[Haskell-cafe] More experiments with ATs

[Stephen Tetley]

Hello Andrew

The non-type-changing map is sometimes useful as a type class - in my
graphics lib Wumpus, I call it pointwise:

class Pointwise  sh where
  type Pt sh :: *
  pointwise :: (Pt sh -> Pt sh) -> sh -> sh


For the graphics I want objects to be parametric on unit (which is
usually Double), i.e.:

data Point2 u = P2 !u !u

But I usually don't want to deeply map on the unit, for instance a
bounding box is represented as two corner points, bottom-left and
top-right - for affine transformations I want to map on the points
rather than the unit-of-points, so the Pointwise instance is:

instance Pointwise (BoundingBox u) where
  type Pt (BoundingBox u) = Point2 u
  pointwise f (BBox bl tr) = BBox (f bl) (f tr)

Where Bounding Box is:

data BoundingBox u = BBox
      { ll_corner :: Point2 u
      , ur_corner :: Point2 u
      }

I've seen this typeclass appear on the Cafe a couple of times under
different names of course.