Unexpected behaviour with `Picture` monad and Java2D renderer about doodle

[noelwelsh]

Hmmm ... I don't think flatMap can be correctly implemented for Picture.

Consider

Picture.circle(10).flatMap(_ => Picture.square(10))

What should this draw? The problem is that there is no natural way to combine the circle and the square. Often it isn't desirable to combine them. Something like

Picture.circle(10).width.flatMap(w => Picture.square(w * 2))

is a typical usage of width and flatMap, where flatMap is only called so the width can be used to create a different element.

So I think the solution is:

• Picture has a Functor instance but no Monad
• Picture has a method andThen that is like flatMap but doesn't obey the monad laws (in particular, it doesn't obey the right identity.)

[zainab-ali]

Apologies for the delay - I think that's a good approach.

We do still need to define the behaviour of map, andThen and width with respect to drawing.

What do you think about:

Picture.circle(10).width.andThen(w => Picture.square(w * 2)) // Draws the square, but not the circle.
Picture.circle(10).width // Currently draws the circle
Picture.circle(10).map(identity) // === Picture.circle(10) so should draw the circle