On Tue, May 3, 2011 at 7:12 AM, Yitzchak Gale <gale@sefer.org> wrote:

Hi Edward,

Thanks much for the very useful semigroups
package.

When using it in practice, it would be very useful
to have an analogue to the mconcat method of
Monoid. It has the obvious default implementation,
but allows for an optimized implementation for
specific instances. That turns out to be something
that comes up all the time (at least for me) in
real life.

Thanks,
Yitz

Another unsatisfying detail is no definition is in any way shape or form canonical when folding over a list.

There are at least 3 definitions that make sense. The nice inductive Endo definition above (which differs in semantics from the one you proposed), something like what you propose, with its funny base case, and the option of placing something like the unit I placed in Endo on the other side. Finally, I wasn't able to get any such specialized sconcat to actually speed anything up. =/

I'm more than happy to revisit this decision, as it isn't particularly onerous to add an sconcat definition to Semigroup, but I've yet to see it pay off and it is somewhat disturbing to me that the type doesn't automatically offer up its meaning.

As the Prelude has a general dearth of suitable container types that contain a guarantee of at least one element, my focus was instead upon the use of Foldable1 and Traversable1 from the semigroupoids package. This provides an optimization path, similar to those of Foldable and Traversable by optimizing the non-empty-by-construction container for its use of a semigroup, rather than optimizing the semigroup for its use of by one particularly inappropriate container.

These offer up a wealth of combinators for manipulating Semigroups over suitable containers. Again, I'm more than happy to add it if only for symmetry with Data.Monoid, but I'd be much happier doing so with a compelling example where it actually sped things up, and if there was actually a better motivated inductive definition.