[Axiom-developer] Re: Aldor %% bindings

[Ralf Hemmecke]

On 03/14/2006 09:56 AM, Page, Bill wrote:
> Ralf, and other Aldor experts;
>
> Section "7.5 Subtypes" of the Aldor Users Guide says:
>
>   Note that Aldor is constructed so that a domain is only a
>   member of a named category if it explicitly inherits from
>   the category -- not if it merely exports the same collection
>   of (explicit) declarations\1.

> Footnote \1 says:
>
>   In the current implementation, each named category C
>   implicitly exports a symbol named \%%" with type C (see
>   Section 8.12), whose presence is tested for in checking
>   category membership.
>
> Note: 8.12 is a typo. It should say 8.11.
>
> Section "8.11 With" says::
>
>   A 'with' expression also defines a constant named "%%" for
>   each category from which the 'with' expression inherits.
>   The type of %% is the inherited category, and the value
>   is the domain viewed as a member of that category...
>   The %% bindings are generally most useful for checking
>   conditions.
>
> -------
>
> Can anyone explain the usage of %% and give some examples
> where it is used to "check conditions"?

For example "has" constructs, but I don't know if there is anything else.

#include "aldor"
define CatDummy: Category == PrimitiveType with {foo: () -> ()}

If you compile this with via "aldor -fasy aaa.as" then you get
something like that ...

((|Declare|
    |CatDummy|
    (|Define|
      (|Declare| (|Label| |CatDummy| ()) |Category|)
      (|With|
        |PrimitiveType|
        (|Declare|
          |foo|
          (|Apply| -> (|Comma|) (|Comma|))))))
    ((|catExports|
        (|Declare|
          =
          (|Apply| -> (|Comma| % %) |Boolean|))
        (|Declare|
          ~=
          (|Apply| -> (|Comma| % %) |Boolean|)
          ((|default| . 1))
        (|Declare|
          %%
          |PrimitiveType|)
        (|Declare|
          |foo|
          (|Apply| -> (|Comma|) (|Comma|)))
        (|Declare|
          %%
          |CatDummy|)))))

To make it shorter here, I have removed some
((|symeNameCode| . 243941740) (|symeTypeCode| . 83337439)) stuff.

What you see is that the Category CatDummy, not only exports %% for 
PrimitiveType but also %% for CatDummy.

As I understand this... apart from encoding the category hierarchy in 
that way it also could make the evaluation of "DOM has CatDummy" faster 
since the need only be a lookup whether there is some %% for CatDummy. 
No check for all the corresponding exported functions is necessary. (Am 
I wrong?)

> What does it mean to be a "domain viewed as a member of
> a specific category"?

I have only seen %% in places as above. So I have no idea what that 
could mean. Maybe it is used in conditional exports, I haven't checked that.

> Apparently %% can have multiple bindings. About the
> example in section 8.11 we read that:
>
>   In the example, %% bindings are in scope for the
>   following categories:
>   BinaryAggregate, BooleanArithmeticType,
>   BoundedFiniteLinearStructureType Boolean,
>   BoundedFiniteDataStructureType Boolean,
>   FiniteLinearStructureType Boolean, PrimitiveType,
>   and so on.
>
> How can I access the value (associated domain?) of a
> particular binding?
>
> Any hints about how to understand this would be greatly
> appreciated.

Maybe Stephen Watt or Peter Broadbery could help.

Ralf