The Theory of Classification - A Course on OO Type Systems

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ah. previously metioned when

ah. previously metioned when incomplete (and with a mis-spelt name) here.


I didn't remember this. Looks quite interesting!

Am I missing something...

In his first article, describing the set "Ordinal", he claims that the two axioms suffice, but don't you need to guarantee succ() is invertible (one-to-one)? Have all my maths left me? :)

Any other suggestions for intros to PL mathematics? I would really like to understand all that symbolic logic (?) I often see!!
(e.g. in Modular Set-Based Analysis from Contracts )

I think you're right.

I was thinking the same thing. Not a really big deal, but formal definitions should be just that: formal. In this case it is important to define everything carefully.

Edit: I don't think we need invertable (bijective), just one-to-one (injective).

Reply from Anthony Simons

I received the following from Anthony Simons:

I just want to reassure the poster, whose id is "dbfaken", that s/he is dead right when pointing out the missing third axiom for Ordinal in article #1.

I tried to find out how to correct this, but JOT did not give me a mechanism to do this after publication. I can try again; I also mention this mistake in the subsequent article #5, with a footnote to credit Kim Bruce for pointing out my omission!

Please post this so that your readers can see that I do know about this problem. I'm not a registered Lambda user, so I can't reply myself.

Best regards to all, and thanks for the support!

Updated links to these articles

The Journal JOT has recently migrated to a new server. As a result, the links to some of the above articles may not work (as of 21/04/08 the first three pdf links are dead, though the others seem to work). I think they are moving links of the form:

to slightly longer paths, including a subdirectory for each column, of the form:

I have gathered the entire set of articles under my own research page on the Theory of Classification, if you find that some of the above links don't work for you.

Updated link to Simons bibliography

Oh, and I forgot to say that the old link to my bibliography is no longer valid, but here is the new link to
Anthony Simons' bibliography.