To expand on that, this class basically allows you to prove your relation c holds pointwise across arbitrary binary trees, represented by nested tuples and terminated by ()s. If individual instances of the class had additional ways of constructing values (i.e., proving the relation for the two type parameters), then your trees could contain other types.
For example, if you had another type
data Iso a b = Iso (a -> b) (b -> a) -- the functions must be inverses
you could write an instance of Something for Iso and build a proof that
((), (a, ((), b)) is isomorphic to
((), (c, ((), d)) given
Iso a c and
Iso b d using your class.
I'm not sure I'd bundle the two parts together, but I'd call your pair method (or the class it lives in) something like congruent or ProductsRespectThisRelation :)
Dan
On Tue, May 8, 2012 at 3:15 PM, Daniel Peebles
<pumpkingod@gmail.com> wrote:
FullBinaryTreeRelation? :P
Hi café, a quick question.
Is there a somewhat standard class like this:
class Something c where
unit :: c () ()
pair :: c x y -> c u v -> c (x, u) (y, v)
?
I'm using it heavily in my current project, but I don't want to repeat somebody else's work, and it seems general enough to be defined somewhere; but my quick search on Hackage didn't reveal anything.
I know about arrows; this, however, is something more general, and it's instances aren't always arrows.
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