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1. keysSet :: IntMap a -> IntSet

   containers	Data.IntMap.Lazy

   The set of all keys of the map.

   keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5]
   keysSet empty == Data.IntSet.empty
   

2. fromSet :: (Key -> a) -> IntSet -> IntMap a

   containers	Data.IntMap.Strict

   Build a map from a set of keys and a function which for each key computes its value.

   fromSet (\k -> replicate k 'a') (Data.IntSet.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")]
   fromSet undefined Data.IntSet.empty == empty
   

3. keysSet :: IntMap a -> IntSet

   containers	Data.IntMap.Strict

   The set of all keys of the map.

   keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5]
   keysSet empty == Data.IntSet.empty
   

4. fromSet :: (Key -> a) -> IntSet -> IntMap a

   containers	Data.IntMap.Strict.Internal

   Build a map from a set of keys and a function which for each key computes its value.

   fromSet (\k -> replicate k 'a') (Data.IntSet.fromList [3, 5]) == fromList [(5,"aaaaa"), (3,"aaa")]
   fromSet undefined Data.IntSet.empty == empty
   

5. keysSet :: IntMap a -> IntSet

   containers	Data.IntMap.Strict.Internal

   The set of all keys of the map.

   keysSet (fromList [(5,"a"), (3,"b")]) == Data.IntSet.fromList [3,5]
   keysSet empty == Data.IntSet.empty
   

6. module Data.IntSet

   Finite Int Sets

   The IntSet type represents a set of elements of type Int. For a walkthrough of the most commonly used functions see their sets introduction. These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.

   import Data.IntSet (IntSet)
   import qualified Data.IntSet as IntSet
   

   Performance information

   Many operations have a worst-case complexity of <math>. This means that the operation can become linear in the number of elements with a maximum of <math> -- the number of bits in an Int (32 or 64).

   Implementation

   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 set implementation (see Data.Set).
   • Chris Okasaki and Andy Gill, "Fast Mergeable Integer Maps", Workshop on ML, September 1998, pages 77-86, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.5452
   • D.R. Morrison, "PATRICIA -- Practical Algorithm To Retrieve Information Coded In Alphanumeric", Journal of the ACM, 15(4), October 1968, pages 514-534.
   Additionally, this implementation places bitmaps in the leaves of the tree. Their size is the natural size of a machine word (32 or 64 bits) and greatly reduces the memory footprint and execution times for dense sets, e.g. sets where it is likely that many values lie close to each other. The asymptotics are not affected by this optimization.

7. data IntSet

   containers	Data.IntSet

   A set of integers.

8. isProperSubsetOf :: IntSet -> IntSet -> Bool

   containers	Data.IntSet

   Is this a proper subset? (ie. a subset but not equal).

9. isSubsetOf :: IntSet -> IntSet -> Bool

   containers	Data.IntSet

   Is this a subset? (s1 `isSubsetOf` s2) tells whether s1 is a subset of s2.

10. data IntSet

    containers	Data.IntSet.Internal

    A set of integers.

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