Safe Haskell	None
Language	Haskell2010

Data.Monoid.Monus

Description

A commutative monoid with monus is a Monoid equipped with a subtraction operator.

Synopsis

class Monoid a => Monus a where
(-) :: Monus a => a -> a -> a

Documentation

class Monoid a => Monus a where Source #

A commutative monoid that supports subtraction. The following laws must hold:

x <> (y - x) = y <> (x - y)
(x - y) - z = x - (y <> z)
x - x = mempty
mempty - x = mempty

Minimal complete definition

monus

Methods

monus :: a -> a -> a Source #

Instances

Monus () Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: () -> () -> () Source #
Monus All Source #	Defined as `P - Q = P ∨ ¬Q`
Instance details Defined in Data.Monoid.Monus Methods monus :: All -> All -> All Source #
Monus Any Source #	Defined as `P - Q = P ∧ ¬Q`
Instance details Defined in Data.Monoid.Monus Methods monus :: Any -> Any -> Any Source #
Monus a => Monus [a] Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: [a] -> [a] -> [a] Source #
Monus a => Monus (Maybe a) Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: Maybe a -> Maybe a -> Maybe a Source #
Monus a => Monus (IO a) Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: IO a -> IO a -> IO a Source #
Monus a => Monus (Endo a) Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: Endo a -> Endo a -> Endo a Source #
a ~ Natural => Monus (Sum a) Source #	Unlike the subtraction provided by the `Num` instance of `Natural`, this subtraction is total.
Instance details Defined in Data.Monoid.Monus Methods monus :: Sum a -> Sum a -> Sum a Source #
Ord a => Monus (Set a) Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: Set a -> Set a -> Set a Source #
Monus a => Monus (WrappedMonus a) Source #
Instance details Defined in Data.Monoid.Monus.Generic Methods monus :: WrappedMonus a -> WrappedMonus a -> WrappedMonus a Source #
Monus b => Monus (a -> b) Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: (a -> b) -> (a -> b) -> a -> b Source #
(Monus a, Monus b) => Monus (a, b) Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: (a, b) -> (a, b) -> (a, b) Source #
(Ord k, Monus v, Eq v) => Monus (Map k v) Source #
Instance details Defined in Data.Map.Annihilate Methods monus :: Map k v -> Map k v -> Map k v Source #
(Monus a, Monus b, Monus c) => Monus (a, b, c) Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #
(Monus a, Monus b, Monus c, Monus d) => Monus (a, b, c, d) Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #
(Monus a, Monus b, Monus c, Monus d, Monus e) => Monus (a, b, c, d, e) Source #
Instance details Defined in Data.Monoid.Monus Methods monus :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

(-) :: Monus a => a -> a -> a infixl 6 Source #

An infix synonym for subtraction.