inheritance: is circle an ellipse?

[juan_gandhi]

It's a known puzzle from the depths of object-oriented teaching: is Circle a subclass or Ellipse. From school we know it is; but as we read in books, for programmers, it is not. How come? Oh, "Liskov principle". They use Liskov principle to scare kids.

Actually we know that a circle is an ellipse with both axes being the same length.

But in programming, an ellipse is something different. It is at least stretchable. And it is also moveable. Somehow it is not rotatable, but we can skip it for simplicity.

An ellipse in programming is (almost) always horizontal; it can be moved (by changing coordinates of its center) and it can be stretched/compressed by changing its height and width. Sure a stretchable ellipse is neither an ellipse nor a circle, not even a stretchable circle. A stretchable circle stretches equally in all directions.

That's it, no? Questions? Objections?

Comments

[yigal_s]

* it depends on the axiom of choice actually

How comes? In what way?

[ivan-gandhi.livejournal.com]

See, a stretchable ellipse is a class of ellipses. There's an epimorphism from ellipses to stretchable ellipses; the fact that this epimorphism splits is due to AC: see http://ncatlab.org/nlab/show/axiom+of+choice (http://ncatlab.org/nlab/show/axiom+of+choice).

I can give you an example when this is not the case.

Imagine a curve in space that projects (vertically) on an ellipse. This curve loops twice, in space. So for every point on ellipse there are two points projecting onto it. If we limit ourselves with continuous mappings only, we cannot split this projection.