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
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 =
foldr
mappend 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 newtype
s 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 # | |
Monoid () # | |
Monoid Any # | |
Monoid All # | |
Monoid Lifetime # |
|
Monoid Event # | |
Monoid [a] # | |
Monoid a => Monoid (Maybe a) # | Lift a semigroup into |
Monoid a => Monoid (IO a) # | |
Monoid (Last a) # | |
Monoid (First a) # | |
Num a => Monoid (Product a) # | |
Num a => Monoid (Sum a) # | |
Monoid (Endo a) # | |
Monoid a => Monoid (Dual a) # | |
Semigroup a => Monoid (Option a) # | |
Monoid m => Monoid (WrappedMonoid m) # | |
(Ord a, Bounded a) => Monoid (Max a) # | |
(Ord a, Bounded a) => Monoid (Min a) # | |
Monoid a => Monoid (Identity a) # | |
Monoid b => Monoid (a -> b) # | |
(Monoid a, Monoid b) => Monoid (a, b) # | |
Monoid (Proxy k s) # | |
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) # | |
Alternative f => Monoid (Alt * f a) # | |
Monoid a => Monoid (Const k a b) # | |
(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) # | |
Instances
Monad Dual # | |
Functor Dual # | |
MonadFix Dual # | |
Applicative Dual # | |
Foldable Dual # | |
Traversable Dual # | |
Generic1 Dual # | |
MonadZip Dual # | |
Bounded a => Bounded (Dual a) # | |
Eq a => Eq (Dual a) # | |
Data a => Data (Dual a) # | |
Ord a => Ord (Dual a) # | |
Read a => Read (Dual a) # | |
Show a => Show (Dual a) # | |
Generic (Dual a) # | |
Semigroup a => Semigroup (Dual a) # | |
Monoid a => Monoid (Dual a) # | |
type Rep1 Dual = D1 (MetaData "Dual" "Data.Monoid" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) # | |
type Rep (Dual a) = D1 (MetaData "Dual" "Data.Monoid" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) # |
The monoid of endomorphisms under composition.
Bool
wrappers
Boolean monoid under conjunction (&&
).
Instances
Bounded All # | |
Eq All # | |
Data All # | |
Ord All # | |
Read All # | |
Show All # | |
Generic All # | |
Semigroup All # | |
Monoid All # | |
type Rep All = D1 (MetaData "All" "Data.Monoid" "base" True) (C1 (MetaCons "All" PrefixI True) (S1 (MetaSel (Just Symbol "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool))) # |
Boolean monoid under disjunction (||
).
Instances
Bounded Any # | |
Eq Any # | |
Data Any # | |
Ord Any # | |
Read Any # | |
Show Any # | |
Generic Any # | |
Semigroup Any # | |
Monoid Any # | |
type Rep Any = D1 (MetaData "Any" "Data.Monoid" "base" True) (C1 (MetaCons "Any" PrefixI True) (S1 (MetaSel (Just Symbol "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool))) # |
Num
wrappers
Monoid under addition.
Instances
Monad Sum # | |
Functor Sum # | |
MonadFix Sum # | |
Applicative Sum # | |
Foldable Sum # | |
Traversable Sum # | |
Generic1 Sum # | |
MonadZip Sum # | |
Bounded a => Bounded (Sum a) # | |
Eq a => Eq (Sum a) # | |
Data a => Data (Sum a) # | |
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) # | |
Num a => Monoid (Sum a) # | |
type Rep1 Sum = D1 (MetaData "Sum" "Data.Monoid" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) # | |
type Rep (Sum a) = D1 (MetaData "Sum" "Data.Monoid" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) # |
Monoid under multiplication.
Constructors
Product | |
Fields
|
Instances
Monad Product # | |
Functor Product # | |
MonadFix Product # | |
Applicative Product # | |
Foldable Product # | |
Traversable Product # | |
Generic1 Product # | |
MonadZip Product # | |
Bounded a => Bounded (Product a) # | |
Eq a => Eq (Product a) # | |
Data a => Data (Product a) # | |
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) # | |
Num a => Monoid (Product a) # | |
type Rep1 Product = D1 (MetaData "Product" "Data.Monoid" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) # | |
type Rep (Product a) = D1 (MetaData "Product" "Data.Monoid" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) # |
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.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))
Maybe monoid returning the leftmost non-Nothing value.
is isomorphic to First
a
, but precedes it
historically.Alt
Maybe
a
Instances
Monad First # | |
Functor First # | |
MonadFix First # | |
Applicative First # | |
Foldable First # | |
Traversable First # | |
Generic1 First # | |
MonadZip First # | |
Eq a => Eq (First a) # | |
Data a => Data (First a) # | |
Ord a => Ord (First a) # | |
Read a => Read (First a) # | |
Show a => Show (First a) # | |
Generic (First a) # | |
Semigroup (First a) # | |
Monoid (First a) # | |
type Rep1 First = D1 (MetaData "First" "Data.Monoid" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe))) # | |
type Rep (First a) = D1 (MetaData "First" "Data.Monoid" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a)))) # |
Maybe monoid returning the rightmost non-Nothing value.
is isomorphic to Last
a
, and thus to
Dual
(First
a)Dual
(Alt
Maybe
a)
Instances
Monad Last # | |
Functor Last # | |
MonadFix Last # | |
Applicative Last # | |
Foldable Last # | |
Traversable Last # | |
Generic1 Last # | |
MonadZip Last # | |
Eq a => Eq (Last a) # | |
Data a => Data (Last a) # | |
Ord a => Ord (Last a) # | |
Read a => Read (Last a) # | |
Show a => Show (Last a) # | |
Generic (Last a) # | |
Semigroup (Last a) # | |
Monoid (Last a) # | |
type Rep1 Last = D1 (MetaData "Last" "Data.Monoid" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe))) # | |
type Rep (Last a) = D1 (MetaData "Last" "Data.Monoid" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a)))) # |
Alternative
wrapper
Monoid under <|>
.
Since: 4.8.0.0
Instances