Re: [Axiom-developer] The symbol 4 (was Re: Aldor and Axiom)

[Ralf Hemmecke]

On 02/15/2006 10:25 AM, Martin Rubey wrote:
> Ralf Hemmecke <address@hidden> writes:
>
> > > What other kinds of integers are there? But the symbol 4 can certainly
> > > stand for other things besides the integer 4.
> > Right. 4 is just a symbol consisting of three strokes. If one doesn't bring it
> > into a context its meaning would be totally unclear. Well, nowadays humans tend
> > to interpret this always as an integer, but I think several thousand years ago
> > that was not so clear.

> However, the "guessing" of types in Axiom is tremendously useful and without
> it, I probably would stop using it. Note that MuPAD does no type guessing, and
> thus leaves people in fact with the expression domain by default.
>
> Of course (!!!), type guessing may only be done by the interpreter.

I was never saying anything else. Guessing should be done only by an 
interpreter or maybe implemented via BNatural.

However, I wanted to stress the point that the compiler should be picky 
and reject everything it does not clearly understand from the context. 
No ambiguities allowed.

So for writing libraries the programmer is forced to state explicitly 
what he/she wants.

The user interface is another thing. Clearly there should be a shell 
around all this complicated type stuff which helps the user to solve the 
problem. It should, however, be transparent how the interpreter choses 
appropriate types or in other words. There should be a well documented 
algorithm how the interpreter extends the scope so that it can find 
appropriate functions. Maybe one needs a whole lot of (automatic) 
coercion theory.

Further, maybe, that affects also how libraries have to be written. For 
example, if you have 4 domains A, B, C, D and the following coercion 
functions,

   A ----> B
   |       |
   v       v
   C ----> D

and you type in d(a) in the interpreter where d: D->D and a:A then it is 
vital for the correctness that the above diagram is commutative 
otherwise it would depend on the choice the interpreter makes. Well, 
that says programmers should make sure that any such diagram commutes. 
Maybe that should become a big convention for coercion functions in Axiom.

Ralf