    {-# LANGUAGE CPP #-}
    #if !defined(TESTING) && __GLASGOW_HASKELL__ >= 703
    {-# LANGUAGE Safe #-}
    #endif

    #include "containers.h"

    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Data.IntMap.Lazy
    -- Copyright   :  (c) Daan Leijen 2002
    --                (c) Andriy Palamarchuk 2008
    -- License     :  BSD-style
    -- Maintainer  :  libraries@haskell.org
    -- Stability   :  provisional
    -- Portability :  portable
    --
    -- An efficient implementation of maps from integer keys to values
    -- (dictionaries).
    --
    -- API of this module is strict in the keys, but lazy in the values.
    -- If you need value-strict maps, use "Data.IntMap.Strict" instead.
    -- The 'IntMap' type itself is shared between the lazy and strict modules,
    -- meaning that the same 'IntMap' value can be passed to functions in
    -- both modules (although that is rarely needed).
    --
    -- These modules are intended to be imported qualified, to avoid name
    -- clashes with Prelude functions, e.g.
    --
    -- >  import Data.IntMap.Lazy (IntMap)
    -- >  import qualified Data.IntMap.Lazy as IntMap
    --
    -- The implementation is based on /big-endian patricia trees/.  This data
    -- structure performs especially well on binary operations like 'union'
    -- and 'intersection'.  However, my benchmarks show that it is also
    -- (much) faster on insertions and deletions when compared to a generic
    -- size-balanced map implementation (see "Data.Map").
    --
    --    * Chris Okasaki and Andy Gill,  \"/Fast Mergeable Integer Maps/\",
    --      Workshop on ML, September 1998, pages 77-86,
    --      <http://citeseer.ist.psu.edu/okasaki98fast.html>
    --
    --    * D.R. Morrison, \"/PATRICIA -- Practical Algorithm To Retrieve
    --      Information Coded In Alphanumeric/\", Journal of the ACM, 15(4),
    --      October 1968, pages 514-534.
    --
    -- Operation comments contain the operation time complexity in
    -- the Big-O notation <http://en.wikipedia.org/wiki/Big_O_notation>.
    -- Many operations have a worst-case complexity of /O(min(n,W))/.
    -- This means that the operation can become linear in the number of
    -- elements with a maximum of /W/ -- the number of bits in an 'Int'
    -- (32 or 64).
    -----------------------------------------------------------------------------

    module Data.IntMap.Lazy (
        -- * Strictness properties
        -- $strictness

        -- * Map type
    #if !defined(TESTING)
        IntMap, Key          -- instance Eq,Show
    #else
        IntMap(..), Key          -- instance Eq,Show
    #endif

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

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

        -- * Construction
        , empty
        , singleton

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

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

        -- * Combine

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

        -- ** Difference
        , difference
        , differenceWith
        , differenceWithKey

        -- ** Intersection
        , intersection
        , intersectionWith
        , intersectionWithKey

        -- ** Universal combining function
        , mergeWithKey

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

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

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

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

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

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

        -- * Filter
        , IM.filter
        , filterWithKey
        , partition
        , partitionWithKey

        , mapMaybe
        , mapMaybeWithKey
        , mapEither
        , mapEitherWithKey

        , split
        , splitLookup
        , splitRoot

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

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

        -- * Debugging
        , showTree
        , showTreeWith
        ) where

    import Data.IntMap.Base as IM

    -- $strictness
    --
    -- This module satisfies the following strictness property:
    --
    -- * Key arguments are evaluated to WHNF
    --
    -- Here are some examples that illustrate the property:
    --
    -- > insertWith (\ new old -> old) undefined v m  ==  undefined
    -- > insertWith (\ new old -> old) k undefined m  ==  OK
    -- > delete undefined m  ==  undefined