Contravariance [Was Re: what is easier to learn first?...]

D. Michael McFarland mcfarlan at
Wed Mar 22 05:43:46 CET 2000

>>>>> "WT" == William Tanksley <wtanksle at> writes:

 WT> On Tue, 21 Mar 2000 11:04:23 -0800, Russell E. Owen wrote:
 >> <greene at> wrote:

 >> - Eiffel: supposed to be clean, sensible and industrial
 >> strength. I do not speak from experience, though I want to learn
 >> it.

 WT> Interesting, but not really all that significant, IMO.  Of
 WT> course, I haven't used it for any large projects yet, and I doubt
 WT> I ever will.  I don't agree with the author re: contravariance
 WT> versus covariance.

Twang! (Sound of an engineer being clothes-lined by a CS concept)

I spent much of the last couple of weeks working on a tensor class
(based on code from Konrad Hinsen's Scientific package, stolen and
mangled beyond recognition), implementing some of the many shorthand
notations for contraction of mixed tensors, so the words
"contravariance" and "covariance" here caught my eye.

I hate to reveal my ignorance to this group (again), but I have to
ask: What do these terms mean in this context?

Best regards,

    D. Michael McFarland   <mcfarlan at>

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