[Om3] Skype F2F for calculus3 and condition element in OpenMath

[David Carlisle]

Comments on the note 

page 2/page3

I don't think that you can model diff and partialdiff as a binding operator. (It
may use a binding operator somewhere but if you do that you have to wrap
it in an apply to a free variable.

eg the first example on page 3, which is

d x^2/dx

x is _free_ in that expression.

If we model a functional view of differentiation so need to bind x first
then you need to apply the derivative function to a free variable x at
the end. 

(D(lambda x. x^2))(x)

Of course mathml2 uses bvar here (and also for integration) even though
the variable isn't bound, but in mathml you can give special case
reasoning for each special element but in strict mathml/openmath I don't
think you have that option.




> MathML2 claims that uplimit and lowlimit can be reduced to
> domainofapplication or condition, but the convention 
> ...x shows that this is not directly possible

I'm not sure I agree here, if you write \int_C f(c) the you need to be
integrating over a path C, which you could specify with
domainofapplication as well as anything else. The wording might be a bit
fuzzy, but you can't really in MathML (or even OpenMath) tie down
_exactly_ what is meant by integration. (although adding some extra
variants in thsi area might not be a bad thing, even if it's possble to
normalise all the forms inot one using suitable combinations of lambda
abstraction and application, it may not be wise/helpful to the user to do
so:-)


 

> Our new calculus3 content dictionary supplies a symbol defint that
> takes two real numbers as arguments: the lower and upper limits

maybe I lost the thread here, but what do you propose for your examples
4 and 5, where the range of integration is not specified by upper ahd
lower bounds?


David


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