[Haskell-cafe] Unit and pair

[MigMit]

That's an interesting idea, thanks.

Отправлено с iPad

08.05.2012, в 23:31, Daniel Peebles <pumpkingod at gmail.com> написал(а):

> 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 at gmail.com> wrote:
> FullBinaryTreeRelation? :P
> 
> On Tue, May 8, 2012 at 1:36 PM, MigMit <miguelimo38 at yandex.ru> wrote:
> 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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