[om] semantics of structure sharing

[Andreas Strotmann]

Sorry to talk about this again, but I can't get this problem out of my
head.

I'm beginning to think that "semantic sharing" via label/ref mechanisms
may actually be quite different from a lambda binding mechanism.  Here's
why.

Let's say we have an OpenMath object which represents something like
random().  A decent candidate might be

 OMA(choice, OMA(random_distribution, [-1,1], uniform))

The meaning of this expression is "an application of the choice function
to a uniform random distibution over the interval [-1,1]".

Semantic sharing would mean that the meanings of shared objects are the
same, but in this case the meaning that is shared is that of "a choice of
a random number from a uniform distribution" -- there is nothing in this
interpretation that says it must be the same choice, or is there???  The
shared meaning says "a choice", right?

By contrast, a lambda binding of the above expression to a variable means
"the result of choosing a random number from this distribution", and
references to that variable refer to the same result, which is the same
number.

So, am I right in thinking that lambda binding adds "the result of" to the
meaning, and thus changes it in such a way that lambda binding is
different from "sharing"?

 -- Andreas

______________________________________________________________
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