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Data.Monoid | Portability | portable | Stability | experimental | Maintainer | libraries@haskell.org |
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Description |
A class for monoids (types with an associative binary operation that
has an identity) with various general-purpose instances.
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Synopsis |
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Monoid typeclass
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class Monoid a where |
The class of monoids (types with an associative binary operation that
has an identity). Instances should satisfy the following laws:
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.
| | 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.
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| | Instances | Monoid Ordering | | Monoid () | | Monoid Any | | Monoid All | | Monoid [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 (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) | |
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newtype Dual a |
The dual of a monoid, obtained by swapping the arguments of mappend.
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newtype Endo a |
The monoid of endomorphisms under composition.
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Bool wrappers
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newtype All |
Boolean monoid under conjunction.
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newtype Any |
Boolean monoid under disjunction.
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Num wrappers
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newtype Sum a |
Monoid under addition.
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newtype Product a |
Monoid under multiplication.
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Maybe wrappers
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To implement find or findLast on any Foldable:
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 new
alterA function and either First or Last:
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))
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newtype First a |
Maybe monoid returning the leftmost non-Nothing value.
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newtype Last a |
Maybe monoid returning the rightmost non-Nothing value.
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Produced by Haddock version 2.7.2 |