[Haskell-cafe] Automatic Recognition of Functors

[Nicolas Frisby]

This link might be what you are after:

http://okmij.org/ftp/Haskell/typecast.html#deepest-functor

On 3/1/07, Walter Potter <potter at southwestern.edu> wrote:
> Folks,
>
> Given f:: a -> b it is very natural to lift f to P f :: P a -> P b
> where P is the power set functor. Or L f :: [a] -> [b].
>
> We are modeling structures using repeated application of the power
> functor, via repeated application of [ ].
>
> It would be very nice if Haskell would recognize this lifting. That
> is, if f :: a -> b then one automatically has f :: [a] -> [b]
> without using fMap.
>
> We can do something similar with classes in the following way:
>
> Given
>
> class Addy a where
> (+.) :: a -> a -> a
>
> instance(Addy a) => Addy [ a]
> (+.) w [ ] = w
> (+.) [ ] w = w
> (+.) (a:as) (b:bs) = (a+b) :(as + bs)
>
> Now given
>
> instance Addy Int
> (+.) x y = x+y
>
> One can compute
> [[1,2],[3,4]] +. [ [2,3],[1,2,.3]].
>
> I know I'm asking for a bit more here. I might need to use  fMap f :
> [ a] -> [ b].
> But I can't seem to get by with
> fMap f [[1,2],[3,4]] when f :: Int -> Int
>
> We often need to lift functions to higher power maps.
>
> It would be nice to have a way to do this with ease.
>
> Suggestions are welcome.
>
> Walt
>
>
>
>
>
>
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