[Haskell-beginners] Program reliability and multiple data constructors; polymorphism

[Stephen Tetley]

Idiomatic Haskell for *drawing* shapes is to represent Shapes as
functions from their origin to what they draw (e.g. Bitmap).

type Drawing = Pt2 -> Bitmap

-- Circle needs a radius
type Circle = Float -> Drawing

circle :: Circle
circle r = \pt -> {...}

-- Rect needs width and height
type Rect = Float -> Float -> Drawing

rect :: Rect
rect w h = \pt -> {...}

Transformations like scaling work by pre-transforming the arguments

uniform_scale_rect :: Float -> Rect
uniform_scale_rect sz = \w h -> rect (sz*w) (sz*h)

uniform_scale_scale :: Float -> Circle
uniform_scale_scale sz = \r -> cicle (sz*r)


If you want a polymorphic scale function you will have to make your
shapes individual newtypes so us can write specific instances for
them.

This works very well for drawing, but because Shapes are represented
as functions they cannot support introspection e.g. querying a circle
for its radius. Depending how you design your editor you might find
introspection wasn't a genuine requirement.