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

[Ralf Hemmecke]

Hi Martin,

> > If I knew where to hook libaldor into Axiom, I would already have done
> > so. But libaldor basically starts from zero and for Axiom the whole
> > construction of the domains and categories is still mystical to me.

> > In any case if SPAD should be translated to Aldor one has to start with some
> > domain or category.

> Yes. But what exactly is mystical to you? Everything starts in catdef.spad, and
> in fact the code is very easy to read, I find.

Let me quote the first few lines... (documentation stripped)

AbelianGroup(): Category == CancellationAbelianMonoid with
      "-": % -> %
      "-": (%,%) -> %
      "*": (Integer,%) -> %
    add
      (x:% - y:%):% == x+(-y)
      subtractIfCan(x:%,y:%):Union(%,"failed")==(x-y)::Union(%,"failed")
      n:NonNegativeInteger * x:% == (n::Integer) * x
      import RepeatedDoubling(%)
      if not (% has Ring) then
        n:Integer * x:% ==
          zero? n => 0
          n>0 => double(n pretend PositiveInteger,x)
          double((-n) pretend PositiveInteger,-x)

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. ;-)

So you see, I still find it mystical. I simply don't know what is built 
into the compiler.

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. The interpreter needs something like OutputForm in order 
to print something reasonable on the screen. Is this type builtin?

Does somebody know of a cutpoint between SPAD compiler and the actual 
libraries?

Ralf