Re: Ada Interfaces and the Liskov Substitution Principle

[Georg Bauhaus <rm.tsoh+bauhaus@maps.futureapps.de>]

On Thu, 2007-05-31 at 12:27 +0200, Dmitry A. Kazakov wrote:
> 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. 

I'm saying that programmers do not necessarily write programs
with mathematical structures in their head, but they still succeed.
I don't call that unconscious mathematics, because we can't know
that. It doesn't matter. When they write,
  a := a + 1;
the may not be thinking about a commutative group of integers,
and never use "-" or "0" in their program text. We may suggest, and
many do (in particular in the non-Scheme FPL camp?), that program
design should start from established pure mathematical structures
only (or LSP, or ...). This way we will profit from the wealth of
mathematical knowledge but we might also ignore successful solutions
just because
(1) they do not usually appear on math radar screens, or 
(2) contradict beliefs in known models (see co/contravariance).


> >> 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.

But what is actually going on in /dev/random?