On Tue, Jul 8, 2008 at 5:23 PM, Yixin Cao <[EMAIL PROTECTED]> wrote:
> On Tue, Jul 8, 2008 at 2:06 PM, Gabriel Dos Reis <[EMAIL PROTECTED]> wrote:
>>
>> I'll be using the word `specification' in an informal sense that I
>> hope is clear from context.
>>
>>
>> A /category/ is a collection of specifications.  A /domain/ is a
>> collection of implementations.  An /object/ is any computational
>> values in an OpenAxiom program.  An object has a representation given
>> by a domain.  An object /o/ is said to have type 'd' if 'd' implements
>> the reprsentation for the object /o/.
>
> You defined the category, domain and object, and then clarify the relation
> between
> domain and object. But why missing the relation between domain and category?

as an exercise to the reader :-)

Domains, being collection of implementations, necessarily implement
specifications.  In particular, a domain satisfy (e.g. implement) several
categories simultaneously.

>
> Yes, they are specification and implementation, while the specifications are
> not compulsory.
>
> Interfaces of Java work as the specification, and the classes implement it.
> The difference
> is Java requires the class provides all methods the specified in the
> interface, or else it
> can only be qualified as "abstract".

Java is one language.  C++ is another.  Haskell is yet another.

>
> OpenAxiom does not impose this type of restriction, and provides no
> compensatory mechanism
> to avoid run-time errors brought by this "freedom".
> -------------------------------------------------------------------------

I do not understand.

-- Gaby

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