Comments on: Monads from Comonads

By: zzo38

zzo38 — Wed, 27 Jun 2012 18:42:35 +0000

Does this do anything?

data LeftCo m f x = forall z. LeftCo (f (m z) -> x) (f z);

By: The Comonad.Reader » A Product of an Imperfect Union

The Comonad.Reader » A Product of an Imperfect Union — Fri, 01 Jul 2011 03:49:16 +0000

[...] Monads from Comonads, we built the comonad-to-monad [...]

By: The Comonad.Reader » More on Comonads as Monad Transformers

The Comonad.Reader » More on Comonads as Monad Transformers — Thu, 30 Jun 2011 19:20:03 +0000

[...] time before that in Monads from Comonads we observed that for non-transformer version of [...]

By: The Comonad.Reader » Monad Transformers from Comonads

The Comonad.Reader » Monad Transformers from Comonads — Wed, 29 Jun 2011 01:51:46 +0000

[...] Last time, I showed that we can transform any Comonad in Haskell into a Monad in Haskell. [...]

By: Edward Z. Yang

Edward Z. Yang — Tue, 28 Jun 2011 16:38:59 +0000

Yeah, looks like he never published the slides on the relevant talk. I’ll bug him about that.

By: Edward Kmett

Edward Kmett — Tue, 28 Jun 2011 16:26:17 +0000

Acutally, it _was_ pretty much pulled out of a hat. ;)

It came out as a happy accident in an email discussion with Russell O’Connor and Jacques Carette about exactly in what sense Store and State were dual.

By: Josef Svenningsson

Josef Svenningsson — Tue, 28 Jun 2011 15:54:12 +0000

Thank you for an awesome blog post! Though I wonder where the ‘Co’ data type comes from. You just pull it out of a hat. Is there a story behind it?

By: Edward Kmett

Edward Kmett — Tue, 28 Jun 2011 05:28:20 +0000

@Edward: I can’t find any links to Dominic’s material on the topic other than his subsequent discussions of codo notation. In there the only thing he has that mixes monads with comonads is a notion of ‘bido’ notation, which is pretty much what sigfpe and Uustalu and Vene have independently advocated as ways to deal with distributive laws over monads and comonads. Sadly, I think that approach doesn’t work out well in practice. I prefer working with comonads over a Kleisli category or monads over a Cokleisli category instead, rather than distributing. This lets me get decent computation sharing.

By: Edward Z. Yang

Edward Z. Yang — Tue, 28 Jun 2011 01:10:15 +0000

An interesting consequence of this set of transformations was the long-standing debate on whether or not streams were more appropriately monads or comonads. I believe Dominic Orchard has written on this topic (http://talks.cam.ac.uk/talk/index/31165). I really need to work through this material properly :-)