[Haskell-cafe] Re: Curious Functor Class

[Ashley Yakeley]

Jeremy Gibbons wrote:
> I haven't assimilated the forall here, but datatypes with only one shape 
> of data have been called "Naperian" by Peter Hancock (because they 
> support a notion of logarithm), and they're instances of McBride and 
> Paterson's "idioms" or "applicative functors".
> 
>   http://sneezy.cs.nott.ac.uk/containers/blog/?p=14
>   http://www.cs.nott.ac.uk/~ctm/Idiom.pdf
> 
> As for uses: Bruno Oliveira and I claim an application via The Essence 
> of the Iterator Pattern:
> 
>   
> http://www.comlab.ox.ac.uk/jeremy.gibbons/publications/index.html#iterator

Perhaps the key is that there exist types P and Q s.t. there's an 
isomorphism

   F a <=> (P -> a,Q)

This seems to be intuitively Napierian:

   ln (P -> a,Q) = (P,ln a) | ln Q

I can believe that Hoistables are in fact Idioms, though I know there 
are Idioms that are not Hoistables (Maybe and Either, for instance).

(Also I think "Idiom" is a better class name than "Applicative".)

-- 
Ashley Yakeley
Seattle WA