Re: Discussion on tetrits motion
Nate & P1788
On 23 Apr 2010, at 21:59, Nate Hayes wrote:
> ...
> But how is a user supposed to know just by looking at the bits (T,F,T) if
> somewhere in the history of computation an operand was evaluated entirely
> vs. partially outside its natural domain?
>
> The proposed mapping appears to be counting on the fact that any function
> evaluated entirely outside its natrual domain will produce {empty}, and that
> this is good enough to start a chain-reaction of (F,F,T) tetrits propagating
> through the result all the way to the end.
>
> However, {empty} can be absorbed by a union operation, in which case the
> tetrit can change back to (T,F,T) state. In this case, the fact that a
> serious domain violation ocurred is lost. With priority mapping the
> decoration (F,F) would propagate all the way to the end.
The context in which I have been thinking of the "domain" (also "continuous") property being used is
- f is a point function defined by an expression F
using elementary functions e_i.
- ff is an interval version of f defined by the
same expression F but using the corresponding
interval versions ee_i of the e_i.
Then, union cannot occur since it is not an allowed elementary function for use within a point function.
Nate, you are interested in branch & bound calculations rather than the Brouwer fixed point ones that I know more about; but wouldn't union() be forbidden in your app, for the same reason?
Not that it is forbidden entirely, but may only be used outside the scope of a ff() calculation that sets "domain" or "continuous" trits/tetrits.
Does this avoid the difficulty?
John