[om] A Proposal for extending OpenMath with structure sharing

[Richard Fateman]

I assume that JHD mean the interval from -1 to 1  by [-1,1].
Then JHD asserts that if x= [-1,1],  then  x-x is zero, while
[-1,1]- [-1,1]  is [-2,2].  
I think that x-x pretty much has to be [-2,2],  which of course includes
one
value of  0.
Consider the extension of JHD's rule yielding 0:  p(x) where p is a
program
would not be the result of evaluating each operation as an interval
operation,
but the value [a,b] where a= min(p(x),x in [-1,1]), b = max ....
Now this would be very neat, but might not be computable.


The notion of sharing as a data structure does not have relate to
identicality of elements.  Maple shares common subexpressions regardless
of their origin. Mathematica's notion of mapping from names to values
is also peculiar.

This is yet another area in which there is a solution provided in common
lisp,
which has a notation to read and write expressions with
shared or even circular substructure.
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