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

[Richard Smith]

Don Morrison wrote:

> 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.
>
> Is it equivalent to Iain's recursive algorithm?

I'm fairly convinced that Iain's recursive algorithm, your 
definition above, and my extensions to your original 
definitions (in my post at 04:02 am) are all equivalent. 
The main difference is that Iain's provides something that 
could be coded into a peal prover, your's provides something 
that is very concise but perhaps a bit abstruse, and mine 
provides something that is quite verbose but probably easier 
to understand.

Assuming that multiple non-changing bells besides covers are 
allowed, setting a peal proving program loose on this 
without guidance is a recipe of disaster.  All peals can be 
described in terms of extents on 1 bell with (N-1) 
non-changing bells.

I'm not necessarily using this to argue against allowing 
multiple covers; merely to warn against coding Iain's 
algorithm as the default proving algorithm in a peal prover.

RAS