Portability	portable
Stability	experimental
Maintainer	libraries@haskell.org

Data.Monoid

Contents

Description

A class for monoids (types with an associative binary operation that has an identity) with various general-purpose instances.

Synopsis

classMonoid awhere
- mempty :: a
- mappend :: a -> a -> a
- mconcat :: [a] -> a
newtypeDual a =Dual {
- getDual :: a
}
newtypeEndo a =Endo {
- appEndo :: a -> a
}
newtypeAll =All {
- getAll ::Bool
}
newtypeAny =Any {
- getAny ::Bool
}
newtypeSum a =Sum {
- getSum :: a
}
newtypeProduct a =Product {
- getProduct :: a
}
newtypeFirst a =First {
- getFirst ::Maybe a
}
newtypeLast a =Last {
- getLast ::Maybe a
}

Monoid typeclass

classMonoid awhereSource

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 andmappend.

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 definenewtypes and make those instances ofMonoid, e.g.Sum andProduct.

Methods

mempty :: aSource

Identity ofmappend

mappend :: a -> a -> aSource

An associative operation

mconcat :: [a] -> aSource

Fold a list using the monoid. For most types, the default definition formconcat 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 Any
Monoid All
Monoid Event
Monoid [a]
Monoid a =>Monoid (Maybe a)	Lift a semigroup into`Maybe` forming a`Monoid` according tohttp://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`ee = e` and`es = s = s*e` for all`s S`." Since there is no "Semigroup" typeclass providing just`mappend`, we use`Monoid` instead.
Monoid (Last a)
Monoid (First a)
Num a =>Monoid (Product a)
Num a =>Monoid (Sum a)
Monoid (Endo a)
Monoid a =>Monoid (Dual a)
Monoid b =>Monoid (a -> b)
(Monoid a,Monoid b) =>Monoid (a, b)
(Monoid a,Monoid b,Monoid c) =>Monoid (a, b, c)
(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)

newtypeDual aSource

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

Constructors

Dual
Fields getDual :: a

Instances

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)
Monoid a =>Monoid (Dual a)

newtypeEndo aSource

The monoid of endomorphisms under composition.

Constructors

Endo
Fields appEndo :: a -> a

Instances

Monoid (Endo a)

Bool wrappers

newtypeAll Source

Boolean monoid under conjunction.

Constructors

All
Fields getAll ::Bool

Instances

Bounded All
Eq All
Ord All
Read All
Show All
Monoid All

newtypeAny Source

Boolean monoid under disjunction.

Constructors

Any
Fields getAny ::Bool

Instances

Bounded Any
Eq Any
Ord Any
Read Any
Show Any
Monoid Any

Num wrappers

newtypeSum aSource

Monoid under addition.

Constructors

Sum
Fields getSum :: a

Instances

Bounded a =>Bounded (Sum a)
Eq a =>Eq (Sum a)
Ord a =>Ord (Sum a)
Read a =>Read (Sum a)
Show a =>Show (Sum a)
Num a =>Monoid (Sum a)

newtypeProduct aSource

Monoid under multiplication.

Constructors

Product
Fields getProduct :: a

Instances

Bounded a =>Bounded (Product a)
Eq a =>Eq (Product a)
Ord a =>Ord (Product a)
Read a =>Read (Product a)
Show a =>Show (Product a)
Num a =>Monoid (Product a)

Maybe wrappers

To implementfind orfindLast on anyFoldable:

 findLast :: Foldable t => (a -> Bool) -> t a -> Maybe a findLast pred = getLast . foldMap (x -> if pred x                                            then Last (Just x)                                            else Last Nothing)

Much of Data.Map's interface can be implemented with Data.Map.alter. Some of the rest can be implemented with a newalterA function and eitherFirst orLast:

 alterA :: (Applicative f, Ord k) =>           (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a) instance Monoid a => Applicative ((,) a)  -- from Control.Applicative

 insertLookupWithKey :: Ord k => (k -> v -> v -> v) -> k -> v                     -> Map k v -> (Maybe v, Map k v) insertLookupWithKey combine key value =   Arrow.first getFirst . alterA doChange key   where   doChange Nothing = (First Nothing, Just value)   doChange (Just oldValue) =     (First (Just oldValue),      Just (combine key value oldValue))

newtypeFirst aSource

Maybe monoid returning the leftmost non-Nothing value.

Constructors

First
Fields getFirst ::Maybe a

Instances

Eq a =>Eq (First a)
Ord a =>Ord (First a)
Read a =>Read (First a)
Show a =>Show (First a)
Monoid (First a)

newtypeLast aSource

Maybe monoid returning the rightmost non-Nothing value.

Constructors

Last
Fields getLast ::Maybe a

Instances

Eq a =>Eq (Last a)
Ord a =>Ord (Last a)
Read a =>Read (Last a)
Show a =>Show (Last a)
Monoid (Last a)

Movatterモバイル変換

Monoid typeclass

Bool wrappers

Num wrappers

Maybe wrappers