[Haskell-cafe] Re: The mother of all functors/monads/categories

[Max Bolingbroke]

On 27 June 2010 22:20, Edward Kmett <ekmett at gmail.com> wrote:
> I've pointed out the Codensity Set monad on the Haskell channel.

I spend no time on #haskell but clearly I should :)

> It is an
> interesting novelty, but it unfortunately has somewhat funny semantics in
> that the intermediate sets that you obtain are based on what you would get
> if you reparenthesized all of your binds and associating them to the right.

But by the monad laws this is a totally fine thing to do, so this
shouldn't lead to any unfortunate behaviour in practice, I hope.

> Another thing to note is that Codensity is slightly more powerful than the
> original type you embedded.

That is a very interesting observation. I'll be sure to look at monad-ran.

Can you cast any light on the connection with NBE? It seems like a
deep and powerful connection, so I'm sure it must correspond to some
interesting categorical principal.

All the best,
Max