Wednesday, January 24, 2007

Comonadic functional attribute evaluation

They relate zippers to comonads. Wow!

CoKleisli categories make comonads relevant for analyzing notions of context-dependent
function. If the object D A is viewed as the type of contextually situated
values of A, a context-dependent function from A to B is a map D A -> B in the base
category, i.e., a map from A to B in the coKleisli category. The counit eA : D A -> A
discards the context of its input whereas the coextension k† : D A -> D B of a function k : D A -> B essentially duplicates it (to feed it to k and still have a copy left).

No wonder processes looked like zippers to me - they are about contextually situated values (err, actually computations :( ).

12 comments:

sigfpe said...

I think there's also a monad behind every zipper. It's just that the monad is in the category of vector spaces. But it still captures the form that some zipper-based computations might take.

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