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Data.Monoid | Portability | portable | Stability | experimental | Maintainer | libraries@haskell.org |
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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://citeseer.ist.psu.edu/jones95functional.html)
Advanced School of Functional Programming, 1995.
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Synopsis |
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Monoid typeclass
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The monoid class.
A minimal complete definition must supply mempty and mappend,
and these should satisfy the monoid laws.
| | Methods | | Identity of mappend
| | | An associative operation
| | | 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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The dual of a monoid, obtained by swapping the arguments of mappend.
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The monoid of endomorphisms under composition.
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Bool wrappers
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Boolean monoid under conjunction.
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Boolean monoid under disjunction.
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Num wrappers
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Monoid under addition.
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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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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.
Maybe monoid returning the leftmost non-Nothing value.
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Maybe monoid returning the rightmost non-Nothing value.
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Produced by Haddock version 2.0.0.0 |