[Haskell-beginners] Type for lists with one or more elements

[Brent Yorgey]

On Thu, Jun 06, 2013 at 08:41:47PM -0700, Frerich Raabe wrote:
> 
> On Jun 6, 2013, at 5:56 PM, Brent Yorgey <byorgey at seas.upenn.edu> wrote:
> 
> > On Thu, Jun 06, 2013 at 05:27:11PM -0700, Frerich Raabe wrote:
> >> I could do something like
> >> 
> >>  data List a = Singleton a | Cons a (List a)
> >> 
> >> but before I go ahead I wonder: is there an existing Haskell package
> >> for this? Maybe even with prettier names than what I wrote above, and
> >> convenient functions for transforming from/to plain [] lists? It
> >> would probably be straightforward to write it myself, but because of
> >> that, I suspect that somebody else already did it. :-)
> > 
> > Yes, this exists in the semigroups package:
> > 
> >  http://hackage.haskell.org/packages/archive/semigroups/0.9.2/doc/html/Data-List-NonEmpty.html
> 
> Awesome, thanks a lot for pointing this out! semigroups… I don't even
> know what that would be, pretty sure I wouldn't have found this by
> myself. :-}

A semigroup is simply a set with an associative binary operation. So
all monoids are semigroups, but other things are semigroups as well;
for example, 'max' is an associative binary operation on the real
numbers, so this is a semigroup; but max has no identity element
(there is no smallest real number) so it is not a monoid.  Non-empty
lists come up a lot when working with semigroups (technically this is
because non-empty lists with (++) are the "free semigroup", i.e. the
Mother Of All Semigroups) which is why they are in this package.

If you want to learn more about monoids and semigroups and some ways
they can be applied, you might be interested in my paper from last
year's Haskell Symposium, "Monoids: Theme and Variations", which you
can find at

  http://www.cis.upenn.edu/~byorgey/publications.html

along with a link to a video and slides.

-Brent