[Axiom-developer] Re: [Aldor-l] [Axiom-math] Are Fraction and Complex domains.

[Ralf Hemmecke]

> Please, guys explain clearly you're after.

Trying to clarify what the Aldor compiler does and what it should do.

> I do not take the compiler's behaivour as "God given".

Of course.

> I need clear semantics.

Of course. But what Christian's program from

http://lists.nongnu.org/archive/html/axiom-developer/2006-05/msg00181.html

does is to exhibit a bug either in the Aldor compiler or the 
documentation. I don't think that one can find any better documentation 
than Section 7.3 "Type context" in http://www.aldor.org/AldorUserGuide/.

Interestingly, if the documentation where better, I would even say that 
despite the lines

local a == inc NUM;
local b == inc dec inc NUM;
stdout << "a              : "; stdout << f()$Dom(a); stdout << newline;
stdout << "b              : "; stdout << f()$Dom(b); stdout << newline;

give different output in Christian's program, the compiler still behaves 
 functional. The problem is that the documentation should be more 
precise of what "a equals b" in the above context actually means.

If we replace Integer by TextWriter in Christian's program and do 
something like

stdout << f()$Dom(stdout);
stdout << f()$Dom(stderr);

of course most people would say that it is clear that the output might 
be different because

"stdout is not equal to stderr".                                 (*)

But how can one say that? stdout and stderr are of type TextWriter and 
that type does not export any equality. So the only chance one has to 
give meaning to (*) is to mean pointer equality. I cannot remember that 
I have ever read this in the Aldor User Guide.

> If you're after a non-functional type system, please explain
> clearly what they are useful for, with clear examples.  Explain also
> how one reasons with such type system, how one writes relaible program
> with such a type system.

I, for my part, did never claim that I want a non-functional type 
system. I actually learned through this thread that a functional one 
would be a good thing.

I am sure you could give a reference to illustrative examples that show 
serious problems. Not everyone has studied those things in his/her career.

Ralf

PS: Apart from clarification of functionality of the type system 
Christian's program also shows that its behaviour depends on the 
implementation of AldorInteger. One might get different results on 32 
and 64 bit machines. It's already interesting that one has to take quite 
big integers to make a and b into "different" things.