Re: Ada Interfaces and the Liskov Substitution Principle

["Dmitry A. Kazakov" <mailbox@dmitry-kazakov.de>]

On Wed, 30 May 2007 15:18:27 +0200, Georg Bauhaus wrote:

> I would start with a model that isn't originally inspired
> by mathematics (because higher math typically frowns upon operations,
> that is, the things that computers do).
> My vague model has loop invariants, loop termination,
> and the fact that the type Integer happens to include a successor
> function in its interface.  Now, the type Integer offers much
> more than that, e.g. "*". Still, it seems reasonable to start from
> the mathematical structure that maps to a type like Integer,
> even when I do not need either of the inverse,
> the neutral element, or commutativity, which Integer types have
> (mostly), among other things.

I don't see your point. You are saying that you don't need mathematics to
program, yet you illustrate your point using mathematical vocabulary. There
is something wrong with that. If programming should be based on, say,
mobile phone throwing, then why are you talking about "neutral elements"?

>> Thank you for making my point! What mathematics makes here is all the rest,
>> which could well be incomputable. Consider k a hardware random generator.
>> You could not describe it in any programming language, but you can in the
>> language of probability theory.
> 
> Thank you for making my point! :-) Probability theoretic constructs
> can be mapped into executable computer constructs only in very limited
> ways,

No, the point is that they cannot be mapped (implemented), this is why
mathematics is necessary to describe what is going on, because no machine
would be sufficient for that.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de