[project @ 2005-10-25 09:11:25 by ross]

Change the Monoid instance for functions (as proposed on the libraries
list, and interpreting silence as assent) from composition to pointwise
combination.

Rationale: The new instance is consistent with the instances for tuples,
it's compositional, in that it builds instances for complex types out
of instances for simpler ones, and it makes this module Haskell 98.

Downside: the old instance was easy to use with Writer monads, and ShowS
was a special case.  You can get that effect using the new Endo type,
but you have to wrap and unwrap the newtype.

Also added a few other simple monoids: dual, sum and product.

diff --git a/Data/Monoid.hs b/Data/Monoid.hs
index bc8633b..0524727 100644 (file)
--- a/Data/Monoid.hs
+++ b/Data/Monoid.hs
@@ -7,9 +7,9 @@
 -- 
 -- Maintainer  :  libraries@haskell.org
 -- Stability   :  experimental
--- Portability :  non-portable (requires extended type classes)
+-- Portability :  portable
 --
--- Declaration of the Monoid class, and instances for list and functions.
+-- The Monoid class with various general-purpose instances.
 --
 --       Inspired by the paper
 --       /Functional Programming with Overloading and
@@ -19,7 +19,11 @@
 -----------------------------------------------------------------------------
 
 module Data.Monoid (
-       Monoid(..)
+       Monoid(..),
+       Endo(..),
+       Dual(..),
+       Sum(..),
+       Product(..)
   ) where
 
 import Prelude
@@ -57,9 +61,9 @@ instance Monoid [a] where
        mempty  = []
        mappend = (++)
 
-instance Monoid (a -> a) where
-       mempty  = id
-       mappend = (.)
+instance Monoid b => Monoid (a -> b) where
+       mempty _ = mempty
+       mappend f g x = f x `mappend` g x
 
 instance Monoid () where
        -- Should it be strict?
@@ -97,6 +101,34 @@ instance Monoid Ordering where
        EQ `mappend` y = y
        GT `mappend` _ = GT
 
+-- | The monoid of endomorphisms under composition.
+newtype Endo a = Endo { appEndo :: a -> a }
+
+instance Monoid (Endo a) where
+       mempty = Endo id
+       Endo f `mappend` Endo g = Endo (f . g)
+
+-- | The dual of a monoid, obtained by swapping the arguments of 'mappend'.
+newtype Dual a = Dual { getDual :: a }
+
+instance Monoid a => Monoid (Dual a) where
+       mempty = Dual mempty
+       Dual x `mappend` Dual y = Dual (y `mappend` x)
+
+-- | Monoid under addition.
+newtype Sum a = Sum { getSum :: a }
+
+instance Num a => Monoid (Sum a) where
+       mempty = Sum 0
+       Sum x `mappend` Sum y = Sum (x + y)
+
+-- | Monoid under multiplication.
+newtype Product a = Product { getProduct :: a }
+
+instance Num a => Monoid (Product a) where
+       mempty = Product 1
+       Product x `mappend` Product y = Product (x * y)
+
 instance (Ord k) => Monoid (Map k v) where
     mempty  = Map.empty
     mappend = Map.union