These days I have a lot less time for writing, however. What makes it to this blog are mostly just the things that I found interesting enough to share. To get the message out I largely rely on syndication through planet haskell and reddit, both of which makes the location of the source content less of an issue these days than it used to be. Those have more overlap with would-be readership for this sort of content than almost any mainstream web site I can know of.

> newtype RanT f g c m m’ = (c -> K m) -> T m’

Should be:

> newtype RanT k t c m m’ = (c -> k m) -> t m’

right?

Fixed the LanT definition. (Woops!)

Re the dinatural transformation piece, I’m not as deep as I used to be in this area, so I’ll go back and see what I can dig up from whatever notes I still have from when I wrote this. I recall it seeming quite obvious at the time, but now I can only barely remember what dinaturality is. :) I’d be quite surprised (and pleased) if you came up with a counterexample, however. ;)

data LanT k t c m m’ = LanT (k m -> c) (t m)

should probably be

data LanT k t c m m’ = LanT (k m -> c) (t m’)

though it makes no difference in the definition of Lan.

On a less trivial level, I still don’t know what theorem I could quote to justify that, say,

type DinaturalFromObject x s = x -> forall a. s a a

defines dinaturals from a constant functor. For a specific choice of s dinaturality is a free theorem. But how do you uniformly prove this for all s, implemented in Haskell, with the right c/contravariance in the arguments?