|A class for monoids (types with an associative binary operation that
has an identity) with various general-purpose instances.
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.
|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.
|Monoid ( a)|
|Monoid a => Monoid (Maybe a)|
|Monoid (Last a)|
|Monoid a => Monoid (Dual a)|
|Monoid (Endo a)|
|Num a => Monoid (Sum a)|
|Num a => Monoid (Product a)|
|Monoid (First 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)|
|The dual of a monoid, obtained by swapping the arguments of mappend.
|The monoid of endomorphisms under composition.
|Boolean monoid under conjunction.
|Boolean monoid under disjunction.
|Monoid under addition.
|Monoid under multiplication.
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
doChange Nothing = (First Nothing, Just value)
doChange (Just oldValue) =
(First (Just oldValue),
Just (combine key value oldValue))
|Maybe monoid returning the leftmost non-Nothing value.
|Maybe monoid returning the rightmost non-Nothing value.
|Produced by Haddock version 2.4.2|