Fwd: Proposal: Add Data.Semigroup to base, as a superclass of Monoid

[Johan Tibell]

-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 <johnw at fpcomplete.com> wrote:

> 1. I propose that we add the following package to base:
>
>
> http://hackage.haskell.org/packages/archive/semigroups/0.9.2/doc/html/Data-Semigroup.html
>
>    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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