[om] A Proposal for extending OpenMath with structure sharing

[Richard Fateman]

While labels may solve some problems,
I think labels actually open up a can of worms.

1. What is the scope of a label?
2. Unless an XML parser understands them, any
expression using them could be unsyntactic.
or uncheckable.

I think that circular structures could be described
in other ways, just by listing their elements and
say "make a circular list of them"

It is not clear to me if your other points were
objections to lambda notation, implying that this
would require them, or were independent suggestions.
If OM already has summation, integration, universal or
existential quantification, it already has lambda binding and
must address binding order.

I do not see a need for any special notation for
a fixed point operator or, for that matter, evaluation
or assignment  in OM.

If one were to introduce such things, it would make
it possible to (for example) write a lisp
interpreter in it and by extension, your choice
of a number of computer algebra system (Macsyma, Reduce, Axiom,
"mock"MMa).

RJF

Stephen Watt wrote:

> On Thu, Apr 04, 2002 at 04:12:18PM -0800, Richard Fateman wrote:
> 
>>... 
>>My suggestion is to allow syntactic sharing for transmission, but
>>not to make it the way to imply semantic sharing.  Semantic
>>sharing must be done by lambda binding.
>>
> 
> 
> This is not quite as powerful as labels since lambdas alone
> won't represent cyclic objects.
> 
> We additionally would need something like:
>   
>   * a fixed point operator (so we can do Y lambda), or
>   
>   * specify an evaluation order so we can build fixed points from lambdas, e.g.
>     using lambda f.(lambda x.f(xx))(lambda x.f(xx)) and normal order eval, or
>   
>   * assignment (which is what Schemes typically use with lambda to give letrec).
>   
> 
> Labels seem simpler.
> 
> -- Stephen
> --
> om at openmath.org  -  general discussion on OpenMath
> Post public announcements to om-announce at openmath.org
> Automatic list maintenance software at majordomo at openmath.org
> Mail om-owner at openmath.org for assistance with any problems
> 


--
om at openmath.org  -  general discussion on OpenMath
Post public announcements to om-announce at openmath.org
Automatic list maintenance software at majordomo at openmath.org
Mail om-owner at openmath.org for assistance with any problems