Re: Graph

From: mAsterdam <>
Date: Tue, 15 Jan 2008 14:06:34 +0100
Message-ID: <478cae85$0$85779$>

David BL wrote:
> mAsterdam wrote:

>> David BL wrote:
>>> mAsterdam wrote:
>>>> You did not address my question.
>>>> I'll rephrase it as a statement:
>>>> Having a domain and a codomain is relevant
>>>> to something being a function.
>>>> Having a domain and a codomain is irrelevant
>>>> to wether a function is a kind of relation or not.
>>>> You appear to see that differently. Please explain.
>>> It appears we may have a different interpretation of what "is-a"
>>> means.
>> Now this is a kind of can of worm-like beings!

> Oh yes!
>> I suspect it is more a matter of context: In the context of running
>> programs, objects behave, and there is a concern for consistency in
>> their behaviour: program correctnes, preferably provable. After the
>> object dies, however, there still is data, which may later be used to
>> incarnate similar objects, but also to build completely different objects.
>> For the data sec no such behavioral consistency concern applies.
>> A similar idea can be found at,
>> search for 'envelopes'.

> Yes I agree that it depends on the context. More to the point, I
> think it's important to distinguish between value-types and non-value
> types.
>>> I am assuming that for a function to be a relation, a function
>>> is not permitted to introduce additional information (not available on
>>> the relation).  Instead it is only allow to introduce constraints.
>>> You could compare this to Date's statement that it is wrong to say
>>> that a coloured rectangle is-a rectangle.   This corresponds to
>>> thinking of a subtype as being a subset, and BTW is not the view
>>> generally held by most OO practitioners that assume is-a means LSP:-
>> Which is, if I understood correctly, about behavioral consistency.

> Yes. I only raised it because most programmers are exposed to OO
> concepts, and I think the LSP has coloured some people's concept of
> "is a" in a way that's at odds with the mathematician's perspective.
>>> In a pure mathematical setting, the "subtype = subset" view seems more
>>> appropriate, as for example when we say that a circle is-a ellipse.

> Did I address your question?

Yes, thank you.

Your position on this is not altogether clear yet - but that would be to much to ask in one go. I am still curious whether you found a real context where

        'a function is a kind of relation'

does not hold, but you surely made it imaginable, albeit outside the database-realm.

What you see depends on where you stand.
Received on Tue Jan 15 2008 - 14:06:34 CET

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