Code for manipulation 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`

, and canonical
representatives can be chosen with `repr`

.

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

- data Equivalence i
- emptyEquivalence :: Ix i => (i, i) -> Equivalence i
- repr :: Ix i => Equivalence i -> i -> i
- equiv :: Ix i => Equivalence i -> i -> i -> Bool
- equivalent :: Ix i => Equivalence i -> [i] -> Bool
- equate :: Ix i => i -> i -> Equivalence i -> Equivalence i
- equateAll :: Ix i => [i] -> Equivalence i -> Equivalence i

# 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.

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

`repr`

gives a canonical representative of the equivalence class
containing `x`

. It is chosen arbitrarily, but is always the same for a
given equivalence relation.

This function is slightly unsafe. In particular, it's possible to build
the same equivalence relation by equating values in two different orders,
and the choice of canonical representatives will differ. You can either
think of a value of type `Equivalence`

as an equivalence relation together
with a choice of canonical representatives, or you can consider this not a
pure function. Since `Equivalence`

is not an instance of `Eq`

and equality
is not observable, both perspectives are valid.

equiv :: Ix i => Equivalence i -> i -> i -> BoolSource

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

equivalent :: Ix i => Equivalence i -> [i] -> BoolSource

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.