Safe Haskell | Safe |
---|---|

Language | Haskell2010 |

An efficient implementation of sets.

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

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.

Note that the implementation is *left-biased* -- the elements of a
first argument are always preferred to the second, for example in
`union`

or `insert`

. Of course, left-biasing can only be observed
when equality is an equivalence relation instead of structural
equality.

*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.