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`

, 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
- domain :: Ix i => Equivalence i -> (i, 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.

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

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

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 class and `Equivalence`

value.

If you are using this function, you're probably doing something wrong. Please note that:

- The representative chosen depends on the order in which the equivalence relation was built, and is not always the same for values that represent the same relation.
- The representative is not particularly stable. Uses of
`equate`

are highly likely to change it. - If all you need is some representative of the equivalence class, you have to provide one as input to the function anyway, so you may as well use that.

Because of this, the function may be removed in a future version. Please contact me if you have a compelling use for it.

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.