[Om3] calculus function difference application

[Professor James Davenport]

On Mon, 22 Sep 2008, Jan Willem Knopper wrote:
> There is an elementary calculus symbol I would like to use in my formula
> editor, and I would like to know whether it has been considered in the
> past for inclusion in OpenMath, and if not, whether it might be useful
> to include it in the future. It is not currently present in content
A good question.
> MathML.
> 
> In calculus with definite integration one often writes:
> 
> \int^b_a f'(x)dx = [f(x)]^b_a = f(b)-f(a)
> 
> Semantically the right form means, for a lambda function lambda
> x.f(x), and an interval1.interval [a,b], the difference of the
> application in b and a : f(b)-f(a). 
> 
> To show the binding x, it might be better to write [f(x)]^b_{x=a},
> although this might be confusing for some.
> 
> This is used in highschool here (and also used for example in
> http://en.wikipedia.org/wiki/Integration_by_parts) and I would like to
> be able to express it in OpenMath. I could not find such a symbol in the
> calculus CDs (or in any other CD).
> 
> Any comments on this would be appreciated,
I was gong to point oit that it is really 'syntactic sygar' for two 
evaluations, and so could be
<OMA>
  <OMS name="minus" cd="arith1"/>
  <OMA>
    <OMBIND>
      <OMS name="lambda" cd="fns1"/>
      <OMBVAR>
        <OMV name="x"/>
      </OMBVAR>
      <OMV name="f"/>
    </OMBIND>
    <OMV name="b"/>
  </OMA>
  <OMA>
    <OMBIND>
      <OMS name="lambda" cd="fns1"/>
      <OMBVAR>
        <OMV name="x"/>
      </OMBVAR>
      <OMV name="f"/>
    </OMBIND>
    <OMV name="a"/>
  </OMA>
</OMA>
which is correct, but not exactly helpful.
Presumably what you want is something like
<OMA>
  <OMBIND>
    <OMS name="eval_difference" cd="calculus2"/>
    <!-- hypothetical symbol -->
    <OMBVAR>
      <OMV name="x"/>
    </OMBVAR>
    <OMV name="f"/>
  </OMBIND>
  <OMV name="a"/>
  <OMV name="b"/>
</OMA>

Is this correct?

James