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

[William Sit]

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.

> 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?

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. So
are you simply asking to be able to assign the output of ")show Dom" to a string
variable? Tim may be able to provide such a general assignment construct?

> 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 am not aware of
> a language construct that invokes the compiler during the runtime of a
> program. (The compiler might not even present on the target machine.)
> 

Thanks for this info. The interpreter of Axiom can invoke the compiler of
course. But the above meant calling the compiler from within a compiled function
at run time. Any comments from others?

William