Data.Monoid.Compat

Monoid typeclass

class Monoid a where

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

• mappend mempty x = x

• mappend x mempty = x

• mappend x (mappend y z) = mappend (mappend x y) z

• mconcat = foldr mappend mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Minimal complete definition: mempty and mappend.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

Minimal complete definition

mempty, mappend

Methods

mempty :: a

Identity of mappend

mappend :: a -> a -> a

An associative operation

mconcat :: [a] -> a

Fold a list using the monoid. For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

Instances

Monoid Ordering

Monoid ()

Monoid All

Monoid Any

Monoid [a]

Monoid a => Monoid (Dual a)

Monoid (Endo a)

Num a => Monoid (Sum a)

Num a => Monoid (Product a)

Monoid (First a)

Monoid (Last a)

Monoid a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Monoid b => Monoid (a -> b)

(Monoid a, Monoid b) => Monoid (a, b)

Monoid a => Monoid (Const a b)

Monoid (Proxy * s)

Typeable (* -> Constraint) Monoid

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)

Alternative f => Monoid (Alt * f a)

(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)

(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)

(<>) :: Monoid m => m -> m -> m infixr 6

An infix synonym for mappend.

Since: 4.5.0.0

newtype Dual a :: * -> *

The dual of a monoid, obtained by swapping the arguments of mappend.

Constructors

Dual

Fields

getDual :: a

Instances

Generic1 Dual

Bounded a => Bounded (Dual a)

Eq a => Eq (Dual a)

Ord a => Ord (Dual a)

Read a => Read (Dual a)

Show a => Show (Dual a)

Generic (Dual a)

Monoid a => Monoid (Dual a)

type Rep1 Dual = D1 D1Dual (C1 C1_0Dual (S1 S1_0_0Dual Par1))

type Rep (Dual a) = D1 D1Dual (C1 C1_0Dual (S1 S1_0_0Dual (Rec0 a)))

newtype Endo a :: * -> *

The monoid of endomorphisms under composition.

Constructors

Endo

Fields

appEndo :: a -> a

Instances

Generic (Endo a)

Monoid (Endo a)

type Rep (Endo a) = D1 D1Endo (C1 C1_0Endo (S1 S1_0_0Endo (Rec0 (a -> a))))

Bool wrappers

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

type Rep All = D1 D1All (C1 C1_0All (S1 S1_0_0All (Rec0 Bool)))

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

type Rep Any = D1 D1Any (C1 C1_0Any (S1 S1_0_0Any (Rec0 Bool)))

Num wrappers

newtype Sum a :: * -> *

Monoid under addition.

Constructors

Sum

Fields

getSum :: a

Instances

Generic1 Sum

Bounded a => Bounded (Sum a)

Eq a => Eq (Sum a)

Num a => Num (Sum a)

Ord a => Ord (Sum a)

Read a => Read (Sum a)

Show a => Show (Sum a)

Generic (Sum a)

Num a => Monoid (Sum a)

type Rep1 Sum = D1 D1Sum (C1 C1_0Sum (S1 S1_0_0Sum Par1))

type Rep (Sum a) = D1 D1Sum (C1 C1_0Sum (S1 S1_0_0Sum (Rec0 a)))

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)

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)))

Maybe wrappers

newtype First a :: * -> *

Maybe monoid returning the leftmost non-Nothing value.

Constructors

First

Fields

getFirst :: Maybe a

Instances

Generic1 First

Eq a => Eq (First a)

Ord a => Ord (First a)

Read a => Read (First a)

Show a => Show (First a)

Generic (First a)

Monoid (First a)

type Rep1 First = D1 D1First (C1 C1_0First (S1 S1_0_0First (Rec1 Maybe)))

type Rep (First a) = D1 D1First (C1 C1_0First (S1 S1_0_0First (Rec0 (Maybe a))))

newtype Last a :: * -> *

Maybe monoid returning the rightmost non-Nothing value.

Constructors

Last

Fields

getLast :: Maybe a

Instances

Generic1 Last

Eq a => Eq (Last a)

Ord a => Ord (Last a)

Read a => Read (Last a)

Show a => Show (Last a)

Generic (Last a)

Monoid (Last a)

type Rep1 Last = D1 D1Last (C1 C1_0Last (S1 S1_0_0Last (Rec1 Maybe)))

type Rep (Last a) = D1 D1Last (C1 C1_0Last (S1 S1_0_0Last (Rec0 (Maybe a))))

Alternative wrapper

newtype Alt f a

Monoid under <|>.

Since: 4.8.0.0

Constructors

Alt

Fields

getAlt :: f a

Instances

Alternative f => Alternative (Alt * f)

Monad m => Monad (Alt * m)

Functor f => Functor (Alt * f)

MonadPlus m => MonadPlus (Alt * m)

Applicative f => Applicative (Alt * f)

Generic1 (Alt * f)

Enum (f a) => Enum (Alt k f a)

Eq (f a) => Eq (Alt k f a)

Num (f a) => Num (Alt k f a)

Ord (f a) => Ord (Alt k f a)

Read (f a) => Read (Alt k f a)

Show (f a) => Show (Alt k f a)

Generic (Alt k f a)

Alternative f => Monoid (Alt * f a)

type Rep1 (Alt k f)

type Rep (Alt k f a)