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Data.Monoid

Portability | portable
Stability | experimental
Maintainer | libraries@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 | Source

The monoid class. A minimal complete definition must supply `mempty` and `mappend`, and these should satisfy the monoid laws.
Methods

mempty :: a | Source

Identity of `mappend`

mappend :: a -> a -> a | Source

An associative operation

mconcat :: [a] -> a | Source

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 ([] 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 | Source

The dual of a monoid, obtained by swapping the arguments of `mappend`.
Constructors

Dual |

getDual :: a |

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 | Source

The monoid of endomorphisms under composition.
Constructors

Endo |

appEndo :: a -> a |

Instances

Monoid (Endo a)

Bool wrappers

newtype All | Source

Boolean monoid under conjunction.
Constructors

All |

getAll :: Bool |

Instances

Bounded All
Eq All
Ord All
Read All
Show All
Monoid All

newtype Any | Source

Boolean monoid under disjunction.
Constructors

Any |

getAny :: Bool |

Instances

Bounded Any
Eq Any
Ord Any
Read Any
Show Any
Monoid Any

Num wrappers

newtype Sum a | Source

Monoid under addition.
Constructors

Sum |

getSum :: a |

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 | Source

Monoid under multiplication.
Constructors

Product |

getProduct :: a |

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 | Source

Maybe monoid returning the leftmost non-Nothing value.
Constructors

First |

getFirst :: Maybe a |

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 | Source

Maybe monoid returning the rightmost non-Nothing value.
Constructors

Last |

getLast :: Maybe a |

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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