[om] DefMP elements

[Professor James Davenport]

On Thu, 4 Dec 2003, Andreas Strotmann wrote:
> Professor James Davenport wrote:
> >On Thu, 4 Dec 2003, Andreas Strotmann wrote:
> >>Professor James Davenport wrote:
> >>>On Wed, 3 Dec 2003, Bill Naylor wrote:
> >I was thinking of a Pascal phrasebook that replaces sec(x) with 1/cos(x), 
> >but can't necessarily write Pascal recursive procedures.
> If you replace Pascal with Fortran, you have a point, but that's a very 
> unlikely candidate for digesting OM CDs, I would have thought.
No - I meant what I said. 
> >>definition of functions, be it factorials or Ackermann functions. I 
> >>believe that we should take serious the advice of previous posts that 
> >>this restriction would essentially cripple DefMP.
> >It cripples ONE FORM OF DefMP, the type that is explcitly declared to be 
> >non-recursive. Mayve the other sort should be called 'recursive' rathen 
> >than 'evaluating'.
> You're right -- my mistake. 
I want to make a simplistic phrasebook easy to implement.
Maybe I chose the wrong words, but if ML can have "let" and "letrec", why 
not OpenMath.? 
> I'm rather sceptical that this is feasible at all, except perhaps in 
> extremely simple cases (csc might be one such case, but given the 
> content of your "uncouth" SIGSAM paper, I'm sceptical even in this case 
> that you wouldn't have to go through some special process of defining 
> the complex domain of csc that would go beyond the simple sample 
> definition in your DefMP paper.)
> 
> In particular, I don't think that the definition of sine in terms of exp 
> in your paper meets this requirement:
> 
> a) It would *not* be OK to make that replacement in the context of a 
> high-school geometry textbook, where sin and cos are perfectly well 
> defined in terms of quotients of lengths of sides of triangles, but exp 
> is still several years ahead, completely outside the scope of geometry 
> in fact (and therefore anything but intellectually prior). 
But then the application understands sin/cos. 
> b) I would even argue that that replacement is not even OK in the 
> context of real analysis, since it involves complex numbers, which are 
> not intellectually prior either.
James
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