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[Axiom-math] Re: [open-axiom-devel] [fricas-devel] Re: [fricas-devel] Re


From: Ralf Hemmecke
Subject: [Axiom-math] Re: [open-axiom-devel] [fricas-devel] Re: [fricas-devel] Re: [fricas-devel] Re: iterators and cartesian product.
Date: Wed, 24 Oct 2007 03:24:17 +0200
User-agent: Thunderbird 2.0.0.6 (X11/20070728)

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.

Well, if you have somewhere a function

   generator: T -> Generator(Something)

(where T is the type of X) around, then Aldor should be able to silently
insert that function for you.


I said only "like Aldor". In my proposal for an extension of Spad and
the Axiom interpreter, I expect that X must supply this generator
(iterator), i.e. satisfy some specific language-defined category that
includes this export.

I must say, I am totally happy with just *one* "for" construction.

That is exactly what I am suggesting. There should be no special cases
of the "for" construct - only one, where X is as I describe.

I am currently not seeing much use in the domain 1..9, i.e. the finite set
{1, ..., 9}.


The point of this whole thread is discussion of suggested constructions like

  [ f(i,j) for i in 1..9 repeat for j in 1..4 ]

i.e. some kind of "cross-product" extension of the for-loop iteration
such as the CROSS construction that Gaby described in Boot. Rather
than extending the language with this sort of imperative syntax, I
would like to write this in a more "functional" manner instead:

  [ f(x.1,x.2) for x in Product(1..9,1..4) ]

(Right now Product provides only 'selectfirst' and 'selectsecond'
instead of .1 and .2 but that is easily fixed.)

Or better

  map(f,expand()$Product(1..9,1..4))

which requires some slightly more general implementation of function
application over such domains.

Regards,
Bill Page.

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;
    }
}

???

What you want is available now and no need of 1..9 being a domain.

Ralf




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