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The Theory of Classification - A Course on OO Type Systems

This seems to be an introductory ("aimed specifically at non-theoreticians") set of articles on OO type theory. The author is Tony Simons and the articles were all published in the Journal of Object Technology.

  1. Perspectives on Type Compatibility (pdf)
  2. The Scratch-Built Typechecker (pdf)
  3. Object Encodings and Recursion (pdf)
  4. Object Types and Subtyping (pdf)
  5. Axioms, Assertions and Subtyping (pdf)
  6. The Subtyping Inquisition (pdf)
  7. A Class is a Family of Types (pdf)
  8. Classification and Inheritance (pdf)
  9. Inheritance and Self-Reference (pdf)
  10. Method Combination and Super-Reference (pdf)
  11. Adding Class Types to Object Implementations (pdf)
  12. Building the Class Hierarchy (pdf)
  13. Template Classes and Genericity (pdf)
  14. Modification and Objects like Myself (pdf)
  15. Mixins and the Superclass Interface (pdf)
  16. Rules of Extension and the Typing of Inheritance (pdf)
  17. Multiple Inheritance and the Resolution of Inheritance Conflicts (pdf)
  18. Polymorphism Through the Looking Glass (pdf)
  19. The Proliferation of Parameters (pdf)
  20. The Modular Checking of Classtypes (pdf)

If I've made a mistake above, try A Simons's bibliography or here.

By andrew cooke at 2006-02-28 23:22 | OOP | Teaching & Learning | Theory | Type Theory | other blogs | 34597 reads

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ah. previously metioned when

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

By andrew cooke at Tue, 2006-02-28 23:26 | login or register to post comments

Interesting

I didn't remember this. Looks quite interesting!

By Ehud Lamm at Wed, 2006-03-01 13:09 | login or register to post comments

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 )

By dbfaken at Thu, 2006-03-02 17:42 | login or register to post comments

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).

By Benjamin D. Cutler at Thu, 2006-03-02 19:19 | login or register to post comments

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!

By Ehud Lamm at Fri, 2006-08-18 20:54 | login or register to post comments

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:

http://www.jot.fm/issues/issue_2002_05/column5.pdf

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

http://www.jot.fm/issues/issue_2002_05/column5/column5.pdf

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.

By AJHSimons at Mon, 2008-04-21 11:04 | login or register to post comments

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.

By AJHSimons at Mon, 2008-04-21 11:09 | login or register to post comments