[Axiom-math] Re: [open-axiom-devel] [fricas-devel] Re: [fricas-devel] Re: [fricas-devel] Re: [fricas-devel] Re: iterators and cartesian product.

[Ralf Hemmecke]

Hi Bill,

On 10/24/2007 03:56 AM, Bill Page wrote:
> On 10/23/07, Ralf Hemmecke wrote:
> > On 10/24/2007 03:07 AM, Bill Page wrote:
> > > On 10/23/07, Ralf Hemmecke wrote:
> > > > > > Seems OK, but, of course the _domain_ 1..9 is then inappropriate in a
> > > > > > construction like
> > > > > >
> > > > > >    for i in 1..9 repeat ...
> > > > > >
> > > > > > don't you agree?
> > > > > No. My proposal also includes the idea that the construct
> > > > >
> > > > >     for i in X repeat
> > > > >
> > > > > should expect X to be any domain that supplies a generator (like Aldor).
> > > > In Aldor, at the place of X there must be an element of type
> > > > "Generator(Something)", not a domain.
> > > Can you give an example of an "element of type Generator(Something)"
> > > that is not a domain?
> > g: Generator(Integer) := generate {yield 0}
> >
> > Take g.
>
> Ok, yes I see what you mean. But this requires some new basic
> functionality in the language, right?

I cannot live anymore without "Generator". And I very much hope it will 
make it into SPAD.

> Contrast this with 'Stream' in
> Axiom which (so far as I understand) does not require such an
> extension of Spad.

For me a stream is like a generator with memory. If I step a generator 
then I can never repeat that step. Take (Aldor)

g: Generator Integer := generate yield 1;

l1: List Integer := [x for x in g];
l2: List Integer := [x for x in g]

that yields l1=[1] and l2=[].

If you replace g by

s: Stream(Integer) := ...

you would probably expect that also l2=[1]

Oh, I am totally wrong. Streams are always infinite, Generators are not.
So I would have to write

  [x for x in s for i in 1..1]

> > Hmmm, didn't you like
> >
> > http://lists.gnu.org/archive/html/axiom-math/2007-10/msg00023.html
> >
> > main(): () == {
> >      import from Z, Product(Z, Z);
> >      s1: Segment Z := 1..3;
> >      s2: Segment Z := 11..12;
> >      for ab in s1 * s2 repeat {
> >          (a, b) := ab;
> >          stdout << a << ", " << b << newline;
> >      }
> > }

> Yes, that is "ok" but ... we already have a domain construction
> Product in the Axiom library that takes two *domains* as it's
> parameters.

OK if you like that so much then OK. As Martin said, that is very much 
what we do in Aldor-combinat. There is a Product functor that takes two 
species and produces the product species. Each species comes with a function

  structures: SetSpecies L -> Generator %;

So for us it would mean

  for s in structures([1,2,3,4])$Times(F, G)(Integer) repeat ...

where F and G would be the species corresponding to 1..9 and 1..4.
I don't see that this makes life easier.

I am sure one could simplify some libraries so that you end up with

  for s in generator()$Product(1..9, 1..9) repeat

where 1..9 should be interpreted as a domain that also provides a function

  generator: () -> Generator %

Fine. But look closer and you see that I build again on the concept of 
Generator.

If I understand you correctly, you basically want to have the same 
functions but like the compiler to allow you to write

  for s in Product(1..9, 1..9) ...

as syntactic sugar for my line above.

I hopefully don't introduce too much confusion here. I don't know enough 
of the limitations of SPAD.

Ralf