2008/11/18 Conal Elliott <conal@conal.net>

Is there a simple existing library that provides views of data types in terms of unit, product and sum?

Here's what I threw together for my own use. I used associated types, though functional dependencies would work as well.

    class HasView t where
      type View t
      view   :: t -> View t
      unview :: View t -> t

    -- View instances

    instance HasView (Maybe a) where
      type View (Maybe a) = Either () a

      view   Nothing      = (Left ())
      view   (Just a)     = (Right a)

      unview (Left ())    = Nothing
      unview (Right a)    = (Just a)

    instance HasView [a] where
      type View [a]         = Either () (a,[a])

      view   []             = (Left ())
      view   (a:as)         = (Right (a,as))

      unview (Left ())     = []
      unview (Right (a,as)) = (a:as)

    onView2 :: (HasView a, HasView b, HasView c) =>
           (View a -> View b -> View c)
        -> (a -> b -> c)
    onView2 op a b = unview (view a `op` view b)

Thanks, - Conal

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