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

[Bill Page]

On 31 Oct 2007 20:38:43 +0100, Francois Maltey wrote:
> Hello, again
>
> > It's ok, but way should we require the dummy variable 't' when we can
> > operate directly on functions with the higher-order function
> > 'product'? I think
> >
> >    t +-> [|wholePart t, sin t|]
> >
> > is just a slightly awkward way to write:
> >
> >   product(wholePart,sin)
>
> Is it the reason why you want a ?function? product (A->X, A->Y, ...) ?
>

No, not the real reason. My main reason for wanting the higher-order
function (i.e. functional? or maybe sometimes called functor?) is that
such functions arise naturally when you try to given the formal
(categorical) semantics of exactly what you mean by the domain called
Product (or Record).

> >
> > > It's a good thing that record will remain mutable and the other
> > > structure product won't be mutable. So there is no ambiguity.
> > >
> >
> > Maybe there should be both 'Record' and 'Record!' where as usual the !
> > denotes mutability?
> >
> I'm mot sure : mathematics don't speak about record but product
> or << couples or triplets or n-uplet in French >> or Tupple ?
>

You are right. Now Axiom and Aldor has a confusing mixture of
terminology about Product, DirectProduct, Tuple, Cross, Record, ...
All of these are (almost) the same kind of thing.

> And Record! is the most logic, but perhaps not usable because everybody
> think << Record >>.
>

I think it is good if 'Record' is not mutable by default and one is
required to use a slightly more exotic name if you want mutability.

Regards,
Bill Page.