If you want to enforce associativity just create your own Eq instance and
make it a pattern there.
Initially when I started doing Haskell it seemed that you could just type
an equation of constructors and have it enforced as a rule. This actually
isn't the case (someone correct me if I'm wrong) but it is being researched
ATM.
Dan
On 5/31/07, Stefan Holdermans
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.
If you provide an instance of the class you could use testing framework, e.g., QuickCheck [1], to assert that the required properties hold.
Cheers,
Stefan
[1] www.cs.chalmers.se/~rjmh/QuickCheck/
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