
    forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sz (k1 -> k2
f k1
k) a
x (forall k1 k2 a. (k1 -> k2) -> Map k1 a -> Map k2 a
mapKeysMonotonic k1 -> k2
f Map k1 a
l) (forall k1 k2 a. (k1 -> k2) -> Map k1 a -> Map k2 a
mapKeysMonotonic k1 -> k2
f Map k1 a
r)

{--------------------------------------------------------------------
  Folds
--------------------------------------------------------------------}

-- | \(O(n)\). 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 -> Map k a -> b
foldr :: forall a b k. (a -> b -> b) -> b -> Map k a -> b
foldr a -> b -> b
f b
z = b -> Map k a -> b
go b
z
  where
    go :: b -> Map k a -> b
go b
z' Map k a
Tip             = b
z'
    go b
z' (Bin Size
_ k
_ a
x Map k a
l Map k a
r) = b -> Map k a -> b
go (a -> b -> b
f a
x (b -> Map k a -> b
go b
z' Map k a
r)) Map k 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 -> Map k a -> b
foldr' :: forall a b k. (a -> b -> b) -> b -> Map k a -> b
foldr' a -> b -> b
f b
z = b -> Map k a -> b
go b
z
  where
    go :: b -> Map k a -> b
go !b
z' Map k a
Tip            = b
z'
    go b
z' (Bin Size
_ k
_ a
x Map k a
l Map k a
r) = b -> Map k a -> b
go (a -> b -> b
f a
x forall a b. (a -> b) -> a -> b
$! b -> Map k a -> b
go b
z' Map k a
r) Map k 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 -> Map k b -> a
foldl :: forall a b k. (a -> b -> a) -> a -> Map k b -> a
foldl a -> b -> a
f a
z = a -> Map k b -> a
go a
z
  where
    go :: a -> Map k b -> a
go a
z' Map k b
Tip             = a
z'
    go a
z' (Bin Size
_ k
_ b
x Map k b
l Map k b
r) = a -> Map k b -> a
go (a -> b -> a
f (a -> Map k b -> a
go a
z' Map k b
l) b
x) Map k 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 -> Map k b -> a
foldl' :: forall a b k. (a -> b -> a) -> a -> Map k b -> a
foldl' a -> b -> a
f a
z = a -> Map k b -> a
go a
z
  where
    go :: a -> Map k b -> a
go !a
z' Map k b
Tip            = a
z'
    go a
z' (Bin Size
_ k
_ b
x Map k b
l Map k b
r) =
      let !z'' :: a
z'' = a -> Map k b -> a
go a
z' Map k b
l
      in a -> Map k b -> a
go (a -> b -> a
f a
z'' b
x) Map k 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 :: (k -> a -> b -> b) -> b -> Map k a -> b
foldrWithKey :: forall k a b. (k -> a -> b -> b) -> b -> Map k a -> b
foldrWithKey k -> a -> b -> b
f b
z = b -> Map k a -> b
go b
z
  where
    go :: b -> Map k a -> b
go b
z' Map k a
Tip             = b
z'
    go b
z' (Bin Size
_ k
kx a
x Map k a
l Map k a
r) = b -> Map k a -> b
go (k -> a -> b -> b
f k
kx a
x (b -> Map k a -> b
go b
z' Map k a
r)) Map k 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' :: (k -> a -> b -> b) -> b -> Map k a -> b
foldrWithKey' :: forall k a b. (k -> a -> b -> b) -> b -> Map k a -> b
foldrWithKey' k -> a -> b -> b
f b
z = b -> Map k a -> b
go b
z
  where
    go :: b -> Map k a -> b
go !b
z' Map k a
Tip              = b
z'
    go b
z' (Bin Size
_ k
kx a
x Map k a
l Map k a
r) = b -> Map k a -> b
go (k -> a -> b -> b
f k
kx a
x forall a b. (a -> b) -> a -> b
$! b -> Map k a -> b
go b
z' Map k a
r) Map k 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 -> k -> b -> a) -> a -> Map k b -> a
foldlWithKey :: forall a k b. (a -> k -> b -> a) -> a -> Map k b -> a
foldlWithKey a -> k -> b -> a
f a
z = a -> Map k b -> a
go a
z
  where
    go :: a -> Map k b -> a
go a
z' Map k b
Tip              = a
z'
    go a
z' (Bin Size
_ k
kx b
x Map k b
l Map k b
r) = a -> Map k b -> a
go (a -> k -> b -> a
f (a -> Map k b -> a
go a
z' Map k b
l) k
kx b
x) Map k 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 -> k -> b -> a) -> a -> Map k b -> a
foldlWithKey' :: forall a k b. (a -> k -> b -> a) -> a -> Map k b -> a
foldlWithKey' a -> k -> b -> a
f a
z = a -> Map k b -> a
go a
z
  where
    go :: a -> Map k b -> a
go !a
z' Map k b
Tip             = a
z'
    go a
z' (Bin Size
_ k
kx b
x Map k b
l Map k b
r) =
      let !z'' :: a
z'' = a -> Map k b -> a
go a
z' Map k b
l
      in a -> Map k b -> a
go (a -> k -> b -> a
f a
z'' k
kx b
x) Map k 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 => (k -> a -> m) -> Map k a -> m
foldMapWithKey :: forall m k a. Monoid m => (k -> a -> m) -> Map k a -> m
foldMapWithKey k -> a -> m
f = Map k a -> m
go
  where
    go :: Map k a -> m
go Map k a
Tip             = forall a. Monoid a => a
mempty
    go (Bin Size
1 k
k a
v Map k a
_ Map k a
_) = k -> a -> m
f k
k a
v
    go (Bin Size
_ k
k a
v Map k a
l Map k a
r) = Map k a -> m
go Map k a
l forall a. Monoid a => a -> a -> a
`mappend` (k -> a -> m
f k
k a
v forall a. Monoid a => a -> a -> a
`mappend` Map k a -> m
go Map k 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 :: Map k a -> [a]
elems :: forall k a. Map k a -> [a]
elems = forall a b k. (a -> b -> b) -> b -> Map k 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  :: Map k a -> [k]
keys :: forall k a. Map k a -> [k]
keys = forall k a b. (k -> a -> b -> b) -> b -> Map k a -> b
foldrWithKey (\k
k a
_ [k]
ks -> k
k forall a. a -> [a] -> [a]
: [k]
ks) []

-- | \(O(n)\). An alias for 'toAscList'. Return 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 :: Map k a -> [(k,a)]
assocs :: forall k a. Map k a -> [(k, a)]
assocs Map k a
m
  = forall k a. Map k a -> [(k, a)]
toAscList Map k a
m

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

keysSet :: Map k a -> Set.Set k
keysSet :: forall k a. Map k a -> Set k
keysSet Map k a
Tip = forall a. Set a
Set.Tip
keysSet (Bin Size
sz k
kx a
_ Map k a
l Map k a
r) = forall a. Size -> a -> Set a -> Set a -> Set a
Set.Bin Size
sz k
kx (forall k a. Map k a -> Set k
keysSet Map k a
l) (forall k a. Map k a -> Set k
keysSet Map k a
r)

-- | \(O(n)\). The set of all elements of the map contained in 'Arg's.
--
-- > argSet (fromList [(5,"a"), (3,"b")]) == Data.Set.fromList [Arg 3 "b",Arg 5 "a"]
-- > argSet empty == Data.Set.empty

argSet :: Map k a -> Set.Set (Arg k a)
argSet :: forall k a. Map k a -> Set (Arg k a)
argSet Map k a
Tip = forall a. Set a
Set.Tip
argSet (Bin Size
sz k
kx a
x Map k a
l Map k a
r) = forall a. Size -> a -> Set a -> Set a -> Set a
Set.Bin Size
sz (forall a b. a -> b -> Arg a b
Arg k
kx a
x) (forall k a. Map k a -> Set (Arg k a)
argSet Map k a
l) (forall k a. Map k a -> Set (Arg k a)
argSet Map k a
r)

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

fromSet :: (k -> a) -> Set.Set k -> Map k a
fromSet :: forall k a. (k -> a) -> Set k -> Map k a
fromSet k -> a
_ Set k
Set.Tip = forall k a. Map k a
Tip
fromSet k -> a
f (Set.Bin Size
sz k
x Set k
l Set k
r) = forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sz k
x (k -> a
f k
x) (forall k a. (k -> a) -> Set k -> Map k a
fromSet k -> a
f Set k
l) (forall k a. (k -> a) -> Set k -> Map k a
fromSet k -> a
f Set k
r)

-- | \(O(n)\). Build a map from a set of elements contained inside 'Arg's.
--
-- > fromArgSet (Data.Set.fromList [Arg 3 "aaa", Arg 5 "aaaaa"]) == fromList [(5,"aaaaa"), (3,"aaa")]
-- > fromArgSet Data.Set.empty == empty

fromArgSet :: Set.Set (Arg k a) -> Map k a
fromArgSet :: forall k a. Set (Arg k a) -> Map k a
fromArgSet Set (Arg k a)
Set.Tip = forall k a. Map k a
Tip
fromArgSet (Set.Bin Size
sz (Arg k
x a
v) Set (Arg k a)
l Set (Arg k a)
r) = forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sz k
x a
v (forall k a. Set (Arg k a) -> Map k a
fromArgSet Set (Arg k a)
l) (forall k a. Set (Arg k a) -> Map k a
fromArgSet Set (Arg k a)
r)

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

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

-- | \(O(n \log n)\). Build a map from a list of key\/value pairs. See also 'fromAscList'.
-- If the list contains more than one value for the same key, the last value
-- for the key is retained.
--
-- If the keys of the list are ordered, a linear-time implementation is used.
--
-- > 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")]

-- For some reason, when 'singleton' is used in fromList or in
-- create, it is not inlined, so we inline it manually.
fromList :: Ord k => [(k,a)] -> Map k a
fromList :: forall k a. Ord k => [(k, a)] -> Map k a
fromList [] = forall k a. Map k a
Tip
fromList [(k
kx, a
x)] = forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
kx a
x forall k a. Map k a
Tip forall k a. Map k a
Tip
fromList ((k
kx0, a
x0) : [(k, a)]
xs0) | forall {a} {b}. Ord a => a -> [(a, b)] -> Bool
not_ordered k
kx0 [(k, a)]
xs0 = forall {t :: * -> *} {k} {a}.
(Foldable t, Ord k) =>
Map k a -> t (k, a) -> Map k a
fromList' (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
kx0 a
x0 forall k a. Map k a
Tip forall k a. Map k a
Tip) [(k, a)]
xs0
                           | Bool
otherwise = forall {k} {t} {a}.
(Ord k, Num t, Bits t) =>
t -> Map k a -> [(k, a)] -> Map k a
go (Size
1::Int) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
kx0 a
x0 forall k a. Map k a
Tip forall k a. Map k a
Tip) [(k, a)]
xs0
  where
    not_ordered :: a -> [(a, b)] -> Bool
not_ordered a
_ [] = Bool
False
    not_ordered a
kx ((a
ky,b
_) : [(a, b)]
_) = a
kx forall a. Ord a => a -> a -> Bool
>= a
ky
    {-# INLINE not_ordered #-}

    fromList' :: Map k a -> t (k, a) -> Map k a
fromList' Map k a
t0 t (k, a)
xs = forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' forall {k} {a}. Ord k => Map k a -> (k, a) -> Map k a
ins Map k a
t0 t (k, a)
xs
      where ins :: Map k a -> (k, a) -> Map k a
ins Map k a
t (k
k,a
x) = forall k a. Ord k => k -> a -> Map k a -> Map k a
insert k
k a
x Map k a
t

    go :: t -> Map k a -> [(k, a)] -> Map k a
go !t
_ Map k a
t [] = Map k a
t
    go t
_ Map k a
t [(k
kx, a
x)] = forall k a. k -> a -> Map k a -> Map k a
insertMax k
kx a
x Map k a
t
    go t
s Map k a
l xs :: [(k, a)]
xs@((k
kx, a
x) : [(k, a)]
xss) | forall {a} {b}. Ord a => a -> [(a, b)] -> Bool
not_ordered k
kx [(k, a)]
xss = forall {t :: * -> *} {k} {a}.
(Foldable t, Ord k) =>
Map k a -> t (k, a) -> Map k a
fromList' Map k a
l [(k, a)]
xs
                              | Bool
otherwise = case forall {t} {a} {b}.
(Num t, Ord a, Bits t) =>
t -> [(a, b)] -> (Map a b, [(a, b)], [(a, b)])
create t
s [(k, a)]
xss of
                                  (Map k a
r, [(k, a)]
ys, []) -> t -> Map k a -> [(k, a)] -> Map k a
go (t
s forall a. Bits a => a -> Size -> a
`shiftL` Size
1) (forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
r) [(k, a)]
ys
                                  (Map k a
r, [(k, a)]
_,  [(k, a)]
ys) -> forall {t :: * -> *} {k} {a}.
(Foldable t, Ord k) =>
Map k a -> t (k, a) -> Map k a
fromList' (forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
r) [(k, a)]
ys

    -- The create is returning a triple (tree, xs, ys). Both xs and ys
    -- represent not yet processed elements and only one of them can be nonempty.
    -- If ys is nonempty, the keys in ys are not ordered with respect to tree
    -- and must be inserted using fromList'. Otherwise the keys have been
    -- ordered so far.
    create :: t -> [(a, b)] -> (Map a b, [(a, b)], [(a, b)])
create !t
_ [] = (forall k a. Map k a
Tip, [], [])
    create t
s xs :: [(a, b)]
xs@((a, b)
xp : [(a, b)]
xss)
      | t
s forall a. Eq a => a -> a -> Bool
== t
1 = case (a, b)
xp of (a
kx, b
x) | forall {a} {b}. Ord a => a -> [(a, b)] -> Bool
not_ordered a
kx [(a, b)]
xss -> (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 a
kx b
x forall k a. Map k a
Tip forall k a. Map k a
Tip, [], [(a, b)]
xss)
                                    | Bool
otherwise -> (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 a
kx b
x forall k a. Map k a
Tip forall k a. Map k a
Tip, [(a, b)]
xss, [])
      | Bool
otherwise = case t -> [(a, b)] -> (Map a b, [(a, b)], [(a, b)])
create (t
s forall a. Bits a => a -> Size -> a
`shiftR` Size
1) [(a, b)]
xs of
                      res :: (Map a b, [(a, b)], [(a, b)])
res@(Map a b
_, [], [(a, b)]
_) -> (Map a b, [(a, b)], [(a, b)])
res
                      (Map a b
l, [(a
ky, b
y)], [(a, b)]
zs) -> (forall k a. k -> a -> Map k a -> Map k a
insertMax a
ky b
y Map a b
l, [], [(a, b)]
zs)
                      (Map a b
l, ys :: [(a, b)]
ys@((a
ky, b
y):[(a, b)]
yss), [(a, b)]
_) | forall {a} {b}. Ord a => a -> [(a, b)] -> Bool
not_ordered a
ky [(a, b)]
yss -> (Map a b
l, [], [(a, b)]
ys)
                                               | Bool
otherwise -> case t -> [(a, b)] -> (Map a b, [(a, b)], [(a, b)])
create (t
s forall a. Bits a => a -> Size -> a
`shiftR` Size
1) [(a, b)]
yss of
                                                   (Map a b
r, [(a, b)]
zs, [(a, b)]
ws) -> (forall k a. k -> a -> Map k a -> Map k a -> Map k a
link a
ky b
y Map a b
l Map a b
r, [(a, b)]
zs, [(a, b)]
ws)
#if __GLASGOW_HASKELL__
{-# INLINABLE fromList #-}
#endif

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

fromListWith :: Ord k => (a -> a -> a) -> [(k,a)] -> Map k a
fromListWith :: forall k a. Ord k => (a -> a -> a) -> [(k, a)] -> Map k a
fromListWith a -> a -> a
f [(k, a)]
xs
  = forall k a. Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
fromListWithKey (\k
_ a
x a
y -> a -> a -> a
f a
x a
y) [(k, a)]
xs
#if __GLASGOW_HASKELL__
{-# INLINABLE fromListWith #-}
#endif

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

fromListWithKey :: Ord k => (k -> a -> a -> a) -> [(k,a)] -> Map k a
fromListWithKey :: forall k a. Ord k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
fromListWithKey k -> a -> a -> a
f [(k, a)]
xs
  = forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' Map k a -> (k, a) -> Map k a
ins forall k a. Map k a
empty [(k, a)]
xs
  where
    ins :: Map k a -> (k, a) -> Map k a
ins Map k a
t (k
k,a
x) = forall k a.
Ord k =>
(k -> a -> a -> a) -> k -> a -> Map k a -> Map k a
insertWithKey k -> a -> a -> a
f k
k a
x Map k a
t
#if __GLASGOW_HASKELL__
{-# INLINABLE fromListWithKey #-}
#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 :: Map k a -> [(k,a)]
toList :: forall k a. Map k a -> [(k, a)]
toList = forall k a. Map k a -> [(k, 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 :: Map k a -> [(k,a)]
toAscList :: forall k a. Map k a -> [(k, a)]
toAscList = forall k a b. (k -> a -> b -> b) -> b -> Map k a -> b
foldrWithKey (\k
k a
x [(k, a)]
xs -> (k
k,a
x)forall a. a -> [a] -> [a]
:[(k, 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 :: Map k a -> [(k,a)]
toDescList :: forall k a. Map k a -> [(k, a)]
toDescList = forall a k b. (a -> k -> b -> a) -> a -> Map k b -> a
foldlWithKey (\[(k, a)]
xs k
k a
x -> (k
k,a
x)forall a. a -> [a] -> [a]
:[(k, 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 :: (k -> a -> b -> b) -> b -> Map k a -> b
foldrFB :: forall k a b. (k -> a -> b -> b) -> b -> Map k a -> b
foldrFB = forall k a b. (k -> a -> b -> b) -> b -> Map k a -> b
foldrWithKey
{-# INLINE[0] foldrFB #-}
foldlFB :: (a -> k -> b -> a) -> a -> Map k b -> a
foldlFB :: forall a k b. (a -> k -> b -> a) -> a -> Map k b -> a
foldlFB = forall a k b. (a -> k -> b -> a) -> a -> Map k 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 "Map.elems" [~1] forall m . elems m = build (\c n -> foldrFB (\_ x xs -> c x xs) n m) #-}
{-# RULES "Map.elemsBack" [1] foldrFB (\_ x xs -> x : xs) [] = elems #-}
{-# RULES "Map.keys" [~1] forall m . keys m = build (\c n -> foldrFB (\k _ xs -> c k xs) n m) #-}
{-# RULES "Map.keysBack" [1] foldrFB (\k _ xs -> k : xs) [] = keys #-}
{-# RULES "Map.toAscList" [~1] forall m . toAscList m = build (\c n -> foldrFB (\k x xs -> c (k,x) xs) n m) #-}
{-# RULES "Map.toAscListBack" [1] foldrFB (\k x xs -> (k, x) : xs) [] = toAscList #-}
{-# RULES "Map.toDescList" [~1] forall m . toDescList m = build (\c n -> foldlFB (\xs k x -> c (k,x) xs) n m) #-}
{-# RULES "Map.toDescListBack" [1] foldlFB (\xs k x -> (k, x) : xs) [] = toDescList #-}
#endif

{--------------------------------------------------------------------
  Building trees from ascending/descending lists can be done in linear time.

  Note that if [xs] is ascending that:
    fromAscList xs       == fromList xs
    fromAscListWith f xs == fromListWith f xs
--------------------------------------------------------------------}
-- | \(O(n)\). Build a map from an ascending list in linear time.
-- /The precondition (input list is ascending) is not checked./
--
-- > fromAscList [(3,"b"), (5,"a")]          == fromList [(3, "b"), (5, "a")]
-- > fromAscList [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "b")]
-- > valid (fromAscList [(3,"b"), (5,"a"), (5,"b")]) == True
-- > valid (fromAscList [(5,"a"), (3,"b"), (5,"b")]) == False

fromAscList :: Eq k => [(k,a)] -> Map k a
fromAscList :: forall k a. Eq k => [(k, a)] -> Map k a
fromAscList [(k, a)]
xs
  = forall k a. [(k, a)] -> Map k a
fromDistinctAscList (forall {a} {b}. Eq a => [(a, b)] -> [(a, b)]
combineEq [(k, a)]
xs)
  where
  -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs]
  combineEq :: [(a, b)] -> [(a, b)]
combineEq [(a, b)]
xs'
    = case [(a, b)]
xs' of
        []     -> []
        [(a, b)
x]    -> [(a, b)
x]
        ((a, b)
x:[(a, b)]
xx) -> forall {a} {b}. Eq a => (a, b) -> [(a, b)] -> [(a, b)]
combineEq' (a, b)
x [(a, b)]
xx

  combineEq' :: (a, b) -> [(a, b)] -> [(a, b)]
combineEq' (a, b)
z [] = [(a, b)
z]
  combineEq' z :: (a, b)
z@(a
kz,b
_) (x :: (a, b)
x@(a
kx,b
xx):[(a, b)]
xs')
    | a
kxforall a. Eq a => a -> a -> Bool
==a
kz    = (a, b) -> [(a, b)] -> [(a, b)]
combineEq' (a
kx,b
xx) [(a, b)]
xs'
    | Bool
otherwise = (a, b)
zforall a. a -> [a] -> [a]
:(a, b) -> [(a, b)] -> [(a, b)]
combineEq' (a, b)
x [(a, b)]
xs'
#if __GLASGOW_HASKELL__
{-# INLINABLE fromAscList #-}
#endif

-- | \(O(n)\). Build a map from a descending list in linear time.
-- /The precondition (input list is descending) is not checked./
--
-- > fromDescList [(5,"a"), (3,"b")]          == fromList [(3, "b"), (5, "a")]
-- > fromDescList [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "b")]
-- > valid (fromDescList [(5,"a"), (5,"b"), (3,"b")]) == True
-- > valid (fromDescList [(5,"a"), (3,"b"), (5,"b")]) == False
--
-- @since 0.5.8

fromDescList :: Eq k => [(k,a)] -> Map k a
fromDescList :: forall k a. Eq k => [(k, a)] -> Map k a
fromDescList [(k, a)]
xs = forall k a. [(k, a)] -> Map k a
fromDistinctDescList (forall {a} {b}. Eq a => [(a, b)] -> [(a, b)]
combineEq [(k, a)]
xs)
  where
  -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs]
  combineEq :: [(a, b)] -> [(a, b)]
combineEq [(a, b)]
xs'
    = case [(a, b)]
xs' of
        []     -> []
        [(a, b)
x]    -> [(a, b)
x]
        ((a, b)
x:[(a, b)]
xx) -> forall {a} {b}. Eq a => (a, b) -> [(a, b)] -> [(a, b)]
combineEq' (a, b)
x [(a, b)]
xx

  combineEq' :: (a, b) -> [(a, b)] -> [(a, b)]
combineEq' (a, b)
z [] = [(a, b)
z]
  combineEq' z :: (a, b)
z@(a
kz,b
_) (x :: (a, b)
x@(a
kx,b
xx):[(a, b)]
xs')
    | a
kxforall a. Eq a => a -> a -> Bool
==a
kz    = (a, b) -> [(a, b)] -> [(a, b)]
combineEq' (a
kx,b
xx) [(a, b)]
xs'
    | Bool
otherwise = (a, b)
zforall a. a -> [a] -> [a]
:(a, b) -> [(a, b)] -> [(a, b)]
combineEq' (a, b)
x [(a, b)]
xs'
#if __GLASGOW_HASKELL__
{-# INLINABLE fromDescList #-}
#endif

-- | \(O(n)\). Build a map from an ascending list in linear time with a combining function for equal keys.
-- /The precondition (input list is ascending) is not checked./
--
-- > fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")] == fromList [(3, "b"), (5, "ba")]
-- > valid (fromAscListWith (++) [(3,"b"), (5,"a"), (5,"b")]) == True
-- > valid (fromAscListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False

fromAscListWith :: Eq k => (a -> a -> a) -> [(k,a)] -> Map k a
fromAscListWith :: forall k a. Eq k => (a -> a -> a) -> [(k, a)] -> Map k a
fromAscListWith a -> a -> a
f [(k, a)]
xs
  = forall k a. Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
fromAscListWithKey (\k
_ a
x a
y -> a -> a -> a
f a
x a
y) [(k, a)]
xs
#if __GLASGOW_HASKELL__
{-# INLINABLE fromAscListWith #-}
#endif

-- | \(O(n)\). Build a map from a descending list in linear time with a combining function for equal keys.
-- /The precondition (input list is descending) is not checked./
--
-- > fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "ba")]
-- > valid (fromDescListWith (++) [(5,"a"), (5,"b"), (3,"b")]) == True
-- > valid (fromDescListWith (++) [(5,"a"), (3,"b"), (5,"b")]) == False
--
-- Also see the performance note on 'fromListWith'.
--
-- @since 0.5.8

fromDescListWith :: Eq k => (a -> a -> a) -> [(k,a)] -> Map k a
fromDescListWith :: forall k a. Eq k => (a -> a -> a) -> [(k, a)] -> Map k a
fromDescListWith a -> a -> a
f [(k, a)]
xs
  = forall k a. Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
fromDescListWithKey (\k
_ a
x a
y -> a -> a -> a
f a
x a
y) [(k, a)]
xs
#if __GLASGOW_HASKELL__
{-# INLINABLE fromDescListWith #-}
#endif

-- | \(O(n)\). Build a map from an ascending list in linear time with a
-- combining function for equal keys.
-- /The precondition (input list is ascending) is not checked./
--
-- > let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2
-- > fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")] == fromList [(3, "b"), (5, "5:b5:ba")]
-- > valid (fromAscListWithKey f [(3,"b"), (5,"a"), (5,"b"), (5,"b")]) == True
-- > valid (fromAscListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False
--
-- Also see the performance note on 'fromListWith'.

fromAscListWithKey :: Eq k => (k -> a -> a -> a) -> [(k,a)] -> Map k a
fromAscListWithKey :: forall k a. Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
fromAscListWithKey k -> a -> a -> a
f [(k, a)]
xs
  = forall k a. [(k, a)] -> Map k a
fromDistinctAscList ((k -> a -> a -> a) -> [(k, a)] -> [(k, a)]
combineEq k -> a -> a -> a
f [(k, a)]
xs)
  where
  -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs]
  combineEq :: (k -> a -> a -> a) -> [(k, a)] -> [(k, a)]
combineEq k -> a -> a -> a
_ [(k, a)]
xs'
    = case [(k, a)]
xs' of
        []     -> []
        [(k, a)
x]    -> [(k, a)
x]
        ((k, a)
x:[(k, a)]
xx) -> (k, a) -> [(k, a)] -> [(k, a)]
combineEq' (k, a)
x [(k, a)]
xx

  combineEq' :: (k, a) -> [(k, a)] -> [(k, a)]
combineEq' (k, a)
z [] = [(k, a)
z]
  combineEq' z :: (k, a)
z@(k
kz,a
zz) (x :: (k, a)
x@(k
kx,a
xx):[(k, a)]
xs')
    | k
kxforall a. Eq a => a -> a -> Bool
==k
kz    = let yy :: a
yy = k -> a -> a -> a
f k
kx a
xx a
zz in (k, a) -> [(k, a)] -> [(k, a)]
combineEq' (k
kx,a
yy) [(k, a)]
xs'
    | Bool
otherwise = (k, a)
zforall a. a -> [a] -> [a]
:(k, a) -> [(k, a)] -> [(k, a)]
combineEq' (k, a)
x [(k, a)]
xs'
#if __GLASGOW_HASKELL__
{-# INLINABLE fromAscListWithKey #-}
#endif

-- | \(O(n)\). Build a map from a descending list in linear time with a
-- combining function for equal keys.
-- /The precondition (input list is descending) is not checked./
--
-- > let f k a1 a2 = (show k) ++ ":" ++ a1 ++ a2
-- > fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")] == fromList [(3, "b"), (5, "5:b5:ba")]
-- > valid (fromDescListWithKey f [(5,"a"), (5,"b"), (5,"b"), (3,"b")]) == True
-- > valid (fromDescListWithKey f [(5,"a"), (3,"b"), (5,"b"), (5,"b")]) == False
--
-- Also see the performance note on 'fromListWith'.

fromDescListWithKey :: Eq k => (k -> a -> a -> a) -> [(k,a)] -> Map k a
fromDescListWithKey :: forall k a. Eq k => (k -> a -> a -> a) -> [(k, a)] -> Map k a
fromDescListWithKey k -> a -> a -> a
f [(k, a)]
xs
  = forall k a. [(k, a)] -> Map k a
fromDistinctDescList ((k -> a -> a -> a) -> [(k, a)] -> [(k, a)]
combineEq k -> a -> a -> a
f [(k, a)]
xs)
  where
  -- [combineEq f xs] combines equal elements with function [f] in an ordered list [xs]
  combineEq :: (k -> a -> a -> a) -> [(k, a)] -> [(k, a)]
combineEq k -> a -> a -> a
_ [(k, a)]
xs'
    = case [(k, a)]
xs' of
        []     -> []
        [(k, a)
x]    -> [(k, a)
x]
        ((k, a)
x:[(k, a)]
xx) -> (k, a) -> [(k, a)] -> [(k, a)]
combineEq' (k, a)
x [(k, a)]
xx

  combineEq' :: (k, a) -> [(k, a)] -> [(k, a)]
combineEq' (k, a)
z [] = [(k, a)
z]
  combineEq' z :: (k, a)
z@(k
kz,a
zz) (x :: (k, a)
x@(k
kx,a
xx):[(k, a)]
xs')
    | k
kxforall a. Eq a => a -> a -> Bool
==k
kz    = let yy :: a
yy = k -> a -> a -> a
f k
kx a
xx a
zz in (k, a) -> [(k, a)] -> [(k, a)]
combineEq' (k
kx,a
yy) [(k, a)]
xs'
    | Bool
otherwise = (k, a)
zforall a. a -> [a] -> [a]
:(k, a) -> [(k, a)] -> [(k, a)]
combineEq' (k, a)
x [(k, a)]
xs'
#if __GLASGOW_HASKELL__
{-# INLINABLE fromDescListWithKey #-}
#endif


-- | \(O(n)\). Build a map from an ascending list of distinct elements in linear time.
-- /The precondition is not checked./
--
-- > fromDistinctAscList [(3,"b"), (5,"a")] == fromList [(3, "b"), (5, "a")]
-- > valid (fromDistinctAscList [(3,"b"), (5,"a")])          == True
-- > valid (fromDistinctAscList [(3,"b"), (5,"a"), (5,"b")]) == False

-- For some reason, when 'singleton' is used in fromDistinctAscList or in
-- create, it is not inlined, so we inline it manually.

-- See Note [fromDistinctAscList implementation] in Data.Set.Internal.
fromDistinctAscList :: [(k,a)] -> Map k a
fromDistinctAscList :: forall k a. [(k, a)] -> Map k a
fromDistinctAscList = forall k a. FromDistinctMonoState k a -> Map k a
fromDistinctAscList_linkAll forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' forall k a.
FromDistinctMonoState k a -> (k, a) -> FromDistinctMonoState k a
next (forall k a. Stack k a -> FromDistinctMonoState k a
State0 forall k a. Stack k a
Nada)
  where
    next :: FromDistinctMonoState k a -> (k,a) -> FromDistinctMonoState k a
    next :: forall k a.
FromDistinctMonoState k a -> (k, a) -> FromDistinctMonoState k a
next (State0 Stack k a
stk) (!k
kx, a
x) = forall k a. Map k a -> Stack k a -> FromDistinctMonoState k a
fromDistinctAscList_linkTop (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
kx a
x forall k a. Map k a
Tip forall k a. Map k a
Tip) Stack k a
stk
    next (State1 Map k a
l Stack k a
stk) (k
kx, a
x) = forall k a. Stack k a -> FromDistinctMonoState k a
State0 (forall k a. k -> a -> Map k a -> Stack k a -> Stack k a
Push k
kx a
x Map k a
l Stack k a
stk)
{-# INLINE fromDistinctAscList #-}  -- INLINE for fusion

fromDistinctAscList_linkTop :: Map k a -> Stack k a -> FromDistinctMonoState k a
fromDistinctAscList_linkTop :: forall k a. Map k a -> Stack k a -> FromDistinctMonoState k a
fromDistinctAscList_linkTop r :: Map k a
r@(Bin Size
rsz k
_ a
_ Map k a
_ Map k a
_) (Push k
kx a
x l :: Map k a
l@(Bin Size
lsz k
_ a
_ Map k a
_ Map k a
_) Stack k a
stk)
  | Size
rsz forall a. Eq a => a -> a -> Bool
== Size
lsz = forall k a. Map k a -> Stack k a -> FromDistinctMonoState k a
fromDistinctAscList_linkTop (forall k a. k -> a -> Map k a -> Map k a -> Map k a
bin k
kx a
x Map k a
l Map k a
r) Stack k a
stk
fromDistinctAscList_linkTop Map k a
l Stack k a
stk = forall k a. Map k a -> Stack k a -> FromDistinctMonoState k a
State1 Map k a
l Stack k a
stk
{-# INLINABLE fromDistinctAscList_linkTop #-}

fromDistinctAscList_linkAll :: FromDistinctMonoState k a -> Map k a
fromDistinctAscList_linkAll :: forall k a. FromDistinctMonoState k a -> Map k a
fromDistinctAscList_linkAll (State0 Stack k a
stk)    = forall b k a. (b -> k -> a -> Map k a -> b) -> b -> Stack k a -> b
foldl'Stack (\Map k a
r k
kx a
x Map k a
l -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
r) forall k a. Map k a
Tip Stack k a
stk
fromDistinctAscList_linkAll (State1 Map k a
r0 Stack k a
stk) = forall b k a. (b -> k -> a -> Map k a -> b) -> b -> Stack k a -> b
foldl'Stack (\Map k a
r k
kx a
x Map k a
l -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
r) Map k a
r0 Stack k a
stk
{-# INLINABLE fromDistinctAscList_linkAll #-}

-- | \(O(n)\). Build a map from a descending list of distinct elements in linear time.
-- /The precondition is not checked./
--
-- > fromDistinctDescList [(5,"a"), (3,"b")] == fromList [(3, "b"), (5, "a")]
-- > valid (fromDistinctDescList [(5,"a"), (3,"b")])          == True
-- > valid (fromDistinctDescList [(5,"a"), (5,"b"), (3,"b")]) == False
--
-- @since 0.5.8

-- For some reason, when 'singleton' is used in fromDistinctDescList or in
-- create, it is not inlined, so we inline it manually.

-- See Note [fromDistinctAscList implementation] in Data.Set.Internal.
fromDistinctDescList :: [(k,a)] -> Map k a
fromDistinctDescList :: forall k a. [(k, a)] -> Map k a
fromDistinctDescList = forall k a. FromDistinctMonoState k a -> Map k a
fromDistinctDescList_linkAll forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
Foldable.foldl' forall k a.
FromDistinctMonoState k a -> (k, a) -> FromDistinctMonoState k a
next (forall k a. Stack k a -> FromDistinctMonoState k a
State0 forall k a. Stack k a
Nada)
  where
    next :: FromDistinctMonoState k a -> (k,a) -> FromDistinctMonoState k a
    next :: forall k a.
FromDistinctMonoState k a -> (k, a) -> FromDistinctMonoState k a
next (State0 Stack k a
stk) (!k
kx, a
x) = forall k a. Map k a -> Stack k a -> FromDistinctMonoState k a
fromDistinctDescList_linkTop (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
kx a
x forall k a. Map k a
Tip forall k a. Map k a
Tip) Stack k a
stk
    next (State1 Map k a
r Stack k a
stk) (k
kx, a
x) = forall k a. Stack k a -> FromDistinctMonoState k a
State0 (forall k a. k -> a -> Map k a -> Stack k a -> Stack k a
Push k
kx a
x Map k a
r Stack k a
stk)
{-# INLINE fromDistinctDescList #-}  -- INLINE for fusion

fromDistinctDescList_linkTop :: Map k a -> Stack k a -> FromDistinctMonoState k a
fromDistinctDescList_linkTop :: forall k a. Map k a -> Stack k a -> FromDistinctMonoState k a
fromDistinctDescList_linkTop l :: Map k a
l@(Bin Size
lsz k
_ a
_ Map k a
_ Map k a
_) (Push k
kx a
x r :: Map k a
r@(Bin Size
rsz k
_ a
_ Map k a
_ Map k a
_) Stack k a
stk)
  | Size
lsz forall a. Eq a => a -> a -> Bool
== Size
rsz = forall k a. Map k a -> Stack k a -> FromDistinctMonoState k a
fromDistinctDescList_linkTop (forall k a. k -> a -> Map k a -> Map k a -> Map k a
bin k
kx a
x Map k a
l Map k a
r) Stack k a
stk
fromDistinctDescList_linkTop Map k a
r Stack k a
stk = forall k a. Map k a -> Stack k a -> FromDistinctMonoState k a
State1 Map k a
r Stack k a
stk
{-# INLINABLE fromDistinctDescList_linkTop #-}

fromDistinctDescList_linkAll :: FromDistinctMonoState k a -> Map k a
fromDistinctDescList_linkAll :: forall k a. FromDistinctMonoState k a -> Map k a
fromDistinctDescList_linkAll (State0 Stack k a
stk)    = forall b k a. (b -> k -> a -> Map k a -> b) -> b -> Stack k a -> b
foldl'Stack (\Map k a
l k
kx a
x Map k a
r -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
r) forall k a. Map k a
Tip Stack k a
stk
fromDistinctDescList_linkAll (State1 Map k a
l0 Stack k a
stk) = forall b k a. (b -> k -> a -> Map k a -> b) -> b -> Stack k a -> b
foldl'Stack (\Map k a
l k
kx a
x Map k a
r -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
r) Map k a
l0 Stack k a
stk
{-# INLINABLE fromDistinctDescList_linkAll #-}

data FromDistinctMonoState k a
  = State0 !(Stack k a)
  | State1 !(Map k a) !(Stack k a)

data Stack k a = Push !k a !(Map k a) !(Stack k a) | Nada

foldl'Stack :: (b -> k -> a -> Map k a -> b) -> b -> Stack k a -> b
foldl'Stack :: forall b k a. (b -> k -> a -> Map k a -> b) -> b -> Stack k a -> b
foldl'Stack b -> k -> a -> Map k a -> b
f = b -> Stack k a -> b
go
  where
    go :: b -> Stack k a -> b
go !b
z Stack k a
Nada = b
z
    go b
z (Push k
kx a
x Map k a
t Stack k a
stk) = b -> Stack k a -> b
go (b -> k -> a -> Map k a -> b
f b
z k
kx a
x Map k a
t) Stack k a
stk
{-# INLINE foldl'Stack #-}

{-
-- Functions very similar to these were used to implement
-- hedge union, intersection, and difference algorithms that we no
-- longer use. These functions, however, seem likely to be useful
-- in their own right, so I'm leaving them here in case we end up
-- exporting them.

{--------------------------------------------------------------------
  [filterGt b t] filter all keys >[b] from tree [t]
  [filterLt b t] filter all keys <[b] from tree [t]
--------------------------------------------------------------------}
filterGt :: Ord k => k -> Map k v -> Map k v
filterGt !_ Tip = Tip
filterGt !b (Bin _ kx x l r) =
  case compare b kx of LT -> link kx x (filterGt b l) r
                       EQ -> r
                       GT -> filterGt b r
#if __GLASGOW_HASKELL__
{-# INLINABLE filterGt #-}
#endif

filterLt :: Ord k => k -> Map k v -> Map k v
filterLt !_ Tip = Tip
filterLt !b (Bin _ kx x l r) =
  case compare kx b of LT -> link kx x l (filterLt b r)
                       EQ -> l
                       GT -> filterLt b l
#if __GLASGOW_HASKELL__
{-# INLINABLE filterLt #-}
#endif
-}

{--------------------------------------------------------------------
  Split
--------------------------------------------------------------------}
-- | \(O(\log n)\). The expression (@'split' k map@) is a pair @(map1,map2)@ where
-- the keys in @map1@ are smaller than @k@ and the 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 :: Ord k => k -> Map k a -> (Map k a,Map k a)
split :: forall k a. Ord k => k -> Map k a -> (Map k a, Map k a)
split !k
k0 Map k a
t0 = forall a b. StrictPair a b -> (a, b)
toPair forall a b. (a -> b) -> a -> b
$ forall {k} {a}.
Ord k =>
k -> Map k a -> StrictPair (Map k a) (Map k a)
go k
k0 Map k a
t0
  where
    go :: k -> Map k a -> StrictPair (Map k a) (Map k a)
go k
k Map k a
t =
      case Map k a
t of
        Map k a
Tip            -> forall k a. Map k a
Tip forall a b. a -> b -> StrictPair a b
:*: forall k a. Map k a
Tip
        Bin Size
_ k
kx a
x Map k a
l Map k a
r -> case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
          Ordering
LT -> let (Map k a
lt :*: Map k a
gt) = k -> Map k a -> StrictPair (Map k a) (Map k a)
go k
k Map k a
l in Map k a
lt forall a b. a -> b -> StrictPair a b
:*: forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
gt Map k a
r
          Ordering
GT -> let (Map k a
lt :*: Map k a
gt) = k -> Map k a -> StrictPair (Map k a) (Map k a)
go k
k Map k a
r in forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
lt forall a b. a -> b -> StrictPair a b
:*: Map k a
gt
          Ordering
EQ -> (Map k a
l forall a b. a -> b -> StrictPair a b
:*: Map k a
r)
#if __GLASGOW_HASKELL__
{-# INLINABLE split #-}
#endif

-- | \(O(\log n)\). The expression (@'splitLookup' k map@) splits a map just
-- like 'split' but also returns @'lookup' k 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 :: Ord k => k -> Map k a -> (Map k a,Maybe a,Map k a)
splitLookup :: forall k a. Ord k => k -> Map k a -> (Map k a, Maybe a, Map k a)
splitLookup k
k0 Map k a
m = case forall k a.
Ord k =>
k -> Map k a -> StrictTriple (Map k a) (Maybe a) (Map k a)
go k
k0 Map k a
m of
     StrictTriple Map k a
l Maybe a
mv Map k a
r -> (Map k a
l, Maybe a
mv, Map k a
r)
  where
    go :: Ord k => k -> Map k a -> StrictTriple (Map k a) (Maybe a) (Map k a)
    go :: forall k a.
Ord k =>
k -> Map k a -> StrictTriple (Map k a) (Maybe a) (Map k a)
go !k
k Map k a
t =
      case Map k a
t of
        Map k a
Tip            -> forall a b c. a -> b -> c -> StrictTriple a b c
StrictTriple forall k a. Map k a
Tip forall a. Maybe a
Nothing forall k a. Map k a
Tip
        Bin Size
_ k
kx a
x Map k a
l Map k a
r -> case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
          Ordering
LT -> let StrictTriple Map k a
lt Maybe a
z Map k a
gt = forall k a.
Ord k =>
k -> Map k a -> StrictTriple (Map k a) (Maybe a) (Map k a)
go k
k Map k a
l
                    !gt' :: Map k a
gt' = forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
gt Map k a
r
                in forall a b c. a -> b -> c -> StrictTriple a b c
StrictTriple Map k a
lt Maybe a
z Map k a
gt'
          Ordering
GT -> let StrictTriple Map k a
lt Maybe a
z Map k a
gt = forall k a.
Ord k =>
k -> Map k a -> StrictTriple (Map k a) (Maybe a) (Map k a)
go k
k Map k a
r
                    !lt' :: Map k a
lt' = forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
lt
                in forall a b c. a -> b -> c -> StrictTriple a b c
StrictTriple Map k a
lt' Maybe a
z Map k a
gt
          Ordering
EQ -> forall a b c. a -> b -> c -> StrictTriple a b c
StrictTriple Map k a
l (forall a. a -> Maybe a
Just a
x) Map k a
r
#if __GLASGOW_HASKELL__
{-# INLINABLE splitLookup #-}
#endif

-- | \(O(\log n)\). A variant of 'splitLookup' that indicates only whether the
-- key was present, rather than producing its value. This is used to
-- implement 'intersection' to avoid allocating unnecessary 'Just'
-- constructors.
splitMember :: Ord k => k -> Map k a -> (Map k a,Bool,Map k a)
splitMember :: forall k a. Ord k => k -> Map k a -> (Map k a, Bool, Map k a)
splitMember k
k0 Map k a
m = case forall k a.
Ord k =>
k -> Map k a -> StrictTriple (Map k a) Bool (Map k a)
go k
k0 Map k a
m of
     StrictTriple Map k a
l Bool
mv Map k a
r -> (Map k a
l, Bool
mv, Map k a
r)
  where
    go :: Ord k => k -> Map k a -> StrictTriple (Map k a) Bool (Map k a)
    go :: forall k a.
Ord k =>
k -> Map k a -> StrictTriple (Map k a) Bool (Map k a)
go !k
k Map k a
t =
      case Map k a
t of
        Map k a
Tip            -> forall a b c. a -> b -> c -> StrictTriple a b c
StrictTriple forall k a. Map k a
Tip Bool
False forall k a. Map k a
Tip
        Bin Size
_ k
kx a
x Map k a
l Map k a
r -> case forall a. Ord a => a -> a -> Ordering
compare k
k k
kx of
          Ordering
LT -> let StrictTriple Map k a
lt Bool
z Map k a
gt = forall k a.
Ord k =>
k -> Map k a -> StrictTriple (Map k a) Bool (Map k a)
go k
k Map k a
l
                    !gt' :: Map k a
gt' = forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
gt Map k a
r
                in forall a b c. a -> b -> c -> StrictTriple a b c
StrictTriple Map k a
lt Bool
z Map k a
gt'
          Ordering
GT -> let StrictTriple Map k a
lt Bool
z Map k a
gt = forall k a.
Ord k =>
k -> Map k a -> StrictTriple (Map k a) Bool (Map k a)
go k
k Map k a
r
                    !lt' :: Map k a
lt' = forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
lt
                in forall a b c. a -> b -> c -> StrictTriple a b c
StrictTriple Map k a
lt' Bool
z Map k a
gt
          Ordering
EQ -> forall a b c. a -> b -> c -> StrictTriple a b c
StrictTriple Map k a
l Bool
True Map k a
r
#if __GLASGOW_HASKELL__
{-# INLINABLE splitMember #-}
#endif

data StrictTriple a b c = StrictTriple !a !b !c

{--------------------------------------------------------------------
  Utility functions that maintain the balance properties of the tree.
  All constructors assume that all values in [l] < [k] and all values
  in [r] > [k], and that [l] and [r] are valid trees.

  In order of sophistication:
    [Bin sz k x l r]  The type constructor.
    [bin k x l r]     Maintains the correct size, assumes that both [l]
                      and [r] are balanced with respect to each other.
    [balance k x l r] Restores the balance and size.
                      Assumes that the original tree was balanced and
                      that [l] or [r] has changed by at most one element.
    [link k x l r]    Restores balance and size.

  Furthermore, we can construct a new tree from two trees. Both operations
  assume that all values in [l] < all values in [r] and that [l] and [r]
  are valid:
    [glue l r]        Glues [l] and [r] together. Assumes that [l] and
                      [r] are already balanced with respect to each other.
    [link2 l r]       Merges two trees and restores balance.
--------------------------------------------------------------------}

{--------------------------------------------------------------------
  Link
--------------------------------------------------------------------}
link :: k -> a -> Map k a -> Map k a -> Map k a
link :: forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
Tip Map k a
r  = forall k a. k -> a -> Map k a -> Map k a
insertMin k
kx a
x Map k a
r
link k
kx a
x Map k a
l Map k a
Tip  = forall k a. k -> a -> Map k a -> Map k a
insertMax k
kx a
x Map k a
l
link k
kx a
x l :: Map k a
l@(Bin Size
sizeL k
ky a
y Map k a
ly Map k a
ry) r :: Map k a
r@(Bin Size
sizeR k
kz a
z Map k a
lz Map k a
rz)
  | Size
deltaforall a. Num a => a -> a -> a
*Size
sizeL forall a. Ord a => a -> a -> Bool
< Size
sizeR  = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
kz a
z (forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
l Map k a
lz) Map k a
rz
  | Size
deltaforall a. Num a => a -> a -> a
*Size
sizeR forall a. Ord a => a -> a -> Bool
< Size
sizeL  = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y Map k a
ly (forall k a. k -> a -> Map k a -> Map k a -> Map k a
link k
kx a
x Map k a
ry Map k a
r)
  | Bool
otherwise            = forall k a. k -> a -> Map k a -> Map k a -> Map k a
bin k
kx a
x Map k a
l Map k a
r


-- insertMin and insertMax don't perform potentially expensive comparisons.
insertMax,insertMin :: k -> a -> Map k a -> Map k a
insertMax :: forall k a. k -> a -> Map k a -> Map k a
insertMax k
kx a
x Map k a
t
  = case Map k a
t of
      Map k a
Tip -> forall k a. k -> a -> Map k a
singleton k
kx a
x
      Bin Size
_ k
ky a
y Map k a
l Map k a
r
          -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
ky a
y Map k a
l (forall k a. k -> a -> Map k a -> Map k a
insertMax k
kx a
x Map k a
r)

insertMin :: forall k a. k -> a -> Map k a -> Map k a
insertMin k
kx a
x Map k a
t
  = case Map k a
t of
      Map k a
Tip -> forall k a. k -> a -> Map k a
singleton k
kx a
x
      Bin Size
_ k
ky a
y Map k a
l Map k a
r
          -> forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y (forall k a. k -> a -> Map k a -> Map k a
insertMin k
kx a
x Map k a
l) Map k a
r

{--------------------------------------------------------------------
  [link2 l r]: merges two trees.
--------------------------------------------------------------------}
link2 :: Map k a -> Map k a -> Map k a
link2 :: forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
Tip Map k a
r   = Map k a
r
link2 Map k a
l Map k a
Tip   = Map k a
l
link2 l :: Map k a
l@(Bin Size
sizeL k
kx a
x Map k a
lx Map k a
rx) r :: Map k a
r@(Bin Size
sizeR k
ky a
y Map k a
ly Map k a
ry)
  | Size
deltaforall a. Num a => a -> a -> a
*Size
sizeL forall a. Ord a => a -> a -> Bool
< Size
sizeR = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
ky a
y (forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
l Map k a
ly) Map k a
ry
  | Size
deltaforall a. Num a => a -> a -> a
*Size
sizeR forall a. Ord a => a -> a -> Bool
< Size
sizeL = forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
kx a
x Map k a
lx (forall k a. Map k a -> Map k a -> Map k a
link2 Map k a
rx Map k a
r)
  | Bool
otherwise           = forall k a. Map k a -> Map k a -> Map k a
glue Map k a
l Map k a
r

{--------------------------------------------------------------------
  [glue l r]: glues two trees together.
  Assumes that [l] and [r] are already balanced with respect to each other.
--------------------------------------------------------------------}
glue :: Map k a -> Map k a -> Map k a
glue :: forall k a. Map k a -> Map k a -> Map k a
glue Map k a
Tip Map k a
r = Map k a
r
glue Map k a
l Map k a
Tip = Map k a
l
glue l :: Map k a
l@(Bin Size
sl k
kl a
xl Map k a
ll Map k a
lr) r :: Map k a
r@(Bin Size
sr k
kr a
xr Map k a
rl Map k a
rr)
  | Size
sl forall a. Ord a => a -> a -> Bool
> Size
sr = let !(MaxView k
km a
m Map k a
l') = forall k a. k -> a -> Map k a -> Map k a -> MaxView k a
maxViewSure k
kl a
xl Map k a
ll Map k a
lr in forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
km a
m Map k a
l' Map k a
r
  | Bool
otherwise = let !(MinView k
km a
m Map k a
r') = forall k a. k -> a -> Map k a -> Map k a -> MinView k a
minViewSure k
kr a
xr Map k a
rl Map k a
rr in forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
km a
m Map k a
l Map k a
r'

data MinView k a = MinView !k a !(Map k a)
data MaxView k a = MaxView !k a !(Map k a)

minViewSure :: k -> a -> Map k a -> Map k a -> MinView k a
minViewSure :: forall k a. k -> a -> Map k a -> Map k a -> MinView k a
minViewSure = forall k a. k -> a -> Map k a -> Map k a -> MinView k a
go
  where
    go :: t -> t -> Map t t -> Map t t -> MinView t t
go t
k t
x Map t t
Tip Map t t
r = forall k a. k -> a -> Map k a -> MinView k a
MinView t
k t
x Map t t
r
    go t
k t
x (Bin Size
_ t
kl t
xl Map t t
ll Map t t
lr) Map t t
r =
      case t -> t -> Map t t -> Map t t -> MinView t t
go t
kl t
xl Map t t
ll Map t t
lr of
        MinView t
km t
xm Map t t
l' -> forall k a. k -> a -> Map k a -> MinView k a
MinView t
km t
xm (forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR t
k t
x Map t t
l' Map t t
r)
{-# NOINLINE minViewSure #-}

maxViewSure :: k -> a -> Map k a -> Map k a -> MaxView k a
maxViewSure :: forall k a. k -> a -> Map k a -> Map k a -> MaxView k a
maxViewSure = forall k a. k -> a -> Map k a -> Map k a -> MaxView k a
go
  where
    go :: t -> t -> Map t t -> Map t t -> MaxView t t
go t
k t
x Map t t
l Map t t
Tip = forall k a. k -> a -> Map k a -> MaxView k a
MaxView t
k t
x Map t t
l
    go t
k t
x Map t t
l (Bin Size
_ t
kr t
xr Map t t
rl Map t t
rr) =
      case t -> t -> Map t t -> Map t t -> MaxView t t
go t
kr t
xr Map t t
rl Map t t
rr of
        MaxView t
km t
xm Map t t
r' -> forall k a. k -> a -> Map k a -> MaxView k a
MaxView t
km t
xm (forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL t
k t
x Map t t
l Map t t
r')
{-# NOINLINE maxViewSure #-}

-- | \(O(\log n)\). Delete and find the minimal element.
--
-- > deleteFindMin (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((3,"b"), fromList[(5,"a"), (10,"c")])
-- > deleteFindMin empty                                      Error: can not return the minimal element of an empty map

deleteFindMin :: Map k a -> ((k,a),Map k a)
deleteFindMin :: forall k a. Map k a -> ((k, a), Map k a)
deleteFindMin Map k a
t = case forall k a. Map k a -> Maybe ((k, a), Map k a)
minViewWithKey Map k a
t of
  Maybe ((k, a), Map k a)
Nothing -> (forall a. HasCallStack => [Char] -> a
error [Char]
"Map.deleteFindMin: can not return the minimal element of an empty map", forall k a. Map k a
Tip)
  Just ((k, a), Map k a)
res -> ((k, a), Map k a)
res

-- | \(O(\log n)\). Delete and find the maximal element.
--
-- > deleteFindMax (fromList [(5,"a"), (3,"b"), (10,"c")]) == ((10,"c"), fromList [(3,"b"), (5,"a")])
-- > deleteFindMax empty                                      Error: can not return the maximal element of an empty map

deleteFindMax :: Map k a -> ((k,a),Map k a)
deleteFindMax :: forall k a. Map k a -> ((k, a), Map k a)
deleteFindMax Map k a
t = case forall k a. Map k a -> Maybe ((k, a), Map k a)
maxViewWithKey Map k a
t of
  Maybe ((k, a), Map k a)
Nothing -> (forall a. HasCallStack => [Char] -> a
error [Char]
"Map.deleteFindMax: can not return the maximal element of an empty map", forall k a. Map k a
Tip)
  Just ((k, a), Map k a)
res -> ((k, a), Map k a)
res

{--------------------------------------------------------------------
  [balance l x r] balances two trees with value x.
  The sizes of the trees should balance after decreasing the
  size of one of them. (a rotation).

  [delta] is the maximal relative difference between the sizes of
          two trees, it corresponds with the [w] in Adams' paper.
  [ratio] is the ratio between an outer and inner sibling of the
          heavier subtree in an unbalanced setting. It determines
          whether a double or single rotation should be performed
          to restore balance. It is corresponds with the inverse
          of $\alpha$ in Adam's article.

  Note that according to the Adam's paper:
  - [delta] should be larger than 4.646 with a [ratio] of 2.
  - [delta] should be larger than 3.745 with a [ratio] of 1.534.

  But the Adam's paper is erroneous:
  - It can be proved that for delta=2 and delta>=5 there does
    not exist any ratio that would work.
  - Delta=4.5 and ratio=2 does not work.

  That leaves two reasonable variants, delta=3 and delta=4,
  both with ratio=2.

  - A lower [delta] leads to a more 'perfectly' balanced tree.
  - A higher [delta] performs less rebalancing.

  In the benchmarks, delta=3 is faster on insert operations,
  and delta=4 has slightly better deletes. As the insert speedup
  is larger, we currently use delta=3.

--------------------------------------------------------------------}
delta,ratio :: Int
delta :: Size
delta = Size
3
ratio :: Size
ratio = Size
2

-- The balance function is equivalent to the following:
--
--   balance :: k -> a -> Map k a -> Map k a -> Map k a
--   balance k x l r
--     | sizeL + sizeR <= 1    = Bin sizeX k x l r
--     | sizeR > delta*sizeL   = rotateL k x l r
--     | sizeL > delta*sizeR   = rotateR k x l r
--     | otherwise             = Bin sizeX k x l r
--     where
--       sizeL = size l
--       sizeR = size r
--       sizeX = sizeL + sizeR + 1
--
--   rotateL :: a -> b -> Map a b -> Map a b -> Map a b
--   rotateL k x l r@(Bin _ _ _ ly ry) | size ly < ratio*size ry = singleL k x l r
--                                     | otherwise               = doubleL k x l r
--
--   rotateR :: a -> b -> Map a b -> Map a b -> Map a b
--   rotateR k x l@(Bin _ _ _ ly ry) r | size ry < ratio*size ly = singleR k x l r
--                                     | otherwise               = doubleR k x l r
--
--   singleL, singleR :: a -> b -> Map a b -> Map a b -> Map a b
--   singleL k1 x1 t1 (Bin _ k2 x2 t2 t3)  = bin k2 x2 (bin k1 x1 t1 t2) t3
--   singleR k1 x1 (Bin _ k2 x2 t1 t2) t3  = bin k2 x2 t1 (bin k1 x1 t2 t3)
--
--   doubleL, doubleR :: a -> b -> Map a b -> Map a b -> Map a b
--   doubleL k1 x1 t1 (Bin _ k2 x2 (Bin _ k3 x3 t2 t3) t4) = bin k3 x3 (bin k1 x1 t1 t2) (bin k2 x2 t3 t4)
--   doubleR k1 x1 (Bin _ k2 x2 t1 (Bin _ k3 x3 t2 t3)) t4 = bin k3 x3 (bin k2 x2 t1 t2) (bin k1 x1 t3 t4)
--
-- It is only written in such a way that every node is pattern-matched only once.

balance :: k -> a -> Map k a -> Map k a -> Map k a
balance :: forall k a. k -> a -> Map k a -> Map k a -> Map k a
balance k
k a
x Map k a
l Map k a
r = case Map k a
l of
  Map k a
Tip -> case Map k a
r of
           Map k a
Tip -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip
           (Bin Size
_ k
_ a
_ Map k a
Tip Map k a
Tip) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
2 k
k a
x forall k a. Map k a
Tip Map k a
r
           (Bin Size
_ k
rk a
rx Map k a
Tip rr :: Map k a
rr@(Bin Size
_ k
_ a
_ Map k a
_ Map k a
_)) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
3 k
rk a
rx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip) Map k a
rr
           (Bin Size
_ k
rk a
rx (Bin Size
_ k
rlk a
rlx Map k a
_ Map k a
_) Map k a
Tip) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
3 k
rlk a
rlx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
rk a
rx forall k a. Map k a
Tip forall k a. Map k a
Tip)
           (Bin Size
rs k
rk a
rx rl :: Map k a
rl@(Bin Size
rls k
rlk a
rlx Map k a
rll Map k a
rlr) rr :: Map k a
rr@(Bin Size
rrs k
_ a
_ Map k a
_ Map k a
_))
             | Size
rls forall a. Ord a => a -> a -> Bool
< Size
ratioforall a. Num a => a -> a -> a
*Size
rrs -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rs) k
rk a
rx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rls) k
k a
x forall k a. Map k a
Tip Map k a
rl) Map k a
rr
             | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rs) k
rlk a
rlx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
rll) k
k a
x forall k a. Map k a
Tip Map k a
rll) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rrsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
rlr) k
rk a
rx Map k a
rlr Map k a
rr)

  (Bin Size
ls k
lk a
lx Map k a
ll Map k a
lr) -> case Map k a
r of
           Map k a
Tip -> case (Map k a
ll, Map k a
lr) of
                    (Map k a
Tip, Map k a
Tip) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
2 k
k a
x Map k a
l forall k a. Map k a
Tip
                    (Map k a
Tip, (Bin Size
_ k
lrk a
lrx Map k a
_ Map k a
_)) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
3 k
lrk a
lrx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
lk a
lx forall k a. Map k a
Tip forall k a. Map k a
Tip) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip)
                    ((Bin Size
_ k
_ a
_ Map k a
_ Map k a
_), Map k a
Tip) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
3 k
lk a
lx Map k a
ll (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip)
                    ((Bin Size
lls k
_ a
_ Map k a
_ Map k a
_), (Bin Size
lrs k
lrk a
lrx Map k a
lrl Map k a
lrr))
                      | Size
lrs forall a. Ord a => a -> a -> Bool
< Size
ratioforall a. Num a => a -> a -> a
*Size
lls -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
ls) k
lk a
lx Map k a
ll (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lrs) k
k a
x Map k a
lr forall k a. Map k a
Tip)
                      | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
ls) k
lrk a
lrx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
llsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
lrl) k
lk a
lx Map k a
ll Map k a
lrl) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
lrr) k
k a
x Map k a
lrr forall k a. Map k a
Tip)
           (Bin Size
rs k
rk a
rx Map k a
rl Map k a
rr)
              | Size
rs forall a. Ord a => a -> a -> Bool
> Size
deltaforall a. Num a => a -> a -> a
*Size
ls  -> case (Map k a
rl, Map k a
rr) of
                   (Bin Size
rls k
rlk a
rlx Map k a
rll Map k a
rlr, Bin Size
rrs k
_ a
_ Map k a
_ Map k a
_)
                     | Size
rls forall a. Ord a => a -> a -> Bool
< Size
ratioforall a. Num a => a -> a -> a
*Size
rrs -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
rk a
rx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rls) k
k a
x Map k a
l Map k a
rl) Map k a
rr
                     | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
rlk a
rlx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
rll) k
k a
x Map k a
l Map k a
rll) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rrsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
rlr) k
rk a
rx Map k a
rlr Map k a
rr)
                   (Map k a
_, Map k a
_) -> forall a. HasCallStack => [Char] -> a
error [Char]
"Failure in Data.Map.balance"
              | Size
ls forall a. Ord a => a -> a -> Bool
> Size
deltaforall a. Num a => a -> a -> a
*Size
rs  -> case (Map k a
ll, Map k a
lr) of
                   (Bin Size
lls k
_ a
_ Map k a
_ Map k a
_, Bin Size
lrs k
lrk a
lrx Map k a
lrl Map k a
lrr)
                     | Size
lrs forall a. Ord a => a -> a -> Bool
< Size
ratioforall a. Num a => a -> a -> a
*Size
lls -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
lk a
lx Map k a
ll (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rsforall a. Num a => a -> a -> a
+Size
lrs) k
k a
x Map k a
lr Map k a
r)
                     | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
lrk a
lrx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
llsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
lrl) k
lk a
lx Map k a
ll Map k a
lrl) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
lrr) k
k a
x Map k a
lrr Map k a
r)
                   (Map k a
_, Map k a
_) -> forall a. HasCallStack => [Char] -> a
error [Char]
"Failure in Data.Map.balance"
              | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
k a
x Map k a
l Map k a
r
{-# NOINLINE balance #-}

-- Functions balanceL and balanceR are specialised versions of balance.
-- balanceL only checks whether the left subtree is too big,
-- balanceR only checks whether the right subtree is too big.

-- balanceL is called when left subtree might have been inserted to or when
-- right subtree might have been deleted from.
balanceL :: k -> a -> Map k a -> Map k a -> Map k a
balanceL :: forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceL k
k a
x Map k a
l Map k a
r = case Map k a
r of
  Map k a
Tip -> case Map k a
l of
           Map k a
Tip -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip
           (Bin Size
_ k
_ a
_ Map k a
Tip Map k a
Tip) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
2 k
k a
x Map k a
l forall k a. Map k a
Tip
           (Bin Size
_ k
lk a
lx Map k a
Tip (Bin Size
_ k
lrk a
lrx Map k a
_ Map k a
_)) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
3 k
lrk a
lrx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
lk a
lx forall k a. Map k a
Tip forall k a. Map k a
Tip) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip)
           (Bin Size
_ k
lk a
lx ll :: Map k a
ll@(Bin Size
_ k
_ a
_ Map k a
_ Map k a
_) Map k a
Tip) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
3 k
lk a
lx Map k a
ll (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip)
           (Bin Size
ls k
lk a
lx ll :: Map k a
ll@(Bin Size
lls k
_ a
_ Map k a
_ Map k a
_) lr :: Map k a
lr@(Bin Size
lrs k
lrk a
lrx Map k a
lrl Map k a
lrr))
             | Size
lrs forall a. Ord a => a -> a -> Bool
< Size
ratioforall a. Num a => a -> a -> a
*Size
lls -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
ls) k
lk a
lx Map k a
ll (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lrs) k
k a
x Map k a
lr forall k a. Map k a
Tip)
             | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
ls) k
lrk a
lrx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
llsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
lrl) k
lk a
lx Map k a
ll Map k a
lrl) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
lrr) k
k a
x Map k a
lrr forall k a. Map k a
Tip)

  (Bin Size
rs k
_ a
_ Map k a
_ Map k a
_) -> case Map k a
l of
           Map k a
Tip -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rs) k
k a
x forall k a. Map k a
Tip Map k a
r

           (Bin Size
ls k
lk a
lx Map k a
ll Map k a
lr)
              | Size
ls forall a. Ord a => a -> a -> Bool
> Size
deltaforall a. Num a => a -> a -> a
*Size
rs  -> case (Map k a
ll, Map k a
lr) of
                   (Bin Size
lls k
_ a
_ Map k a
_ Map k a
_, Bin Size
lrs k
lrk a
lrx Map k a
lrl Map k a
lrr)
                     | Size
lrs forall a. Ord a => a -> a -> Bool
< Size
ratioforall a. Num a => a -> a -> a
*Size
lls -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
lk a
lx Map k a
ll (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rsforall a. Num a => a -> a -> a
+Size
lrs) k
k a
x Map k a
lr Map k a
r)
                     | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
lrk a
lrx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
llsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
lrl) k
lk a
lx Map k a
ll Map k a
lrl) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
lrr) k
k a
x Map k a
lrr Map k a
r)
                   (Map k a
_, Map k a
_) -> forall a. HasCallStack => [Char] -> a
error [Char]
"Failure in Data.Map.balanceL"
              | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
k a
x Map k a
l Map k a
r
{-# NOINLINE balanceL #-}

-- balanceR is called when right subtree might have been inserted to or when
-- left subtree might have been deleted from.
balanceR :: k -> a -> Map k a -> Map k a -> Map k a
balanceR :: forall k a. k -> a -> Map k a -> Map k a -> Map k a
balanceR k
k a
x Map k a
l Map k a
r = case Map k a
l of
  Map k a
Tip -> case Map k a
r of
           Map k a
Tip -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip
           (Bin Size
_ k
_ a
_ Map k a
Tip Map k a
Tip) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
2 k
k a
x forall k a. Map k a
Tip Map k a
r
           (Bin Size
_ k
rk a
rx Map k a
Tip rr :: Map k a
rr@(Bin Size
_ k
_ a
_ Map k a
_ Map k a
_)) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
3 k
rk a
rx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip) Map k a
rr
           (Bin Size
_ k
rk a
rx (Bin Size
_ k
rlk a
rlx Map k a
_ Map k a
_) Map k a
Tip) -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
3 k
rlk a
rlx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
k a
x forall k a. Map k a
Tip forall k a. Map k a
Tip) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
1 k
rk a
rx forall k a. Map k a
Tip forall k a. Map k a
Tip)
           (Bin Size
rs k
rk a
rx rl :: Map k a
rl@(Bin Size
rls k
rlk a
rlx Map k a
rll Map k a
rlr) rr :: Map k a
rr@(Bin Size
rrs k
_ a
_ Map k a
_ Map k a
_))
             | Size
rls forall a. Ord a => a -> a -> Bool
< Size
ratioforall a. Num a => a -> a -> a
*Size
rrs -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rs) k
rk a
rx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rls) k
k a
x forall k a. Map k a
Tip Map k a
rl) Map k a
rr
             | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rs) k
rlk a
rlx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
rll) k
k a
x forall k a. Map k a
Tip Map k a
rll) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rrsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
rlr) k
rk a
rx Map k a
rlr Map k a
rr)

  (Bin Size
ls k
_ a
_ Map k a
_ Map k a
_) -> case Map k a
r of
           Map k a
Tip -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
ls) k
k a
x Map k a
l forall k a. Map k a
Tip

           (Bin Size
rs k
rk a
rx Map k a
rl Map k a
rr)
              | Size
rs forall a. Ord a => a -> a -> Bool
> Size
deltaforall a. Num a => a -> a -> a
*Size
ls  -> case (Map k a
rl, Map k a
rr) of
                   (Bin Size
rls k
rlk a
rlx Map k a
rll Map k a
rlr, Bin Size
rrs k
_ a
_ Map k a
_ Map k a
_)
                     | Size
rls forall a. Ord a => a -> a -> Bool
< Size
ratioforall a. Num a => a -> a -> a
*Size
rrs -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
rk a
rx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rls) k
k a
x Map k a
l Map k a
rl) Map k a
rr
                     | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
rlk a
rlx (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
rll) k
k a
x Map k a
l Map k a
rll) (forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
rrsforall a. Num a => a -> a -> a
+forall k a. Map k a -> Size
size Map k a
rlr) k
rk a
rx Map k a
rlr Map k a
rr)
                   (Map k a
_, Map k a
_) -> forall a. HasCallStack => [Char] -> a
error [Char]
"Failure in Data.Map.balanceR"
              | Bool
otherwise -> forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (Size
1forall a. Num a => a -> a -> a
+Size
lsforall a. Num a => a -> a -> a
+Size
rs) k
k a
x Map k a
l Map k a
r
{-# NOINLINE balanceR #-}


{--------------------------------------------------------------------
  The bin constructor maintains the size of the tree
--------------------------------------------------------------------}
bin :: k -> a -> Map k a -> Map k a -> Map k a
bin :: forall k a. k -> a -> Map k a -> Map k a -> Map k a
bin k
k a
x Map k a
l Map k a
r
  = forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin (forall k a. Map k a -> Size
size Map k a
l forall a. Num a => a -> a -> a
+ forall k a. Map k a -> Size
size Map k a
r forall a. Num a => a -> a -> a
+ Size
1) k
k a
x Map k a
l Map k a
r
{-# INLINE bin #-}


{--------------------------------------------------------------------
  Eq converts the tree to a list. In a lazy setting, this
  actually seems one of the faster methods to compare two trees
  and it is certainly the simplest :-)
--------------------------------------------------------------------}
instance (Eq k,Eq a) => Eq (Map k a) where
  Map k a
t1 == :: Map k a -> Map k a -> Bool
== Map k a
t2  = (forall k a. Map k a -> Size
size Map k a
t1 forall a. Eq a => a -> a -> Bool
== forall k a. Map k a -> Size
size Map k a
t2) Bool -> Bool -> Bool
&& (forall k a. Map k a -> [(k, a)]
toAscList Map k a
t1 forall a. Eq a => a -> a -> Bool
== forall k a. Map k a -> [(k, a)]
toAscList Map k a
t2)

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

instance (Ord k, Ord v) => Ord (Map k v) where
    compare :: Map k v -> Map k v -> Ordering
compare Map k v
m1 Map k v
m2 = forall a. Ord a => a -> a -> Ordering
compare (forall k a. Map k a -> [(k, a)]
toAscList Map k v
m1) (forall k a. Map k a -> [(k, a)]
toAscList Map k v
m2)

{--------------------------------------------------------------------
  Lifted instances
--------------------------------------------------------------------}

-- | @since 0.5.9
instance Eq2 Map where
    liftEq2 :: forall a b c d.
(a -> b -> Bool) -> (c -> d -> Bool) -> Map a c -> Map b d -> Bool
liftEq2 a -> b -> Bool
eqk c -> d -> Bool
eqv Map a c
m Map b d
n =
        forall k a. Map k a -> Size
size Map a c
m forall a. Eq a => a -> a -> Bool
== forall k a. Map k a -> Size
size Map b d
n Bool -> Bool -> Bool
&& forall (f :: * -> *) a b.
Eq1 f =>
(a -> b -> Bool) -> f a -> f b -> Bool
liftEq (forall (f :: * -> * -> *) a b c d.
Eq2 f =>
(a -> b -> Bool) -> (c -> d -> Bool) -> f a c -> f b d -> Bool
liftEq2 a -> b -> Bool
eqk c -> d -> Bool
eqv) (forall k a. Map k a -> [(k, a)]
toList Map a c
m) (forall k a. Map k a -> [(k, a)]
toList Map b d
n)

-- | @since 0.5.9
instance Eq k => Eq1 (Map k) where
    liftEq :: forall a b. (a -> b -> Bool) -> Map k a -> Map k b -> Bool
liftEq = forall (f :: * -> * -> *) a b c d.
Eq2 f =>
(a -> b -> Bool) -> (c -> d -> Bool) -> f a c -> f b d -> Bool
liftEq2 forall a. Eq a => a -> a -> Bool
(==)

-- | @since 0.5.9
instance Ord2 Map where
    liftCompare2 :: forall a b c d.
(a -> b -> Ordering)
-> (c -> d -> Ordering) -> Map a c -> Map b d -> Ordering
liftCompare2 a -> b -> Ordering
cmpk c -> d -> Ordering
cmpv Map a c
m Map b d
n =
        forall (f :: * -> *) a b.
Ord1 f =>
(a -> b -> Ordering) -> f a -> f b -> Ordering
liftCompare (forall (f :: * -> * -> *) a b c d.
Ord2 f =>
(a -> b -> Ordering)
-> (c -> d -> Ordering) -> f a c -> f b d -> Ordering
liftCompare2 a -> b -> Ordering
cmpk c -> d -> Ordering
cmpv) (forall k a. Map k a -> [(k, a)]
toList Map a c
m) (forall k a. Map k a -> [(k, a)]
toList Map b d
n)

-- | @since 0.5.9
instance Ord k => Ord1 (Map k) where
    liftCompare :: forall a b. (a -> b -> Ordering) -> Map k a -> Map k b -> Ordering
liftCompare = forall (f :: * -> * -> *) a b c d.
Ord2 f =>
(a -> b -> Ordering)
-> (c -> d -> Ordering) -> f a c -> f b d -> Ordering
liftCompare2 forall a. Ord a => a -> a -> Ordering
compare

-- | @since 0.5.9
instance Show2 Map where
    liftShowsPrec2 :: forall a b.
(Size -> a -> ShowS)
-> ([a] -> ShowS)
-> (Size -> b -> ShowS)
-> ([b] -> ShowS)
-> Size
-> Map a b
-> ShowS
liftShowsPrec2 Size -> a -> ShowS
spk [a] -> ShowS
slk Size -> b -> ShowS
spv [b] -> ShowS
slv Size
d Map a b
m =
        forall a. (Size -> a -> ShowS) -> [Char] -> Size -> a -> ShowS
showsUnaryWith (forall (f :: * -> *) a.
Show1 f =>
(Size -> a -> ShowS) -> ([a] -> ShowS) -> Size -> f a -> ShowS
liftShowsPrec Size -> (a, b) -> ShowS
sp [(a, b)] -> ShowS
sl) [Char]
"fromList" Size
d (forall k a. Map k a -> [(k, a)]
toList Map a b
m)
      where
        sp :: Size -> (a, b) -> ShowS
sp = forall (f :: * -> * -> *) a b.
Show2 f =>
(Size -> a -> ShowS)
-> ([a] -> ShowS)
-> (Size -> b -> ShowS)
-> ([b] -> ShowS)
-> Size
-> f a b
-> ShowS
liftShowsPrec2 Size -> a -> ShowS
spk [a] -> ShowS
slk Size -> b -> ShowS
spv [b] -> ShowS
slv
        sl :: [(a, b)] -> ShowS
sl = forall (f :: * -> * -> *) a b.
Show2 f =>
(Size -> a -> ShowS)
-> ([a] -> ShowS)
-> (Size -> b -> ShowS)
-> ([b] -> ShowS)
-> [f a b]
-> ShowS
liftShowList2 Size -> a -> ShowS
spk [a] -> ShowS
slk Size -> b -> ShowS
spv [b] -> ShowS
slv

-- | @since 0.5.9
instance Show k => Show1 (Map k) where
    liftShowsPrec :: forall a.
(Size -> a -> ShowS) -> ([a] -> ShowS) -> Size -> Map k a -> ShowS
liftShowsPrec = forall (f :: * -> * -> *) a b.
Show2 f =>
(Size -> a -> ShowS)
-> ([a] -> ShowS)
-> (Size -> b -> ShowS)
-> ([b] -> ShowS)
-> Size
-> f a b
-> ShowS
liftShowsPrec2 forall a. Show a => Size -> a -> ShowS
showsPrec forall a. Show a => [a] -> ShowS
showList

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

{--------------------------------------------------------------------
  Functor
--------------------------------------------------------------------}
instance Functor (Map k) where
  fmap :: forall a b. (a -> b) -> Map k a -> Map k b
fmap a -> b
f Map k a
m  = forall a b k. (a -> b) -> Map k a -> Map k b
map a -> b
f Map k a
m
#ifdef __GLASGOW_HASKELL__
  a
_ <$ :: forall a b. a -> Map k b -> Map k a
<$ Map k b
Tip = forall k a. Map k a
Tip
  a
a <$ (Bin Size
sx k
kx b
_ Map k b
l Map k b
r) = forall k a. Size -> k -> a -> Map k a -> Map k a -> Map k a
Bin Size
sx k
kx a
a (a
a forall (f :: * -> *) a b. Functor f => a -> f b -> f a
<$ Map k b
l) (a
a forall (f :: * -> *) a b. Functor f => a -> f b -> f a
<$ Map k b
r)
#endif

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

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

          go :: t -> Map k t -> t
go !t
m Map k t
Tip = t
m
          go t
m (Bin Size
_ k
_ t
v Map k t
l Map k t
r) = t -> Map k t -> t
go (t -> Map k t -> t
go (forall a. Ord a => a -> a -> a
max t
m t
v) Map k t
l) Map k t
r
  {-# INLINABLE maximum #-}
  minimum :: forall a. Ord a => Map k a -> a
minimum = forall {a} {k}. Ord a => Map k a -> a
start
    where start :: Map k a -> a
start Map k a
Tip = forall a. HasCallStack => [Char] -> a
error [Char]
"Data.Foldable.minimum (for Data.Map): empty map"
          start (Bin Size
_ k
_ a
v Map k a
l Map k a
r) = forall {t} {k}. Ord t => t -> Map k t -> t
go (forall {t} {k}. Ord t => t -> Map k t -> t
go a
v Map k a
l) Map k a
r

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

-- | @since 0.6.3.1
instance Bifoldable Map where
  bifold :: forall m. Monoid m => Map m m -> m
bifold = forall m. Monoid m => Map m m -> m
go
    where go :: Map a a -> a
go Map a a
Tip = forall a. Monoid a => a
mempty
          go (Bin Size
1 a
k a
v Map a a
_ Map a a
_) = a
k forall a. Monoid a => a -> a -> a
`mappend` a
v
          go (Bin Size
_ a
k a
v Map a a
l Map a a
r) = Map a a -> a
go Map a a
l forall a. Monoid a => a -> a -> a
`mappend` (a
k forall a. Monoid a => a -> a -> a
`mappend` (a
v forall a. Monoid a => a -> a -> a
`mappend` Map a a -> a
go Map a a
r))
  {-# INLINABLE bifold #-}
  bifoldr :: forall a c b. (a -> c -> c) -> (b -> c -> c) -> c -> Map a b -> c
bifoldr a -> c -> c
f b -> c -> c
g c
z = c -> Map a b -> c
go c
z
    where go :: c -> Map a b -> c
go c
z' Map a b
Tip             = c
z'
          go c
z' (Bin Size
_ a
k b
v Map a b
l Map a b
r) = c -> Map a b -> c
go (a -> c -> c
f a
k (b -> c -> c
g b
v (c -> Map a b -> c
go c
z' Map a b
r))) Map a b
l
  {-# INLINE bifoldr #-}
  bifoldl :: forall c a b. (c -> a -> c) -> (c -> b -> c) -> c -> Map a b -> c
bifoldl c -> a -> c
f c -> b -> c
g c
z = c -> Map a b -> c
go c
z
    where go :: c -> Map a b -> c
go c
z' Map a b
Tip             = c
z'
          go c
z' (Bin Size
_ a
k b
v Map a b
l Map a b
r) = c -> Map a b -> c
go (c -> b -> c
g (c -> a -> c
f (c -> Map a b -> c
go c
z' Map a b
l) a
k) b
v) Map a b
r
  {-# INLINE bifoldl #-}
  bifoldMap :: forall m a b. Monoid m => (a -> m) -> (b -> m) -> Map a b -> m
bifoldMap a -> m
f b -> m
g Map a b
t = Map a b -> m
go Map a b
t
    where go :: Map a b -> m
go Map a b
Tip = forall a. Monoid a => a
mempty
          go (Bin Size
1 a
k b
v Map a b
_ Map a b
_) = a -> m
f a
k forall a. Monoid a => a -> a -> a
`mappend` b -> m
g b
v
          go (Bin Size
_ a
k b
v Map a b
l Map a b
r) = Map a b -> m
go Map a b
l forall a. Monoid a => a -> a -> a
`mappend` (a -> m
f a
k forall a. Monoid a => a -> a -> a
`mappend` (b -> m
g b
v forall a. Monoid a => a -> a -> a
`mappend` Map a b -> m
go Map a b
r))
  {-# INLINE bifoldMap #-}

instance (NFData k, NFData a) => NFData (Map k a) where
    rnf :: Map k a -> ()
rnf Map k a
Tip = ()
    rnf (Bin Size
_ k
kx a
x Map k a
l Map k a
r) = forall a. NFData a => a -> ()
rnf k
kx seq :: forall a b. a -> b -> b
`seq` forall a. NFData a => a -> ()
rnf a
x seq :: forall a b. a -> b -> b
`seq` forall a. NFData a => a -> ()
rnf Map k a
l seq :: forall a b. a -> b -> b
`seq` forall a. NFData a => a -> ()
rnf Map k a
r

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

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

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

{--------------------------------------------------------------------
  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] ['a'..])) ==
-- >   [fromList [(1,'a'),(2,'b'),(3,'c')],fromList [(4,'d')],fromList [(5,'e'),(6,'f')]]
--
-- > splitRoot empty == []
--
--  Note that the current implementation does not return more than three submaps,
--  but you should not depend on this behaviour because it can change in the
--  future without notice.
--
-- @since 0.5.4
splitRoot :: Map k b -> [Map k b]
splitRoot :: forall k b. Map k b -> [Map k b]
splitRoot Map k b
orig =
  case Map k b
orig of
    Map k b
Tip           -> []
    Bin Size
_ k
k b
v Map k b
l Map k b
r -> [Map k b
l, forall k a. k -> a -> Map k a
singleton k
k b
v, Map k b
r]
{-# INLINE splitRoot #-}