rings-0.0.2.1: Rings, semirings, and dioids.

Safe HaskellSafe
LanguageHaskell2010

Data.Group

Synopsis

Documentation

class Monoid a => Group a where Source #

A Group is a Monoid plus a function, negate, such that:

a << negate a == mempty
negate a << a == mempty

Minimal complete definition

(negate | (<<))

Methods

negate :: a -> a Source #

(<<) :: a -> a -> a infixl 6 Source #

Instances
Group Int Source # 
Instance details

Defined in Data.Int.Instance

Methods

negate :: Int -> Int Source #

(<<) :: Int -> Int -> Int Source #

Group Int8 Source # 
Instance details

Defined in Data.Int.Instance

Methods

negate :: Int8 -> Int8 Source #

(<<) :: Int8 -> Int8 -> Int8 Source #

Group Int16 Source # 
Instance details

Defined in Data.Int.Instance

Group Int32 Source # 
Instance details

Defined in Data.Int.Instance

Group Int64 Source # 
Instance details

Defined in Data.Int.Instance

Group Integer Source # 
Instance details

Defined in Data.Int.Instance

Group Uni Source # 
Instance details

Defined in Data.Fixed.Instance

Methods

negate :: Uni -> Uni Source #

(<<) :: Uni -> Uni -> Uni Source #

Group Deci Source # 
Instance details

Defined in Data.Fixed.Instance

Methods

negate :: Deci -> Deci Source #

(<<) :: Deci -> Deci -> Deci Source #

Group Centi Source # 
Instance details

Defined in Data.Fixed.Instance

Group Milli Source # 
Instance details

Defined in Data.Fixed.Instance

Group Micro Source # 
Instance details

Defined in Data.Fixed.Instance

Group Nano Source # 
Instance details

Defined in Data.Fixed.Instance

Methods

negate :: Nano -> Nano Source #

(<<) :: Nano -> Nano -> Nano Source #

Group Pico Source # 
Instance details

Defined in Data.Fixed.Instance

Methods

negate :: Pico -> Pico Source #

(<<) :: Pico -> Pico -> Pico Source #

(Monoid (Complex a), Group a) => Group (Complex a) Source # 
Instance details

Defined in Data.Group

Methods

negate :: Complex a -> Complex a Source #

(<<) :: Complex a -> Complex a -> Complex a Source #