[Axiom-developer] Re: [Aldor-l] [Axiom-math] Are Fraction and Complex domains.

[Ralf Hemmecke]

> | System(): with {
> |    timestamp: Integer;
> |    cpuTemperature: Integer;
> | } == add {
> |    timestamp: Integer == { obtain the timestamp somehow }
> |    cpuTemperature: Integer == { obtain the timestamp somehow }
> | }
>
> If this must be a type, what are the terms that inhabit it?

In Aldor there are packages and domains. Their only difference is that 
the latter exports something involving %. The above code doesn't do this 
so it is a package. In oo-speak its a class that only exports static 
constants. There are no instantiations of elements of that package.

> | Of course, you can rewrite it to
> | 
> | System: with {
> |    grabData: () -> %
> |    timestamp: % -> Integer;
> |    cpuTemperature: % -> Integer;
> | } == add {
> |    macro Rep == Record( ts: Integer, temp: Integer );
> | 
> |    grabData(): % == {
> |       per record( obtain the timestamp somehow, obtain the temperature  
> | somehow );
> |    }
> | 
> |    timestamp( a: % ): Integer == { (rep a) . ts; };
> |    cpuTemperature( a: % ): Integer == { (rep a) . temp; };
> | }
> | 
> | , but would that be better? The latter version is the one we are more used  
> | to, but is it really better?

> I would claim is it better.  However, I would challenge the claim that
> the former is a function that define types.

I would also claim the second is better. Christian, if you call the 
first System() only once then you wouldn't make it a function, but you 
certainly like to call System() several times.

> | To determine the given temperature and timestamp for the system involves 1  
> | Function call for non functional Domains and 3 for functional Domains.

I guess you are wrong.

In the first case, each time you want a time-temperature pair you must 
do like...

S == System();
t := timeStamp$S;
T := cpuTemperature$S;

in the second case it is

d := grabData()$System;
t := timeStamp(d)$System;
T := cpuTemperature(d)$System;

So what do you gain?

> If I do not have a functional type system, how am I supposed to do 
> "separate compilation"?  How am I supposed to do calls?

I first thought you make a point, but

Cat1: Category == with {..}

Cat1 is a constant. Fine.


Cat2(R: Sometype): Category == with {...}

is equivalent to

Cat2: (R: SomeType) -> Category ==
  (R: SomeType): Category +-> with {...}

Again Cat2 is a constant. Also fine.

Dom1: Cat2(blah) == add {...}

That is a constant. But it should not be defined that way. In order to 
avoid complications it should be done via

Cat2BLAH == Cat2(bla);
Dom1: Cat2BLAH == add {...}

because later you might want to ask

if Dom1 has Cat2(blah) then ...

Of course, with a non-functional type system that might turn out to be 
false.

So, for every domain whose category involves a parameter one has to 
introduce a constant category with exactly that parameter. The same 
happens one level down. For every element of a parametrised domain, one 
has to introduce a constant domain (without parameter) before the 
element can be defined.

I have the impression that soon becomes unhandy. So I feel more on 
Gaby's side. Non-functional language at the element level, functional at 
type level.

But it has to be discussed what "equality of arguments" actually means 
in order to be able to speak about the functionality property, since not 
every type exports "=: (%, %) -> %".

Ralf