[Aldor-l] [fricas-devel] Re: Indexed Union

[Bill Page]

On Wed, Apr 2, 2008 at 11:40 AM, Bill Page wrote:
> ...
> >  > Consider the canonical example of a function that takes and a
>  >  > non-negative Integer 'n' and returns the zero "vector" of type
>  >  > 'DirectProduct(n,Integer)'
>  >  >
>  >  >    zeroVector(n:NonNegativeInteger):DirectProduct(n,Integer)
>  >  >
>  >  > As far as I know it is impossible to write such a function in any
>  >  > version of Axiom as it stands today but this is possible in Aldor.
>  >
> On Wed, Apr 2, 2008 at 4:38 AM, Ralf Hemmecke wrote:
>
>  >  I think, no matter whether or not this is possible in Aldor, it looks
>  >  like a bad construction.
>  >
>  >  Suppose you implement the DirectProduct constructor with only
>  >  vectors of  length n in mind. You would probably want your zero
>  >  vector to have signature
>  >
>  >    0: %
>  >
>  >  and not
>  >
>  >    zeroVector: NNI -> %
>  >
>
>  No 'zeroVector' is not a vector. [0,0,0] is a member of 'zeroVector(3)'.
>

Oops, sorry. Re-reading I see that what I wrote above is nonsense.
What I should have said is that in this example 'zeroVector' is not an
operation exported by DirectProduct.

Of course DirectProduct in Axiom does define 0 that way and one can
certainly write:

  0$DirectProduct(3,Integer)

I don't agree that my 'zeroVector' is a "bad construction" although I
have to admit that it is somewhat artificial. The point of the example
is a function whose result type depends on the value of it's
arguments. The situation can be much more complicated than this.

Regards,
Bill Page.