[Aldor-l] [fricas-devel] Re: Axiom interface

[Ralf Hemmecke]

Martin,

> The only slight awkwardness I can imagine is as follows: If I export, say, in
> Polynomial
> 
> coefficientRing: () -> Ring
> 
> then the result of baseRing will be a Ring, and may have "forgotten" all the
> other categories it possibly satisfies. Hm, it seems I will never understand
> "has" completely - Ralf, could you remind me why the following output is
> produced by Aldor?

Maybe you google for something like

+"static type" +"dynamic type" +aldor

Christian's remarks should be correct.

It is as simple as this: with "has" you refer to all the exports of a 
domain. So if

A: with {foo: () -> ()} ==   add {foo(): () == {}}
B: with {bar: () -> ()} == A add {bar(): () == {}}

then B (statically) only exports bar, but if you look at the right hand 
side of the definition of B then there is a (anonymous) domain

   A add {bar(): () == {}}

which is of type

   with {
     foo: () -> ()
     bar: () -> ()
   }

and all this can be seen by "has" from B, too.
So

   B has with {foo: () -> ()}

returns true.

I don't say that I like that since one can easily produce code that 
looks typesafe but is completely wrong (see end of mail). Note that 
suddenly, -1 is a member of NNI.

Ralf


---BEGIN HasSemantics.as
#include "aldor"
#include "aldorio"

NNI: with {
	+: (%, %) -> %;
	coerce: Integer -> %;
	<<: (TextWriter, %) -> TextWriter;
} == Integer add {
	Rep == Integer;
	import from Rep;
	coerce(x: Integer): % == per x;
	(p: TextWriter) << (x: %): TextWriter == p << rep x;
}

main(): () == {
	import from Integer;
	stdout << "NNI has with -: % -> % ---- ";
	stdout << (NNI has with {-:%->%}) << newline;
	a: NNI := 1::NNI;
	if NNI has with {-:%->%} then {
		b: NNI := -a;
		stdout << "-(1 at NNI) = " << b << newline;
	}
	stdout << "INT has IntegerType --- ";
	stdout << (Integer has IntegerType) << newline;
	stdout << "NNI has IntegerType --- ";
	stdout << (NNI has IntegerType) << newline;
	stdout << "NNI has OrderedArithmeticType --- ";
	stdout << (NNI has OrderedArithmeticType) << newline;
	stdout << "NNI has with <: (%,%) -> Boolean ---- ";
	stdout << (NNI has with {<:(%,%)->Boolean}) << newline;
}
main();
---END HasSemantics.as