persistent-equivalence-0.1: Persistent equivalence relations (aka union-find)

Data.Equivalence.Persistent

Description

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
```

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.

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.