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
discerning equivalence relations can be obtained with
equateAll. The relation can be tested with
canonical representatives can be chosen with
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
Equivalence is an equivalence relation on a range of values of some
emptyEquivalence is an equivalence relation that equates two values
only when they are equal to each other. It is the most discerning such
Gets the domain of an equivalence relation, as the ordered pair of index bounds.
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
equateare 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.
Determines if two values are equivalent under the given equivalence relation.
Determines if all of the given values are equivalent under the given equivalence relation.
Construct the equivalence relation obtained by equating the given two values. This combines equivalence classes.