[om] A Proposal for extending OpenMath with structure sharing
fateman at cs.berkeley.edu
Fri Apr 5 18:41:27 CEST 2002
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.
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,
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
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