Re: [Axiom-math] if-expression and variables

[Raymond Rogers]

On 05/03/2011 11:01 AM, Ralf Hemmecke wrote:
> > But the question is not intrinsically a "programing construct".
>
> What does that mean?
More or less I mean a tree structure where the nodes have evaluation 
contents; say Boolean evaluations or calculations.  Then nodes may have 
left/right (true/false) subbranches or terminate.   In the case of 
"case" the subbranches could be most anything.  When the tree 
terminates, reaches an end node,  then return  the terminating 
evaluation/value (for debuging the option of returning the path might be 
nice).  If a mid-level evaluation doesn't match a subsequent branch then 
return failure; of course the lack of a subbranch would be taken as 
matching anything.

This isn't what I meant by "symbolic logic" but is equivalent and seems 
perfectly clear without any evocation of "horn clauses" and such.
> > With some (bulky) symbolic logic constructs one can express it in a
> > mathematical sense. That is: set membership and "exclusive or".
>
> You want to rewrite the if-statement into set membership and exclusive 
> or?
Yes I did; but upon reflection I am reluctant to go there.


> To give a few hints. As Bill already said, Axiom is more an algebraic 
> system rather than a symbolic one. Of course, since Axiom has a proper 
> programming language underneath, one can do everything, but the 
> question is, how much is already implemented.
>
> The first questions, when one programs with Axiom usually are:
> What is my "domain of computation"?
> (That is basically like with universal algebra. What is the carrier 
> set and what are the operations?)
> How are the elements of the carrier set represented in terms of 
> already existing (library) types?
Yes, I think it boils down to second-order logic; in this case a 
category of unevaluated expressions.   As above; stored in the tree and 
then brought front and center and evaluated in the tree accessing 
environment.

Going back to the original question.  It seems the questioner expects to 
fabricate a template and later to create instances of it with varying 
variables.  I would think that keeping the old (hopefully private) 
variables and then assigning incoming variables to the private variables 
might eliminate having multiple copies laying around and perhaps the 
need of a template at all.
Probably doesn't cover all cases though.

Sorry if I have taken the discussion drifting; I merely wanted to point 
out the if/else can be a static data structure rather than in-line code.

Ray