[om] DefMP elements

[Professor James Davenport]

On Fri, 5 Dec 2003, Bruce Miller wrote:

> Jacques Carette wrote:
> > On the multiple facets of sin:  could one instead use trig1, trig2, trig3,
> > ...., trig10 CDs, each with different syntactic FMPs (and correspondingly
> > different used CDs) to build 'equivalent' systems?  One for high-school
> > definitions, one for the exp definition, one for the series definition, etc,
> > etc. I understood that to be the original OM design of having multiple CDs.
> > Each OM application could then use the 'right' CD and not worry about math
> > it does not know (or want).
> 
> But the catch there, is that the _generating_ application has to choose the
> CD's according to the destination application.  If it's doing that, it
> may as well just write maple/mathematica code or whatever.
Absolutely. 
> Here's another terminology: C macros vs Lisp macros :>
> 
> But seriously, I can see the application of James's more restrictive
> FMPs.  However, I can't see that a single simple FMP for a symbol would cover
> all the weaker applications that might benefit from such substitutions.
One can have as many FMPs as one wants: there's one that the CD writer 
flags as the simplifying one.
> Is it feasable to provide multiple simple-FMP's and expect the application
> to choose the one that substitutes in terms of symbols that it does know?
But what happens if it doesn't understand any, but would do after two 
substitutions. One reason for a single one is to avoid this large (and if 
one is not careful infinite) search.
> Alternatively, maybe I don't agree after all. Isn't it a phrasebook issue?
> If an application claims to understand a given CD, then isn't it responsible
> for recognizing all the symbols in that CD? --- possibly by substituting
> in a way that is optimal for itself.
But the defining FMP canonicalises this substitution. If a phrasebook 
wishes to do something else, it can, but the phrasebook author is 
responsible for ensuring that his mapping is mathematically equivalent to 
the CD writer's one.
James
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