| Copyright | (c) Andy Gill 2001, (c) Oregon Graduate Institute of Science and Technology, 2001 |
|---|---|
| License | BSD-style (see the file libraries/base/LICENSE) |
| Maintainer | libraries@haskell.org |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Data.Monoid
Description
A class for monoids (types with an associative binary operation that has an identity) with various general-purpose instances.
- class Monoid a where
- (<>) :: Monoid m => m -> m -> m
- newtype Dual a = Dual {
- getDual :: a
- newtype Endo a = Endo {
- appEndo :: a -> a
- newtype All = All {}
- newtype Any = Any {}
- newtype Sum a = Sum {
- getSum :: a
- newtype Product a = Product {
- getProduct :: a
- newtype First a = First {}
- newtype Last a = Last {}
- newtype Alt f a = Alt {
- getAlt :: f a
Monoid typeclass
class Monoid a where
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:
mappend mempty x = x
mappend x mempty = x
mappend x (mappend y z) = mappend (mappend x y) z
mconcat =
foldrmappend mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
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.
Instances
| Monoid Ordering | |
| Monoid () | |
| Monoid Any | |
| Monoid All | |
| Monoid Lifetime |
|
| Monoid Event | |
| Monoid [a] | |
| Monoid a => Monoid (Maybe a) | Lift a semigroup into |
| 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 (Proxy k s) | |
| Monoid a => Monoid (Const a b) | |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | |
| Alternative f => Monoid (Alt * f a) | |
| (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) |
newtype Dual a
newtype Endo a
The monoid of endomorphisms under composition.
Bool wrappers
Num wrappers
newtype Sum a
Monoid under addition.
Maybe wrappers
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.ApplicativeinsertLookupWithKey :: 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))
newtype First a
newtype Last a
Alternative wrapper
newtype Alt f a
Monoid under <|>.
Since: 4.8.0.0
Instances
| Monad f => Monad (Alt * f) | |
| Functor f => Functor (Alt * f) | |
| Applicative f => Applicative (Alt * f) | |
| Generic1 (Alt * f) | |
| MonadPlus f => MonadPlus (Alt * f) | |
| Alternative f => Alternative (Alt * f) | |
| Enum (f a) => Enum (Alt k f a) | |
| Eq (f a) => Eq (Alt k f a) | |
| Num (f a) => Num (Alt k f a) | |
| Ord (f a) => Ord (Alt k f a) | |
| Read (f a) => Read (Alt k f a) | |
| Show (f a) => Show (Alt k f a) | |
| Generic (Alt k f a) | |
| Alternative f => Monoid (Alt * f a) | |
| type Rep1 (Alt k f) | |
| type Rep (Alt k f a) |