[Haskell-cafe] How to abstract away set representation

[Tom Ellis]

On Sun, Mar 08, 2015 at 09:01:59PM +0000, Tom Ellis wrote:
> On Sun, Mar 08, 2015 at 09:52:50PM +0100, martin wrote:
> > Hello all,
> > 
> > I was trying to construct a data type "Profile" which allows some set-like
> > behavior.  I started with functions to count, add and filter profiles.
> > 
> > type Count = Int
> > 
> > 
> > data Prof a = P {
> >         pCount  :: Count,
> >         pFilter :: (a -> Bool) -> Prof a,
> >         pAdd    :: (Prof a) -> (Prof a)
> >         } |
> >         NoProfile
> [...]
> > What would be a good way to work with set-like behavior without being tied
> > to one particular implementation?
> 
> If you really want the type parameter to be exposed you can use
> 
>     data ProfOps prof = P {
>         pCount  :: forall a. prof a -> Count
>         pFilter :: forall a. (a -> Bool) -> prof a -> prof a
>         pAdd    :: forall a. prof a -> prof a
>     }

Actually the above is the only version which works because pFilter mentions
a.  In that case you need the following package

    listProf :: ProfOps []
    listProf = P {
      pCount  = length,
      pFilter = filter,
      pAdd    = (++)
    }

I also made a mistake with the type of pAdd.  It should be

         pAdd    :: forall a. prof a -> prof a -> prof a