Re: [Axiom-developer] RE: Types as values, and Re: Static versusDynamically typed(was:Philosophy... )

[Ralf Hemmecke]

William Sit wrote:
> Ralf Hemmecke wrote:
>
> > [from www.aldor.org:]
> >
> > > > > > Types and functions are first class entities allowing them to be
> > > > > > constructed and manipulated within Aldor programs just like any
> > > > > > other value.
> >
> > Interesting. If that were so easy, it would be possible to ask a type
> > for the functions it implements.
>
> Exactly. It has been a long standing (but lost) request (I believe from me) that
> Axiom constructors (that include category, domain and packages, but not the
> developers :-)) allow query of their arguments. It is useful, for example, to be
> able to distinguish whether a field is a quotient field of some integral domain
> or just a field to make codes more efficient. The request was not acted upon
> because at the time (around 1990 +/- 3 years?), effort was concentrated on
> developing the Aldor (A#) compiler, which promised to solve such problems.

I am not so sure whether I would really need that kind of reflection. In 
some cases it would be useful, for example, for the implementation of 
something like JUnit for Aldor. However, I somehow do not think that 
being able to query the structure of a type is a good idea. You gave a 
good reason, but isn't there a better way to achieve efficiency?

> > Aldor allows something like
> >
> > #include "aldor"
> > #include "aldorio"
> > Dom: with {
> >   foo: % -> Boolean;
> > } == add {
> >   foo(x: %): Boolean == true;
> > }
> >
> > import from Dom;
> > if Dom has with {foo: % -> Boolean} then {
> >        stdout << "foo is there" << newline;
> > } else {
> >        stdout << "foo is missing" << newline;
> > }
> >
> > However, I cannot, for example, write a function that returns a list of
> > names of functions implemented in Dom. (That is the current knowledge I
> > have.) 

> In other words, if I understand the example, you can't list unless you already
> know?

Exactly. Well, returning the list of function names would certainly be 
do-able, but the next thing a programmer would ask for is: How can I 
call the function with name "foo"? What is the input type? ...

> Listing functions in a domain is not a simple question in Axiom. Functions can
> be inherited from parent constructors or exported as new. It also depends on in
> what form you want the list. Surely, by doing a ")show Dom" (this is in the
> interpreter: I am not aware of any compiler equivalent) you get that list.

Same in "aldor -gloop". By saying then

#include "aldor"
#include "aldorinterp"
Integer

one gets

%1 >> #include "aldor"
                                           Comp: 110 msec, Interp: 0 msec
%2 >> #include "aldorinterp"
                                           Comp: 30 msec, Interp: 0 msec
%3 >> Integer
  () @ Join(
PrimitiveType with
        coerce: BInt -> %
        coerce: % -> BInt
    ==  add ()
,
IntegerType with export to IntegerSegment(%)
    ==  add ()
)
                                           Comp: 10 msec, Interp: 0 msec

But again, that is the interpreter. I cannot do anything useful with 
that output in a stand-alone program.

> > And, of course, I see no way of morphing the result of "foo" to
> > "false" without writing a new function. 

> That is what I was asking: code modification. Like you, I also interpret "first
> class object as data" that way (but that need not be the "official"
> interpretation).

I think I am happy that the Aldor code itself is not modifyable (as in 
Maple).

Ralf