Haskell Hierarchical Libraries (base package)ContentsIndex
Data.Monoid
Portability portable
Stability experimental
Maintainer libraries@haskell.org
Description

The Monoid class with various general-purpose instances.

Inspired by the paper Functional Programming with Overloading and Higher-Order Polymorphism, Mark P Jones (http://www.cse.ogi.edu/~mpj/) Advanced School of Functional Programming, 1995.

Synopsis
class Monoid a where
mempty :: a
mappend :: a -> a -> a
mconcat :: [a] -> a
newtype Dual a = Dual {
getDual :: a
}
newtype Endo a = Endo {
appEndo :: (a -> a)
}
newtype All = All {
getAll :: Bool
}
newtype Any = Any {
getAny :: Bool
}
newtype Sum a = Sum {
getSum :: a
}
newtype Product a = Product {
getProduct :: a
}
Documentation
class Monoid a where
The monoid class. A minimal complete definition must supply mempty and mappend, and these should satisfy the monoid laws.
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 ByteString
Monoid ByteString
Monoid (IntMap a)
Monoid IntSet
Ord k => Monoid (Map k v)
Monoid [a]
Monoid b => Monoid (a -> b)
Monoid ()
(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)
Monoid Ordering
Monoid a => Monoid (Dual a)
Monoid (Endo a)
Monoid All
Monoid Any
Num a => Monoid (Sum a)
Num a => Monoid (Product a)
Monoid (Seq a)
Ord a => Monoid (Set a)
newtype Dual a
The dual of a monoid, obtained by swapping the arguments of mappend.
Constructors
Dual
getDual :: a
Instances
Monoid a => Monoid (Dual a)
newtype Endo a
The monoid of endomorphisms under composition.
Constructors
Endo
appEndo :: (a -> a)
Instances
Monoid (Endo a)
newtype All
Boolean monoid under conjunction.
Constructors
All
getAll :: Bool
Instances
Monoid All
Eq All
Ord All
Read All
Show All
Bounded All
newtype Any
Boolean monoid under disjunction.
Constructors
Any
getAny :: Bool
Instances
Monoid Any
Eq Any
Ord Any
Read Any
Show Any
Bounded Any
newtype Sum a
Monoid under addition.
Constructors
Sum
getSum :: a
Instances
Num a => Monoid (Sum a)
Eq a => Eq (Sum a)
Ord a => Ord (Sum a)
Read a => Read (Sum a)
Show a => Show (Sum a)
Bounded a => Bounded (Sum a)
newtype Product a
Monoid under multiplication.
Constructors
Product
getProduct :: a
Instances
Num a => Monoid (Product a)
Eq a => Eq (Product a)
Ord a => Ord (Product a)
Read a => Read (Product a)
Show a => Show (Product a)
Bounded a => Bounded (Product a)
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