Note: You should use Data.Map.Strict instead of this module if:

• You will eventually need all the values stored.
• The stored values don't represent large virtual data structures to be lazily computed.

An efficient implementation of ordered maps from keys to values (dictionaries).

These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.

 import qualified Data.Map as Map

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, 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 .

Warning : The size of the map must not exceed maxBound::Int . Violation of this condition is not detected and if the size limit is exceeded, its behaviour is undefined.

Operation comments contain the operation time complexity in the Big-O notation ( http://en.wikipedia.org/wiki/Big_O_notation ).