On Tuesday, September 2, 2014 12:23:31 PM UTC-7, Joachim Durchholz wrote:
>
> The makers of RUBI insist that no two rules of a rule set can ever apply 
> to the same subexpression. 
> That's draconic, and verifying that would be, erm, "interesting". 
>
> I'm not sure whether that's worth it, but they do have a point if they 
> say it's the only way to be sure that no rule is applied in an 
> unexpected way, which is what I get is the main point behind most of the 
> problems you mentioned. 
> Also, it would force rule writers to investigate into which rule's turf 
> they are breaking, and reconsider whether their addition is actually an 
> improvement over what's already there. 
>
> I can't say what's the best approach, I'm just collecting potentially 
> relevant arguments here and hope somebody has enough breadth of vision 
> to properly weigh them all. 
>

Having tried to use Rubi  (not the latest version) I can attest to the 
problem that
the ruleset as I used it did lots of problems but failed on some of them in
somewhat mysterious ways.  (I think I reported these to Albert Rich).
Here's my suspicion, and it is sort of different from your concern about 
rule independence.
That is, the rules need to terminate -- either each rule must show progress 
towards some goal,
or some collection of them converge (hill-climbing as necessary) towards a 
termination.

Some of these conditions are delicately dependent on particular 
simplifications.

I was running Rubi using the Mathematica-syntax rules, using MockMMA.  The
pattern syntax and semantics are essentially the same as Mathematica, but 
the
forms for (my version of) FullSimplify are different.  I'm not sure how 
much more
of Mathematica beyond what I wrote might actually be necessary to run all of
the Rubi test suite.  I think I kind of gave up after repeated "infinite 
loops"  about
180 examples in to the tests.

RJF

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