Re: [Axiom-developer] Bootstrap documentation.

[Ralf Hemmecke]

On 05/08/2007 09:25 AM, Gabriel Dos Reis wrote:
> "Bill Page" <address@hidden> writes:

> | > Many of the categories and friends dragged in by Integer do
> | > not seem to be of necessity at the lowest level.  So, you
> | > could start with just the simple data structure Integer with
> | > few operations and extend it as you go.
> | 
> | But for this to be sucessful for the entire Axiom library
> | wouldn't that require that there be no essential mutual
> | recursion between source modules?

An example for Integer...

Suppose you have Integer just defined by

Integer: with == add;

Then you can say

define Ring: with {
   ...
   *: (Integer, %) -> %;
}

extend Integer: Ring == add {...}

No mutual recursion is needed in this case. But I'm sure you knew that 
already.

> Spad needs to move to mutual recursion (with appropriate restrictions)
> anyway.

Does someone know of an instance of mutual recursion in the Axiom 
library that cannot be cured with "extend"? (I am not saying that I 
don't want mutual recursion, but rather whether it is needed for the 
current Axiom library.)

> | I do not see how extend
> | helps in this case. Sure it is possible even to have
> | mutual recursion between extensions, not?

> I don't know what a mutual recursion between extensions mean, but
> definitely mutual recursion between domains is needed for natural
> expressions of domains.

I also don't understand how mutual recursion and extend should work 
together. Surely, it should be possible to extend any domain, no matter 
how it is defined. Bill, can you give an example of what you mean?

Ralf