Re: Value

From: Dmitry A. Kazakov <mailbox_at_dmitry-kazakov.de>
Date: Sat, 23 Feb 2008 14:42:44 +0100
Message-ID: <6ayd0ivjccbc.1c512turhpwer$.dlg_at_40tude.net>


On Sat, 23 Feb 2008 13:38:32 +0100, mAsterdam wrote:

> Dmitry A. Kazakov wrote:
> [re-can Circles & Ellipses]
>

>> "Value" in this context is a CS term. 

>
> I am currently trying to find a helpful piece of text for the cdt
> glossary.
> From what I read at
> http://en.wikipedia.org/wiki/Value_%28computer_science%29 ,
> Value looks like a rather controversial CS term.

I don't see it controversial. I understand why you might dislike it. I support it for the same reason: it clearly, though maybe clumsy, states that 1 integer is not 1 float.

> Do you have a better reference?

You mean one, that would support claims of DB-folks? (:-))



Honestly, I wonder how one could define values otherwise while preserving types. Let me elaborate it a bit informally. The idea of type in mathematics was introduced to get rid of antinomies. In CS it is the same idea with antinomies extended to the cases of incomputability. We cannot judge about equivalences of entities. It could turn undecidable or simply too expensive. So we just don't. We define entities being values with a type assigned to them, merely in order to be able to distinguish them *without* computing P(v1=v2). That's the whole idea. Therefore if a v1 is of the circle type and v2 is of the ellipse type, that makes them automatically distinct. Just *per* construction. This has nothing to do with geometry. It is CS.

Now, when applied to geometry one could reasonably wish v1 and v2 interchangeable in some contexts. That is called substitutability. Note that substitutability assumes that you substitute *one* thing for *another*. So these are *different* things. Substitutability of circle for ellipse is a CS model of circles being a subset of ellipses. Note, just a model of. No physical subsets involved, though not excluded, when for example, circle would inherit the representation of ellipse. Moreover any such model is necessary inadequate as a trivial Circle/Ellipse analysis shows. So, why all this rant?

Just one final stab. Observe that this framework does not exclude "physical" subsets. Neither it specifies the sets where values come from. This automatically makes it more general than any other model based on subsets of values. Whatever you could do on that basis is already included.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
Received on Sat Feb 23 2008 - 14:42:44 CET

Original text of this message