Copyright	(C) 2015 Dimitri Sabadie
License	BSD3
Maintainer	Dimitri Sabadie <dimitri.sabadie@gmail.com>
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

Data.Zero

Description

Synopsis

Documentation

class Semigroup a => Zero a where Source

Semigroup with a zero element. It’s important to understand that the standard Semigroup types – i.e. Maybe and so on – are already biased, because they’re Monoids. That’s why you’ll find a few Zero instances.

Should satisfies the following laws:

Annhilation

 a <> zero = zero <> a = zero

Associativity

 a <> b <> c = (a <> b) <> c = a <> (b <> c)

Minimal complete definition

zero

Methods

zero :: a Source

The zero element.

zconcat :: [a] -> a Source

Concat all the elements according to (<>) and zero.

Instances

Zero () Source
Zero All Source
Semigroup a => Zero (Success a) Source
Num a => Zero (Product a) Source

newtype Product a Source

Zero under multiplication.

Constructors

Product
Fields getProduct :: a

Instances

Bounded a => Bounded (Product a) Source
Eq a => Eq (Product a) Source
Num a => Num (Product a) Source
Ord a => Ord (Product a) Source
Read a => Read (Product a) Source
Show a => Show (Product a) Source
Generic (Product a) Source
Num a => Semigroup (Product a) Source
Num a => Zero (Product a) Source
type Rep (Product a) Source

newtype All Source

Zero under boolean logical and.

Constructors

All
Fields getAll :: Bool

Instances

Bounded All Source
Eq All Source
Ord All Source
Read All Source
Show All Source
Generic All Source
Semigroup All Source
Zero All Source
type Rep All Source

newtype Success a Source

Zero for Maybe.

Constructors

Success
Fields getSuccess :: Maybe a

Instances

Monad Success Source
Functor Success Source
MonadFix Success Source
Applicative Success Source
Foldable Success Source
Traversable Success Source
Eq a => Eq (Success a) Source
Ord a => Ord (Success a) Source
Read a => Read (Success a) Source
Show a => Show (Success a) Source
Semigroup a => Semigroup (Success a) Source
Semigroup a => Zero (Success a) Source