Proposal: merge Data.Functor.Coproduct into transformers

[Andreas Abel]

Standing up against the dictator...

I like neither 'Product' nor 'Sum'.  For one, they are ambiguous already 
in type theory.  They mean something different in the context of simple 
types and the context of dependent types:

                    Sum                      Product
   simple types     set of tagged elements   set of pairs
   dependent types  set of pairs             set of functions

Further they have this number-connotation.  Sum and Product are 
mathematician's terms inspired by the cardinality of the sets they 
construct (in the simply typed setting), or the likeness to summation 
and product terms (in the dependently typed setting).

IMHO, programming is much more based on logics and information theory 
than on mathematics and numbers.  The logical content of 'Sum' is making 
a decision (left or right) and the one of 'Product' is adjoining two 
things, putting them next to each other.  Disjunction and conjunction 
would be the logically correct terms, but we can say it simpler.  I 
think the current Haskell approach to speak of 'Either' and pairing is 
the good one, free of mathematical burden, and it can be extended to 
higher-order kinds:

   Either  :: * -> * -> *
   Either1 :: (* -> *) -> (* -> *) -> (* -> *)
   Either2 :: (* -> * -> *) -> (* -> * -> *) -> (* -> * -> *)

   (,)   :: * -> * -> *
   Pair1 :: (* -> *) -> (* -> *) -> (* -> *)
   Pair2 :: (* -> * -> *) -> (* -> * -> *) -> (* -> * -> *)

Cheers,
Andreas


On 16.12.12 1:57 AM, Ross Paterson wrote:
> On Sat, Dec 15, 2012 at 09:24:48PM +0000, Henning Thielemann wrote:
>> Since I proposed that and became aware of the newtype solution in the
>> meantime, I change my mind to:
>>
>>> data Sum f g a = Sum { getSum :: Either (f a) (g a) }
>
> OK, let's do that.  It matches the treatment of Product.
> (So now they'll both clash with Data.Monoid.)
>
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-- 
Andreas Abel  <><      Du bist der geliebte Mensch.

Theoretical Computer Science, University of Munich
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andreas.abel at ifi.lmu.de
http://www2.tcs.ifi.lmu.de/~abel/