Data.Monus

A class for Monoids with an order and a pseudo-subtraction operator.

Documentation

class (Ord a, Monoid a) => Monus a where

A class for (constructive) totally-ordered commutative monoids. These are monoids such that their ordering respects the <> operator, meaning they obey the following law:

  x <= x <> y

These monoids must also have a pseudo-subtraction operator (|-|), which behaves like an absolute difference function. This operator must obey the following law:

  x <= y ==> x <> (y |-| x) == y

Methods

(|-|) :: a -> a -> a infixl 6

An absolute difference operator.

Instances

Monus Dist

Defined in Data.Monus.Dist

Methods

(|-|) :: Dist -> Dist -> Dist

Monus Prob

Defined in Data.Monus.Prob

Methods

(|-|) :: Prob -> Prob -> Prob

(Num a, Ord a) => Monus (Sum a)

Defined in Data.Monus

Methods

(|-|) :: Sum a -> Sum a -> Sum a