-1 This has the same problem as making Functor a superclass of Monad, all current instances will break.
This is somewhat in the spirit of the AMP proposal: further improving the correctness of our algebraic abstractions.
I don't think building a tower of all possible algebraic abstractions is a
useful goal. We should add those that are actually useful (which functors,
applicative functions, monads, and monoids have proved to be). I don't want
to see us break all current code every time someone decides that we should
add another layer (pointed, say) between e.g. functor and monad.
On Tue, Jun 11, 2013 at 11:46 AM, John Wiegley
1. I propose that we add the following package to base:
http://hackage.haskell.org/packages/archive/semigroups/0.9.2/doc/html/Data-S...
This is somewhat in the spirit of the AMP proposal: further improving the correctness of our algebraic abstractions.
2. That we make Semigroup a superclass of Monoid, so that (minimally):
class Semigroup a where (<>) :: a -> a -> a
class Semigroup a => Monoid a where mempty :: a mconcat :: [a] -> a mconcat = foldr (<>) mempty
mappend :: Semigroup a => a -> a -> a mappend = (<>)
3. (Optional, recommended) There are other useful functions that can be added to Semigroup, such as sconcat and times1p, but I will let Edward speak to whether those should be proposed at this time.
4. (Optional, recommended) That we fix the Monoid instance for Maybe to be:
instance Semigroup a => Semigroup (Maybe a) where Just x <> Just y = Just (x <> y) _ <> _ = Nothing
instance Semigroup a => Monoid (Maybe a) where mempty = Nothing
For some clarification on what semigroups are and why we'd want to change Monoid, I excerpt here a selection from Brent Yorgey's "Monoids and Variations" paper:
Semigroups
A semigroup is like a monoid without the requirement of an identity element: it consists simply of a set with an associative binary operation....
Of course, any monoid is automatically a semigroup (by forgetting about its identity element). In the other direction, to turn a semigroup into a monoid, simply add a new distinguished element to serve as the identity, and extend the definition of the binary operation appropriately. This creates an identity element by definition, and it is not hard to see that it preserves associativity....
Adding a new distinguished element to a type is typically accomplished by wrapping it in Maybe. One might therefore expect to turn an instance of Semigroup into an instance of Monoid by wrapping it in Maybe. Sadly, Data.Monoid does not define semigroups, and has a Monoid instance for Maybe which requires a Monoid constraint on its argument type...
This is somewhat odd: in essence, it ignores the identity element of [the type] and replaces it with a different one.
-- John Wiegley FP Complete Haskell tools, training and consulting http://fpcomplete.com johnw on #haskell/irc.freenode.net
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