base-4.0.0.0: Basic librariesContentsIndex
Data.Monoid
Portabilityportable
Stabilityexperimental
Maintainerlibraries@haskell.org
Contents
Monoid typeclass
Bool wrappers
Num wrappers
Maybe wrappers
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.

Synopsis
class Monoid a where
mempty :: a
mappend :: a -> a -> a
mconcat :: [a] -> a
newtype Dual a = Dual {
getDual :: a
}
newtype Endo a = Endo {
appEndo :: a -> a
}
newtype All = All {
getAll :: Bool
}
newtype Any = Any {
getAny :: Bool
}
newtype Sum a = Sum {
getSum :: a
}
newtype Product a = Product {
getProduct :: a
}
newtype First a = First {
getFirst :: Maybe a
}
newtype Last a = Last {
getLast :: Maybe a
}
Monoid typeclass
class Monoid a where
The monoid class. A minimal complete definition must supply mempty and mappend, and these should satisfy the monoid laws.
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.
show/hide Instances
Monoid Ordering
Monoid ()
Monoid Any
Monoid All
Monoid ([] a)
Monoid a => Monoid (Maybe 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)
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)
newtype Dual a
The dual of a monoid, obtained by swapping the arguments of mappend.
Constructors
Dual
getDual :: a
show/hide Instances
Bounded a => Bounded (Dual a)
Eq a => Eq (Dual a)
Ord a => Ord (Dual a)
Read a => Read (Dual a)
Show a => Show (Dual a)
Monoid a => Monoid (Dual a)
newtype Endo a
The monoid of endomorphisms under composition.
Constructors
Endo
appEndo :: a -> a
show/hide Instances
Bool wrappers
newtype All
Boolean monoid under conjunction.
Constructors
All
getAll :: Bool
show/hide Instances
newtype Any
Boolean monoid under disjunction.
Constructors
Any
getAny :: Bool
show/hide Instances
Num wrappers
newtype Sum a
Monoid under addition.
Constructors
Sum
getSum :: a
show/hide Instances
Bounded a => Bounded (Sum a)
Eq a => Eq (Sum a)
Ord a => Ord (Sum a)
Read a => Read (Sum a)
Show a => Show (Sum a)
Num a => Monoid (Sum a)
newtype Product a
Monoid under multiplication.
Constructors
Product
getProduct :: a
show/hide Instances
Bounded a => Bounded (Product a)
Eq a => Eq (Product a)
Ord a => Ord (Product a)
Read a => Read (Product a)
Show a => Show (Product a)
Num a => Monoid (Product 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))
newtype First a
Maybe monoid returning the leftmost non-Nothing value.
Constructors
First
getFirst :: Maybe a
show/hide Instances
Eq a => Eq (First a)
Ord a => Ord (First a)
Read a => Read (First a)
Show a => Show (First a)
Monoid (First a)
newtype Last a
Maybe monoid returning the rightmost non-Nothing value.
Constructors
Last
getLast :: Maybe a
show/hide Instances
Eq a => Eq (Last a)
Ord a => Ord (Last a)
Read a => Read (Last a)
Show a => Show (Last a)
Monoid (Last a)
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