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|
-----------------------------------------------------------------------------
-- |
-- Module : Data.Monoid
-- 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 : non-portable (requires extended type classes)
--
-- Declaration of the Monoid class, and instances for list and functions.
--
-- Inspired by the paper
-- /Functional Programming with Overloading and
-- Higher-Order Polymorphism/,
-- Mark P Jones (<http://www.cse.ogi.edu/~mpj/>)
-- Advanced School of Functional Programming, 1995.
-----------------------------------------------------------------------------
module Data.Monoid (
Monoid(..)
) where
import Prelude
-- ---------------------------------------------------------------------------
-- | The monoid class.
-- A minimal complete definition must supply 'mempty' and 'mappend',
-- and these should satisfy the monoid laws.
class Monoid a where
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.
mconcat = foldr mappend mempty
-- Monoid instances.
instance Monoid [a] where
mempty = []
mappend = (++)
instance Monoid (a -> a) where
mempty = id
mappend = (.)
instance Monoid () where
-- Should it be strict?
mempty = ()
_ `mappend` _ = ()
mconcat _ = ()
instance (Monoid a, Monoid b) => Monoid (a,b) where
mempty = (mempty, mempty)
(a1,b1) `mappend` (a2,b2) =
(a1 `mappend` a2, b1 `mappend` b2)
instance (Monoid a, Monoid b, Monoid c) => Monoid (a,b,c) where
mempty = (mempty, mempty, mempty)
(a1,b1,c1) `mappend` (a2,b2,c2) =
(a1 `mappend` a2, b1 `mappend` b2, c1 `mappend` c2)
instance (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a,b,c,d) where
mempty = (mempty, mempty, mempty, mempty)
(a1,b1,c1,d1) `mappend` (a2,b2,c2,d2) =
(a1 `mappend` a2, b1 `mappend` b2,
c1 `mappend` c2, d1 `mappend` d2)
instance (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) =>
Monoid (a,b,c,d,e) where
mempty = (mempty, mempty, mempty, mempty, mempty)
(a1,b1,c1,d1,e1) `mappend` (a2,b2,c2,d2,e2) =
(a1 `mappend` a2, b1 `mappend` b2, c1 `mappend` c2,
d1 `mappend` d2, e1 `mappend` e2)
-- lexicographical ordering
instance Monoid Ordering where
mempty = EQ
LT `mappend` _ = LT
EQ `mappend` y = y
GT `mappend` _ = GT
|
