{-# LANGUAGE CPP #-} #if !defined(TESTING) && defined(__GLASGOW_HASKELL__) {-# LANGUAGE Safe #-} #endif #include "containers.h" ----------------------------------------------------------------------------- -- | -- Module : Data.Set -- Copyright : (c) Daan Leijen 2002 -- License : BSD-style -- Maintainer : libraries@haskell.org -- Portability : portable -- -- -- = Finite Sets -- -- The @'Set' e@ type represents a set of elements of type @e@. Most operations -- require that @e@ be an instance of the 'Ord' class. A 'Set' is strict in its -- elements. -- -- For a walkthrough of the most commonly used functions see the -- <https://haskell-containers.readthedocs.io/en/latest/set.html sets introduction>. -- -- Note that the implementation is generally /left-biased/. Functions that take -- two sets as arguments and combine them, such as `union` and `intersection`, -- prefer the entries in the first argument to those in the second. Of course, -- this bias can only be observed when equality is an equivalence relation -- instead of structural equality. -- -- These modules are intended to be imported qualified, to avoid name -- clashes with Prelude functions, e.g. -- -- > import Data.Set (Set) -- > import qualified Data.Set as Set -- -- -- == Warning -- -- The size of the set must not exceed @maxBound::Int@. Violation of -- this condition is not detected and if the size limit is exceeded, its -- behaviour is undefined. -- -- -- == Implementation -- -- The implementation of 'Set' 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>. -- ----------------------------------------------------------------------------- module Data.Set ( -- * Set type #if !defined(TESTING) Set -- instance Eq,Ord,Show,Read,Data,Typeable #else Set(..) #endif -- * Construction , empty , singleton , fromList , fromAscList , fromDescList , fromDistinctAscList , fromDistinctDescList , powerSet -- * Insertion , insert -- * Deletion , delete -- * Query , member , notMember , lookupLT , lookupGT , lookupLE , lookupGE , S.null , size , isSubsetOf , isProperSubsetOf , disjoint -- * Combine , union , unions , difference , (\\) , intersection , cartesianProduct , disjointUnion -- * Filter , S.filter , takeWhileAntitone , dropWhileAntitone , spanAntitone , partition , split , splitMember , splitRoot -- * Indexed , lookupIndex , findIndex , elemAt , deleteAt , S.take , S.drop , S.splitAt -- * Map , S.map , mapMonotonic -- * Folds , S.foldr , S.foldl -- ** Strict folds , foldr' , foldl' -- ** Legacy folds , fold -- * Min\/Max , lookupMin , lookupMax , findMin , findMax , deleteMin , deleteMax , deleteFindMin , deleteFindMax , maxView , minView -- * Conversion -- ** List , elems , toList , toAscList , toDescList -- * Debugging , showTree , showTreeWith , valid #if defined(TESTING) -- Internals (for testing) , bin , balanced , link , merge #endif ) where import Data.Set.Internal as S