On Tue, Jan 06, 2009 at 05:15:46PM -0000, kahl@cas.mcmaster.ca wrote: [...]
Exactly --- that's why I propose qualified import, so one would use, e.g.:
sort . map Ord.Dual
clarifying that one is using the dual Ord instance. (Ordering duality is about the fact that the converse of an ordering relation is an ordering relation again; the Haskell type class |Ord| is the special case of linear orderings. )
This is standard terminology, and I think we should encourage such use of standard terminology and concepts.
In my part of the category-theory world, standard terminology is "opposite category" and thus "opposite ordering" (since a partial order is a special case of a category). But I would not be too surprised to hear "dual ordering" as well. (By the way, a much worse abuse of the name Dual already exists in Data.Monoid, to describe the operation of flipping the arguments of the multiplication in a monoid. This should certainly be called the opposite monoid. Google for "dual monoid" and you will find that all uses of that term are for other concepts.)
Of course, alternatives remain available, in the spirit of Henning Thielemann's ``Warm, fuzzy thing Transformer'':
It was argued that people avoid Haskell because of terms from Category theory like 'Monad'. This problem can now be solved by a wrapper which presents all the WWW without monads! Start e.g. at
;-)
While "opposite" is a term used in category theory, it's also a perfectly ordinary word that has the right connotations to non-mathematicians. "Dual" is a little scary, I think. Regards, Reid