On Fri, 16 Nov 2001, Clemens Hintze wrote:

> Two things I would like to ask you right now:
> 
> - What does subtyping exactly mean in OCaml resp. functional
>   programming?
> - What means covariance and contravariance of types and subtypes?

Not being an Ocaml guru, I shan't attempt the first question.
The second's pretty easy, though: covariance is the sane way of doing OO,
and contravariance is bizarre. (Right, if there's any Eiffel devotees on
here, I've just started a flamewar. :)

Seriously: contravariance breaks the assumption that a subtype is capable
of everything that its parent can do. Essentially, it allows you to narrow
arguments to functions: to use some weird eiffelish pseudocode i had
lying around, you can do this.

class bar

class bar_child is bar

class garment public foo(b: bar ) 
class toga is garment public foo(b: bar_child)
/* narrowing the argument of foo */


class tester public main = let p:garment = toga{} in p.foo(bar{})
/* attempting to call foo method of toga object using object of type bar:
   fails at runtime */


Basically, you expect to be able to call "foo" on any garment, and the
only requirement is that the argument be of type "bar". "toga" narrows it
to "bar_child" and the whole thing falls down in a heap.

Covariance doesn't let this happen. You can actually widen the type in a
child class, I believe: this isn't generally particularly useful, though.


> Regards,
> Clemens.
> 
> PS: Sorry, if my english is not flawless, but it is not my
>     mother-tongue, and I do not speak french a bit, unfortunately.

It's an odd thing: most of the posts with apologies for bad English I've
seen on Usenet have been flawless as far as composition goes.

mrak


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