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

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