Profunctor instance for StateT

[ceedubs]

@vmarquez pointed out to me that StateT forms a Profunctor

[kailuowang]

I gave it a try and failed, since S appears in both input and output, it looks to me that for S it has to be invariant (you need both S => NewS and NewS => S.
@vikraman or @ceedubs mind give some further instruction?
Here is my attempt

def diMap[C, D](f: C => S)(g: A => D)(implicit F: Functor[F]): StateT[F, C, D] =
    new StateT(F.map(runF)(run => (c:C) => F.map(run(f(c)))(p => ((???) , g(p._2))) ))

I need a C in the place of ??? but in p I got only a S

[vmarquez]

Err, I think I pointed out _Indexed_StateT is one. :-)

[kailuowang]

ah, makes sense. since cats doesn't have IndexedStateT shall we close this one?

[ceedubs]

Oops I hadn't thought that through very well :)

Sorry for the false alert. Thanks for giving it a try @kailuowang and thanks for your input, @vmarquez.