Stable Ordered Discriminator

Ord equipped with a compatible stable, ordered discriminator.

Law:

sortingCompare x y ≡ compare x y

O(n). Sort a list using discrimination.

sort = sortWith id

O(n). Sort a list with a Schwartzian transformation by using discrimination.

This linear time replacement for sortWith and sortOn uses discrimination.

Valid definition for compare in terms of Sorting.

O(n). Construct a Map.

This is an asymptotically faster version of fromList, which exploits ordered discrimination.

>>> toMap []
fromList []

>>> toMap [(5,"a"), (3 :: Int,"b"), (5, "c")]
fromList [(3,"b"),(5,"c")]

>>> Map.fromList [(5,"a"), (3 :: Int,"b"), (5, "c")]
fromList [(3,"b"),(5,"c")]

>>> toMap [(5,"c"), (3,"b"), (5 :: Int, "a")]
fromList [(3,"b"),(5,"a")]

>>> Map.fromList [(5,"c"), (3,"b"), (5 :: Int, "a")]
fromList [(3,"b"),(5,"a")]

O(n). Construct a Map, combining values.

This is an asymptotically faster version of fromListWith, which exploits ordered discrimination.

(Note: values combine in anti-stable order for compatibility with fromListWith)

>>> toMapWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5 :: Int,"c")]
fromList [(3,"ab"),(5,"cba")]

>>> Map.fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5 :: Int,"c")]
fromList [(3,"ab"),(5,"cba")]

>>> toMapWith (++) []
fromList []

O(n). Construct a Map, combining values with access to the key.

This is an asymptotically faster version of fromListWithKey, which exploits ordered discrimination.

(Note: the values combine in anti-stable order for compatibility with fromListWithKey)

>>> let f key new_value old_value = show key ++ ":" ++ new_value ++ "|" ++ old_value
>>> toMapWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5 :: Int,"c")]
fromList [(3,"3:a|b"),(5,"5:c|5:b|a")]

>>> toMapWithKey f []
fromList []

O(n). Construct an IntMap.

>>> toIntMap []
fromList []

>>> toIntMap [(5,"a"), (3,"b"), (5, "c")]
fromList [(3,"b"),(5,"c")]

>>> IntMap.fromList [(5,"a"), (3,"b"), (5, "c")]
fromList [(3,"b"),(5,"c")]

>>> toIntMap [(5,"c"), (3,"b"), (5, "a")]
fromList [(3,"b"),(5,"a")]

>>> IntMap.fromList [(5,"c"), (3,"b"), (5, "a")]
fromList [(3,"b"),(5,"a")]

O(n). Construct an IntMap, combining values.

This is an asymptotically faster version of fromListWith, which exploits ordered discrimination.

(Note: values combine in anti-stable order for compatibility with fromListWith)

>>> toIntMapWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")]
fromList [(3,"ab"),(5,"cba")]

>>> IntMap.fromListWith (++) [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")]
fromList [(3,"ab"),(5,"cba")]

>>> toIntMapWith (++) []
fromList []

O(n). Construct a Map, combining values with access to the key.

This is an asymptotically faster version of fromListWithKey, which exploits ordered discrimination.

(Note: the values combine in anti-stable order for compatibility with fromListWithKey)

>>> let f key new_value old_value = show key ++ ":" ++ new_value ++ "|" ++ old_value
>>> toIntMapWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")]
fromList [(3,"3:a|b"),(5,"5:c|5:b|a")]

>>> IntMap.fromListWithKey f [(5,"a"), (5,"b"), (3,"b"), (3,"a"), (5,"c")]
fromList [(3,"3:a|b"),(5,"5:c|5:b|a")]

>>> toIntMapWithKey f []
fromList []

O(n). Construct a Set in linear time.

This is an asymptotically faster version of fromList, which exploits ordered discrimination.

O(n). Construct an IntSet in linear time.

This is an asymptotically faster version of fromList, which exploits ordered discrimination.

Construct a stable ordered discriminator that sorts a list as multisets of elements from another stable ordered discriminator.

The resulting discriminator only cares about the set of keys and their multiplicity, and is sorted as if we'd sorted each key in turn before comparing.

Construct a stable ordered discriminator that sorts a list as sets of elements from another stable ordered discriminator.

The resulting discriminator only cares about the set of keys, and is sorted as if we'd sorted each key in turn before comparing.