| Copyright | (c) Andy Gill 2001 (c) Oregon Graduate Institute of Science and Technology 2001 |
|---|---|
| License | BSD-style (see the file libraries/base/LICENSE) |
| Maintainer | [email protected] |
| 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
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
Identity of mappend
mappend :: a -> a -> a Source #
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.
Instances
| Monoid Ordering # | Since: 2.1 |
| Monoid () # | Since: 2.1 |
| Monoid Any # | Since: 2.1 |
| Monoid All # | Since: 2.1 |
| Monoid Lifetime # |
Since: 4.8.0.0 |
| Monoid Event # | Since: 4.3.1.0 |
| Monoid [a] # | Since: 2.1 |
| Monoid a => Monoid (Maybe a) # | Lift a semigroup into Since: 2.1 |
| Monoid a => Monoid (IO a) # | Since: 4.9.0.0 |
| Monoid (Last a) # | Since: 2.1 |
| Monoid (First a) # | Since: 2.1 |
| Num a => Monoid (Product a) # | Since: 2.1 |
| Num a => Monoid (Sum a) # | Since: 2.1 |
| Monoid (Endo a) # | Since: 2.1 |
| Monoid a => Monoid (Dual a) # | Since: 2.1 |
| Monoid a => Monoid (Identity a) # | |
| Semigroup a => Monoid (Option a) # | Since: 4.9.0.0 |
| Monoid m => Monoid (WrappedMonoid m) # | Since: 4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Max a) # | Since: 4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Min a) # | Since: 4.9.0.0 |
| Monoid b => Monoid (a -> b) # | Since: 2.1 |
| (Monoid a, Monoid b) => Monoid (a, b) # | Since: 2.1 |
| Monoid (Proxy k s) # | Since: 4.7.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) # | Since: 2.1 |
| Alternative f => Monoid (Alt * f a) # | Since: 4.8.0.0 |
| Monoid a => Monoid (Const k a b) # | |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) # | Since: 2.1 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) # | Since: 2.1 |
Instances
| Monad Dual # | Since: 4.8.0.0 |
| Functor Dual # | Since: 4.8.0.0 |
| MonadFix Dual # | Since: 4.8.0.0 |
| Applicative Dual # | Since: 4.8.0.0 |
| Foldable Dual # | Since: 4.8.0.0 |
| Traversable Dual # | Since: 4.8.0.0 |
| MonadZip Dual # | Since: 4.8.0.0 |
| Bounded a => Bounded (Dual a) # | |
| Eq a => Eq (Dual a) # | |
| Data a => Data (Dual a) # | Since: 4.8.0.0 |
| Ord a => Ord (Dual a) # | |
| Read a => Read (Dual a) # | |
| Show a => Show (Dual a) # | |
| Generic (Dual a) # | |
| Semigroup a => Semigroup (Dual a) # | Since: 4.9.0.0 |
| Monoid a => Monoid (Dual a) # | Since: 2.1 |
| Generic1 * Dual # | |
| type Rep (Dual a) # | |
| type Rep1 * Dual # | |
The monoid of endomorphisms under composition.
Bool wrappers
Boolean monoid under conjunction (&&).
Boolean monoid under disjunction (||).
Num wrappers
Monoid under addition.
Instances
| Monad Sum # | Since: 4.8.0.0 |
| Functor Sum # | Since: 4.8.0.0 |
| MonadFix Sum # | Since: 4.8.0.0 |
| Applicative Sum # | Since: 4.8.0.0 |
| Foldable Sum # | Since: 4.8.0.0 |
| Traversable Sum # | Since: 4.8.0.0 |
| MonadZip Sum # | Since: 4.8.0.0 |
| Bounded a => Bounded (Sum a) # | |
| Eq a => Eq (Sum a) # | |
| Data a => Data (Sum a) # | Since: 4.8.0.0 |
| Num a => Num (Sum a) # | |
| Ord a => Ord (Sum a) # | |
| Read a => Read (Sum a) # | |
| Show a => Show (Sum a) # | |
| Generic (Sum a) # | |
| Num a => Semigroup (Sum a) # | Since: 4.9.0.0 |
| Num a => Monoid (Sum a) # | Since: 2.1 |
| Generic1 * Sum # | |
| type Rep (Sum a) # | |
| type Rep1 * Sum # | |
Monoid under multiplication.
Constructors
| Product | |
Fields
| |
Instances
| Monad Product # | Since: 4.8.0.0 |
| Functor Product # | Since: 4.8.0.0 |
| MonadFix Product # | Since: 4.8.0.0 |
| Applicative Product # | Since: 4.8.0.0 |
| Foldable Product # | Since: 4.8.0.0 |
| Traversable Product # | Since: 4.8.0.0 |
| MonadZip Product # | Since: 4.8.0.0 |
| Bounded a => Bounded (Product a) # | |
| Eq a => Eq (Product a) # | |
| Data a => Data (Product a) # | Since: 4.8.0.0 |
| Num a => Num (Product a) # | |
| Ord a => Ord (Product a) # | |
| Read a => Read (Product a) # | |
| Show a => Show (Product a) # | |
| Generic (Product a) # | |
| Num a => Semigroup (Product a) # | Since: 4.9.0.0 |
| Num a => Monoid (Product a) # | Since: 2.1 |
| Generic1 * Product # | |
| type Rep (Product a) # | |
| type Rep1 * Product # | |
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))
Maybe monoid returning the leftmost non-Nothing value.
First aAlt Maybe a
Instances
| Monad First # | |
| Functor First # | |
| MonadFix First # | Since: 4.8.0.0 |
| Applicative First # | |
| Foldable First # | Since: 4.8.0.0 |
| Traversable First # | Since: 4.8.0.0 |
| MonadZip First # | Since: 4.8.0.0 |
| Eq a => Eq (First a) # | |
| Data a => Data (First a) # | Since: 4.8.0.0 |
| Ord a => Ord (First a) # | |
| Read a => Read (First a) # | |
| Show a => Show (First a) # | |
| Generic (First a) # | |
| Semigroup (First a) # | Since: 4.9.0.0 |
| Monoid (First a) # | Since: 2.1 |
| Generic1 * First # | |
| type Rep (First a) # | |
| type Rep1 * First # | |
Maybe monoid returning the rightmost non-Nothing value.
Last aDual (First a)Dual (Alt Maybe a)
Instances
| Monad Last # | |
| Functor Last # | |
| MonadFix Last # | Since: 4.8.0.0 |
| Applicative Last # | |
| Foldable Last # | Since: 4.8.0.0 |
| Traversable Last # | Since: 4.8.0.0 |
| MonadZip Last # | Since: 4.8.0.0 |
| Eq a => Eq (Last a) # | |
| Data a => Data (Last a) # | Since: 4.8.0.0 |
| Ord a => Ord (Last a) # | |
| Read a => Read (Last a) # | |
| Show a => Show (Last a) # | |
| Generic (Last a) # | |
| Semigroup (Last a) # | Since: 4.9.0.0 |
| Monoid (Last a) # | Since: 2.1 |
| Generic1 * Last # | |
| type Rep (Last a) # | |
| type Rep1 * Last # | |
Alternative wrapper
Monoid under <|>.
Since: 4.8.0.0
Instances
| Generic1 k (Alt k f) # | |
| Monad f => Monad (Alt * f) # | |
| Functor f => Functor (Alt * f) # | |
| MonadFix f => MonadFix (Alt * f) # | Since: 4.8.0.0 |
| Applicative f => Applicative (Alt * f) # | |
| MonadPlus f => MonadPlus (Alt * f) # | |
| Alternative f => Alternative (Alt * f) # | |
| MonadZip f => MonadZip (Alt * f) # | Since: 4.8.0.0 |
| Enum (f a) => Enum (Alt k f a) # | |
| Eq (f a) => Eq (Alt k f a) # | |
| (Data (f a), Data a, Typeable (* -> *) f) => Data (Alt * f a) # | Since: 4.8.0.0 |
| 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 => Semigroup (Alt * f a) # | Since: 4.9.0.0 |
| Alternative f => Monoid (Alt * f a) # | Since: 4.8.0.0 |
| type Rep1 k (Alt k f) # | |
| type Rep (Alt k f a) # | |