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

Contents

Semigroups with absorbing element
Num wrappers
Boolean wrappers
Maybe wrappers

Description

Synopsis

Semigroups with absorbing element

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:

Annihilation

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

Num wrappers

newtype Product a :: * -> *

Monoid under multiplication.

Constructors

Product
Fields getProduct :: a

Instances

Generic1 Product
Bounded a => Bounded (Product a)
Eq a => Eq (Product a)
Num a => Num (Product a)
Ord a => Ord (Product a)
Read a => Read (Product a)
Show a => Show (Product a)
Generic (Product a)
Num a => Monoid (Product a)
Num a => Semigroup (Product a)
Num a => Zero (Product a) Source
type Rep1 Product = D1 D1Product (C1 C1_0Product (S1 S1_0_0Product Par1))
type Rep (Product a) = D1 D1Product (C1 C1_0Product (S1 S1_0_0Product (Rec0 a)))

Boolean wrappers

newtype Any :: *

Boolean monoid under disjunction (||).

Constructors

Any
Fields getAny :: Bool

Instances

Bounded Any
Eq Any
Ord Any
Read Any
Show Any
Generic Any
Monoid Any
Semigroup Any
Zero Any Source
type Rep Any = D1 D1Any (C1 C1_0Any (S1 S1_0_0Any (Rec0 Bool)))

newtype All :: *

Boolean monoid under conjunction (&&).

Constructors

All
Fields getAll :: Bool

Instances

Bounded All
Eq All
Ord All
Read All
Show All
Generic All
Monoid All
Semigroup All
Zero All Source
type Rep All = D1 D1All (C1 C1_0All (S1 S1_0_0All (Rec0 Bool)))

Maybe wrappers

newtype Success a Source

Zero for Maybe.

Called Success because of the absorbing law:

  Success (Just a) <> Success Nothing = Nothing

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

success :: a -> Success a Source

A successful value.

failure :: Success a Source

A failure.