Re: [Axiom-developer] Question concerning types...

[Ralf Hemmecke]

http://wiki.axiom-developer.org/public/TheUnknownInComputerAlgebra.pdf

Ah, by the way, I've read the paper and did not find it particularly 
useful. What they do is a bit too complicated in my eyes.

> \begin{spad}
> )abbrev domain PUNINT PureUnknownInteger
> PureUnknownInteger (D,BasicUnknown):Ring == Implementation where
>     D:IntegerNumberSystem
>     BasicUnknown:List Symbol
>   Implementation ==> LocalAlgebra (Polynomial D,D,D) with
>     "/" : ($,D) -> $
>     ++ a/n computes the expression whose value is a/n if it
>     ++ is actually an unknown integer
> \end{spad}

It is certainly a wrong design to implement indefinite integers as 
polynomials.

Why?

Suppose you have a nice algebra library and you want the system to 
understand indefinite objects, then you are certainly not going to add 
any function to existing domains or wrap one (and actually ALL) domains 
with a domain constructor "Indefinite". No. It should be completely 
transparent. The goal is to type

n: Integer;

and not

n: Indefinite(Integer);

Either the interpreter or some layer between interpreter and library 
code should take care about indefinite objects.

I very much believe that this requires reflection from SPAD/Aldor.

Ralf