[Axiom-developer] Aldor %% bindings

[Page, Bill]

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.

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Can anyone explain the usage of %% and give some examples
where it is used to "check conditions"?

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

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.

Regards,
Bill Page.