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.