Re: Neumaier-Pryce proposed decoration system (v03.2)
Vincent, P1788
On 21 Jun 2011, at 09:47, Vincent Lefevre wrote:
> On 2011-06-09 10:03:58 +0100, John Pryce wrote:
>> Herewith, as a position paper, is the current version of the
>> Neumaier-Pryce proposed decoration system, §4.8 of the current draft
>> standard text v03.2.
>
> I've started to look at it, and before going further, I have two
> remarks about (6) and (7).
>
> 1. Concerning the definition of p_{bnd}, I suppose that x is required
> to be non-empty, like in p_{saf}. This is also implied by (8).
>
> 2. There is apparently a contradiction between the definitions (6)
> and the inclusions (7). For instance, (7) implies that:
>
> ein is included in def
>
> But from the definitions, ein contains only pairs (f,x) where x is
> empty and def contains only pairs (f,x) where x is nonempty, so that
> ein and def are disjoint. Since ein is not the empty set, there's a
> contradiction.
I am guilty on both counts. In my current bout of decoration fatigue, I have been rather careless -- waiting for Arnold to come back with his revised proof, I guess.
The inconsistency noted in Item 1 is a typo. However, the two items are related, namely:
- I wanted ein to be up at the *top* of the order. In this case,
it seemed to me, all of bnd, saf and def should allow x to be
empty, so the cure for item 1 is to DELETE "nonempty" from
the p_{saf} and p_{def} definitions, and KEEP it in p_{emp}
and p_{ill}.
- Arnold wants ein at the *bottom*, in which case I think one
must do the opposite, KEEP "nonempty" in p_{bnd}, p_{saf}
and p_{def}, and DELETE it from p_{emp} and p_{ill}.
This view of mine is rather on the basis of intuition. I have been too d-fatigued to check either of these schemes make sense as one follows the proofs leading to the FTDIA.
Vincent, your comments please.
John