[r-t] Another straw man definition of "true"

[Don Morrison]

How does the following work?

  A touch is called true if there exists a partition of the rows it
  contains into sets A0, A1, ... An such that (i) all the rows contained
  within any Ai are of the same stage, Si, with the same non-changing
  bells, and (ii) all the rows in A0 are distinct, and (iii) for i>0 all
  the Ai are extents on Si bells.

I think it subsumes everything that's legal today, and at the same
time provides a definition applicable to arbitrary mixtures of stages
with with arbitrarily many covering or otherwise non-changing bells.

Is it equivalent to Iain's recursive algorithm? It's similar, but I'm
not convinced it's equivalent.

If it really works and captures an appropriate meaning of "true" it
has the virtues of being succinct, universally applicable, and not
special-case-y.

It has the liability of being non-constructive. There is an obvious,
guaranteed to work algorithm for finite numbers of bells which is all
we really care about, but that obvious algorithm is far from
efficient. On the other hand, I think an efficient algorithm could be
easily devised.

The big liability of its non-constructiveness is that it makes it a
bit obscure for the average ringer to follow (obviously, since I'm not
convinced I follow it correctly myself yet, and am looking for
feedback as to whether I've gone off the deep end!).

However, it does have the virtue that the common cases are easy. The
definition flows naturally from the structure of the common cases.
It's only someone wanting to do something subtle and obscure that
needs to do something subtle and obscure to demonstrate the truth of
what they're doing!



-- 
Don Morrison <dfm at ringing.org>
"[Shakey] was the sort of robot a philosopher could admire, a sort
of rolling argument."     -- Daniel Dennett, _Consciousness Explained_