On Thu, 31 May 2007, Stefan Holdermans wrote:
Mingli,
class Lattice e where join :: e -> e -> e meet :: e -> e -> e
-- associative law join x (join y z) = join (join x y) z join (join x y) z = join x (join y z)
If you are not to sell your soul to advanced and perhaps obscure type hacking, you cannot express laws like this *in* Haskell.
More concretely, one usually does not provide such laws as default implementations of a class' methods. Instead, they are stated in, for instance, comments and the documentation that goes with your library. These then form an informal obligation for programmers that provide instances of your class to let these instances obey the laws.
Like here: http://darcs.haskell.org/numericprelude/src/Algebra/Lattice.hs
If you provide an instance of the class you could use testing framework, e.g., QuickCheck [1], to assert that the required properties hold.
I assume they can in some way also be used for GHC's optimizer. http://www.haskell.org/haskellwiki/Playing_by_the_rules