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

[Ralf Hemmecke]

> |   '1..' is another (better?) name for PositiveInteger
>
> No, it is not.  Both behave quite differently in many situations.

What?

Suppose I have given

  PositiveIntegerCategory

and suppose

  PositiveInteger: PositiveIntegerCategory == add {...}

then

  (..)(i: Integer): PositiveIntegerCategory == PositiveInteger

For simplicity I simply ignore the parameter and in the following I 
simply use an existing "IntegerType" from LibAldor.

---BEGIN aaa.as
#include "aldor"
#include "aldorio"
PositiveInteger: IntegerType == Integer add;
(..)(i: Integer): IntegerType == PositiveInteger add;
one:*Integer == 1$Integer;
import from one..;
stdout << 3 << newline;
---END aaa.as

(I don't import from Integer since I use ":*" instead of ":". Remove the 
* and see what the compiler tells you.)

Add the line

for i in one.. repeat stdout << i << newline;

to the program above and try to compile. Of course it must fail.
>aldor -fx -laldor aaa.as
"aaa.as", line 9: for i in one.. repeat stdout << i << newline;
                  ....^.......^
[L9 C5] #2 (Error) No meaning for identifier `i'.
[L9 C13] #1 (Error) Argument 1 of `generator' did not match any possible 
parameter type.
    The rejected type is
                IntegerType with
                    == Posi....
    Expected type String.

Since there is no function (..) which returns a Generator(Something).

But still, I cannot see, why

  one..

behaves in any way different from PositiveInteger.

OK, you speak of SPAD and I demonstrated Aldor, so I should be quiet.

Ralf