Data.Equivalence.Persistent

Description

Code for manipulation of equivalence classes on index types. An Equivalence is an equivalence relation. The empty equivalence relation is constructed over a ranges of values using emptyEquivalence. Less discerning equivalence relations can be obtained with equate and equateAll. The relation can be tested with equiv and equivalent.

An example follows:

 import Data.Equivalence.Persistent

 rel = equateAll [1,3,5,7,9]
     . equate 5 6
     . equate 2 4
     $ emptyEquivalence (1,10)

 test1 = equiv rel 3 5 -- This is True
 test2 = equiv rel 1 6 -- This is True
 test3 = equiv rel 4 6 -- This is False

Synopsis

Documentation

data Equivalence i Source

An Equivalence is an equivalence relation on a range of values of some index type.

emptyEquivalence :: Ix i => (i, i) -> Equivalence iSource

emptyEquivalence is an equivalence relation that equates two values only when they are equal to each other. It is the most discerning such relation possible.

domain :: Ix i => Equivalence i -> (i, i)Source

Gets the domain of an equivalence relation, as the ordered pair of index bounds.

equiv :: Ix i => Equivalence i -> i -> i -> Bool Source

Determines if two values are equivalent under the given equivalence relation.

equivalent :: Ix i => Equivalence i -> [i] -> Bool Source

Determines if all of the given values are equivalent under the given equivalence relation.

equate :: Ix i => i -> i -> Equivalence i -> Equivalence iSource

Construct the equivalence relation obtained by equating the given two values. This combines equivalence classes.

equateAll :: Ix i => [i] -> Equivalence i -> Equivalence iSource

Construct the equivalence relation obtained by equating all of the given values. This combines equivalence classes.