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Re: Discussion on tetrits motion

Dan Zuras Intervals wrote:

I believe a priority mapping, as outlined in my position paper, is
required to overcome this difficulty and integrate the very nice
idea of tetrits into a reliable exception handling mechanism
consistent with Motion 8 semantics. Although I have made a position
paper available, there has not been any discussion about it in the
short time before the current motion.

I'm a little skeptical that we really need to partition decorations
into "most recent operation" vs. "history," but if there turns out
to be a


This, I will grant you, may or may not be useful.

I believe it has diagnostic value but it may not have
value for the sort of branch & bound algorithms that
are favored in interval methods.

It is also something I realized could be cleanly done
only recently.  When I realized that I could split
the evaluation of 'thingy'Sticky from the evaluation
of 'thingy'False, two things became possible.

(1) The separation of which you speak.

(2) The circuit paths needed to evaluate these bits
became independent of one another.



I don't disagree.
This concept does not require the proposed definitions of the current motion, however, and holds true even for the priority mapping idea.
For example, consider a binary operation zz = f(xx,yy). If we have (xx,px) and (yy,py) as operands, where (xx,px) and (yy,py) are decorated intervals comprised of intervals xx, yy and tetrits px, py, respectively, the resulting tetrit of zz must be: 

   inf( inf( px, py ), inf( P(f,xx), P(f,yy) ) ),
where P(f,xx) and P(f,yy) are the respective tetrits for property P of the intervals w.r.t. the function f.
Notice in this example that inf( P(f,xx), P(f,yy) ) is the tetrit ONLY of the current operation!
Also notice, however, that the "sticky" history is a tetrit, i.e., 2-bits, which is the infimum of all tetrits of the operands as well as all new tetrits of the operands w.r.t. the current operation.
I think in the past I have not been clear about this. So I have made a revision of my position paper (attached as a new PDF) which makes this explicit (see, e.g., the new section 2.2). 

I hope this helps.

Nate

Attachment: Tetrits.pdf
Description: Adobe PDF document