Haskell Hierarchical Libraries (base package)Source codeContentsIndex
Data.Monoid
Portabilityportable
Stabilityexperimental
Maintainerlibraries@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.
show/hide Instances
Monoid All
Monoid Any
Monoid ByteString
Monoid ByteString
Monoid IntSet
Monoid Ordering
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 b => Monoid (a -> b)
Monoid a => Monoid (Dual a)
Monoid (Endo a)
Monoid (IntMap a)
Num a => Monoid (Product a)
Monoid (Seq a)
Ord a => Monoid (Set a)
Num a => Monoid (Sum a)
Monoid [a]
Ord k => Monoid (Map k v)
newtype Dual a
The dual of a monoid, obtained by swapping the arguments of mappend.
Constructors
Dual
getDual :: a
show/hide Instances
Monoid a => Monoid (Dual a)
newtype Endo a
The monoid of endomorphisms under composition.
Constructors
Endo
appEndo :: (a -> a)
show/hide Instances
newtype All
Boolean monoid under conjunction.
Constructors
All
getAll :: Bool
show/hide Instances
newtype Any
Boolean monoid under disjunction.
Constructors
Any
getAny :: Bool
show/hide Instances
newtype Sum a
Monoid under addition.
Constructors
Sum
getSum :: a
show/hide Instances
Bounded a => Bounded (Sum a)
Eq a => Eq (Sum a)
Num a => Monoid (Sum a)
Ord a => Ord (Sum a)
Read a => Read (Sum a)
Show a => Show (Sum a)
newtype Product a
Monoid under multiplication.
Constructors
Product
getProduct :: a
show/hide Instances
Bounded a => Bounded (Product a)
Eq a => Eq (Product a)
Num a => Monoid (Product a)
Ord a => Ord (Product a)
Read a => Read (Product a)
Show a => Show (Product a)
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