Re: [Axiom-developer] Re: Aldor and Axiom

[Ralf Hemmecke]

> > Since there is no definition of "Integer" in that file, the compiler must
> > know about that thing or it must look into integer.spad to find what Integer
> > stands for. Yes, yes, I know, here the whole business of circular
> > dependencies begins. I guess, finally, Integer will be an abelian group
> > itself. ;-)

> But as far as I know, for Aldor this situation was abstracted and there is now
> a keyword for dealing with it, I believe it is "extend".

Right. If you look at the sources of libaldor it starts with 
lib/aldor/src/lang/sal_lang.as and then lib/aldor/src/base/sal_base.as.

Interestingly, in the latter file there is some interdependency.

define PrimitiveType: Category == with {
        =: (%, %) -> Boolean;
        ~=: (%, %) -> Boolean;
        default { (a:%) ~= (b:%):Boolean == ~(a = b); }
}

Boolean: PrimitiveType with {
        ~: % -> %;
        coerce: Bool -> %;
        coerce: % -> Bool;
        false:%;
        true:%;
} == add {
        Rep == Bool;
        coerce(b:%):Bool        == rep b;
        coerce(b:Bool):%        == per b;
        false:%                 == address@hidden :: %;
        true:%                  == address@hidden :: %;
        ~(x:%):%                == (~(x::Bool))::%;
        (a:%) = (b:%):%         == (rep a = rep b)::%;
        (a:%) ~= (b:%):%        == (rep a ~= rep b)::%;
}

But obviously, the Aldor compiler can handle this.

> > Let us suppose the following scenario. I remove any file from src/algebra/
> > and any corresponding Makefile entry. Then I start compiling Axiom. Would I
> > end up with an Axiom framework that has no mathematical knowledge.
> >
> > Probably not.
>
>
> Well, I do think so, at least roughly. In fact, as far as I know, debugsys does
> something similar.

Should I know debugsys?

> Furthermore, Tim Daly analysed the circular dependencies to know in which
> "layer" any given domain is. You can see this in the file lattice.pamphlet on
> MathAction or in src/algebre/Makefile.

Thanks. I'll take a look.

> > The interpreter needs something like OutputForm in order to print something
> > reasonable on the screen. Is this type builtin?
>
>
> No, it is defined in outform.spad. And, as long as you don't have a coercion
> function to OUTFORM, you don't need it anyway :-)
>
> Without OUTFORM, you can print using the Lisp function "print".

But how does the Interpreter show the result? Doesn't it rely on the 
fact that a domain satisfies CoercibleTo(OutputForm)?

For example, if you write a file

---MyInt.spad
)abbr domain MYI MyInt
MyInt: with
  x: %
 == Integer add
  x: % == 1
---END

Then
)co MyInt.spad
x:MyInt

it prints just Type: Void but no other output.

So in order to have a reasonable input/output behaviour on the Axiom 
command line, I should meet certain criteria. Is that written somewhere?
References?

Ralf