[om] DefMP elements

[Stephen Braham]

Hi Folks,
	I'd agree with Richard on this one! I think, in the past, that was an 
effort to ensure OM was broad enough to express all mathematical forms 
of discourse. Non-uniqueness of definitions, and recursive properties of 
definitions, are a crucial part of the plain daily realities of 
mathematics, and there have obviously been important discussions in this 
area since the beginning of computer science, let alone computer 
algebra. It may be useful to have some form of warning mechanism to 
CAS-capable engines that they may be handling something "hard", but 
making the world easy isn't good! Or we wouldn't teach students ever 
more-advanced definitions for various concepts.

		Best Wishes from the increasingly spaceflight world,
			Steve


Richard Fateman wrote:

> Why not just say to people defining FMPs that some brain-dead OM
> applications may be unhappy if FMPs are recursive, and so people
> should consider non-recursive ones to be preferred.  I forget
> what FMP stands for, so I may be using the term incorrectly.
> 
> Forbidding recursion seems like a bad idea, and people will
> view it, perhaps correctly, as showing that OM is strictly
> less capable than the systems it is supposed to define.
> 
> In addition to be verbose, complicated, etc.
> 
> RJF
> 
> 
> Professor James Davenport wrote:
> 
>> On Wed, 3 Dec 2003, Bill Naylor wrote:
>>  
>>
>>> 1) Dissallowing self reference during a defining FMP, therefore
>>> dissallowing recursive definition.
>>>   
>>
>> Quite so, in a defining FMP. An evaluating FMP does allow recursive 
>> references. The distinction is made so that a system knows whether the 
>> expansion of the FMP will always terminate, or will only terminate on 
>> concrete nstances (and therefore, if the instance is not concrete, a 
>> fixed-point operator will be required, which is probably beyond the 
>> scope of most OM-capable applications.  
>>
>>> 2) Dissallowing multiple defining FMPs, therefore dissallowing different
>>> but logically equivalent FMPs, e.g. a definition in terms of integrals
>>> versus a definition in terms of recurence relations.
>>>   
>>
>> One could have several FMPs, but the point of the unique defining one 
>> is that the author of the CD is saying that this particular FMP can be 
>> used to eliminate this concept in favour of "simpler" ones.
>> James
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> 
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-- 
Stephen P. Braham			Director, PolyLAB
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