Copyright	(c) Donnacha Oisín Kidney 2021
Maintainer	mail@doisinkidney.com
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Monus

Description

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

Synopsis

class (Ord a, Monoid a) => Monus a where
- (|-|) :: a -> a -> a

Documentation

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

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 Source #

An absolute difference operator.

Instances

Instances details

Monus Any Source #	`>>>` `let bools = [Any False, Any True]``>>>` `and [ x <> (y \|-\| x) == y \| x <- bools, y <- bools, x <= y ]`True
Instance details Defined in Data.Monus Methods (\|-\|) :: Any -> Any -> Any Source #
Monus Dist Source #
Instance details Defined in Data.Monus.Dist Methods (\|-\|) :: Dist -> Dist -> Dist Source #
Monus Prob Source #
Instance details Defined in Data.Monus.Prob Methods (\|-\|) :: Prob -> Prob -> Prob Source #
(Bounded a, Ord a) => Monus (Max a) Source #
Instance details Defined in Data.Monus Methods (\|-\|) :: Max a -> Max a -> Max a Source #
(Num a, Ord a) => Monus (Sum a) Source #
Instance details Defined in Data.Monus Methods (\|-\|) :: Sum a -> Sum a -> Sum a Source #
Ord a => Monus (Max a) Source #
Instance details Defined in Data.Monus.Max Methods (\|-\|) :: Max a -> Max a -> Max a Source #

Monus Any Source #	`>>>` `let bools = [Any False, Any True]``>>>` `and [ x <> (y \|-\| x) == y \| x <- bools, y <- bools, x <= y ]`True
Instance details Defined in Data.Monus Methods (\|-\|) :: Any -> Any -> Any Source #
Monus Dist Source #
Instance details Defined in Data.Monus.Dist Methods (\|-\|) :: Dist -> Dist -> Dist Source #
Monus Prob Source #
Instance details Defined in Data.Monus.Prob Methods (\|-\|) :: Prob -> Prob -> Prob Source #
(Bounded a, Ord a) => Monus (Max a) Source #
Instance details Defined in Data.Monus Methods (\|-\|) :: Max a -> Max a -> Max a Source #
(Num a, Ord a) => Monus (Sum a) Source #
Instance details Defined in Data.Monus Methods (\|-\|) :: Sum a -> Sum a -> Sum a Source #
Ord a => Monus (Max a) Source #
Instance details Defined in Data.Monus.Max Methods (\|-\|) :: Max a -> Max a -> Max a Source #