{-# LANGUAGE CPP #-} #ifdef __GLASGOW_HASKELL__ {-# LANGUAGE Safe #-} #endif #include "containers.h" ----------------------------------------------------------------------------- -- | -- Module : Data.Map -- Copyright : (c) Daan Leijen 2002 -- (c) Andriy Palamarchuk 2008 -- License : BSD-style -- Maintainer : libraries@haskell.org -- Portability : portable -- -- -- = Finite Maps (lazy interface) -- -- This module re-exports the value lazy "Data.Map.Lazy" API. -- -- The @'Map' k v@ type represents a finite map (sometimes called a dictionary) -- from keys of type @k@ to values of type @v@. A 'Map' is strict in its keys but lazy -- in its values. -- -- The functions in "Data.Map.Strict" are careful to force values before -- installing them in a 'Map'. This is usually more efficient in cases where -- laziness is not essential. The functions in this module do not do so. -- -- When deciding if this is the correct data structure to use, consider: -- -- * If you are using 'Prelude.Int' keys, you will get much better performance for most -- operations using "Data.IntMap.Lazy". -- -- * If you don't care about ordering, consider using @Data.HashMap.Lazy@ from the -- <https://hackage.haskell.org/package/unordered-containers unordered-containers> -- package instead. -- -- For a walkthrough of the most commonly used functions see the -- <https://haskell-containers.readthedocs.io/en/latest/map.html maps introduction>. -- -- This module is intended to be imported qualified, to avoid name clashes with -- Prelude functions, e.g. -- -- > import Data.Map (Map) -- > import qualified Data.Map as Map -- -- Note that the implementation is generally /left-biased/. Functions that take -- two maps as arguments and combine them, such as `union` and `intersection`, -- prefer the values in the first argument to those in the second. -- -- -- == Warning -- -- The size of a 'Map' must not exceed @'Prelude.maxBound' :: 'Prelude.Int'@. -- Violation of this condition is not detected and if the size limit is exceeded, -- its behaviour is undefined. -- -- -- == Implementation -- -- 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, -- <https://doi.org/10.1017/S0956796800000885>, -- <https://groups.csail.mit.edu/mac/users/adams/BB/index.html>. -- * J. Nievergelt and E.M. Reingold, -- \"/Binary search trees of bounded balance/\", -- SIAM journal of computing 2(1), March 1973. -- <https://doi.org/10.1137/0202005>. -- * Yoichi Hirai and Kazuhiko Yamamoto, -- \"/Balancing weight-balanced trees/\", -- Journal of Functional Programming 21(3):287-307, 2011, -- <https://doi.org/10.1017/S0956796811000104> -- -- Bounds for 'union', 'intersection', and 'difference' are as given -- by -- -- * Guy Blelloch, Daniel Ferizovic, and Yihan Sun, -- \"/Parallel Ordered Sets Using Join/\", -- <https://arxiv.org/abs/1602.02120v4>. -- -- -- == Performance information -- -- The time complexity is given for each operation in -- [big-O notation](http://en.wikipedia.org/wiki/Big_O_notation), with \(n\) -- referring to the number of entries in the map. -- -- Operations like 'lookup', 'insert', and 'delete' take \(O(\log n)\) time. -- -- Binary set operations like 'union' and 'intersection' take -- \(O\bigl(m \log\bigl(\frac{n}{m}+1\bigr)\bigr)\) time, where \(m\) and \(n\) -- are the sizes of the smaller and larger input maps respectively. -- ----------------------------------------------------------------------------- module Data.Map ( module Data.Map.Lazy ) where import Data.Map.Lazy