Tetrits, bool_set and "discontinuous" bit

["Nate Hayes" <nh@xxxxxxxxxxxxxxxxx>]

P1788,

An argument was recently made to me, something to the extent:

"Why not just change the tetrit priority ranking value R to 3-R and then
take the supremum of two tetrit values? The domain tetrit will then be
consistent with the discontinuous bit (which uses disjunction)."

The reason not to do this is because the IEEE 1788 definition of a tetrit
will then no longer be compatible with the proposed C++ bool_set standard.

For example, the supremum of two tetrits is:
sup  0  1  2  3
 0   0  1  2  3
 1   1  1  2  3
 2   2  2  2  3
 3   3  3  3  3
but the disjunction of two bool_set values is:
dis  0  1  2  3
 0   0  0  0  0
 1   0  1  2  3
 2   0  2  2  3
 3   0  3  3  3
Only the infimum between two tetrits is the same as the conjunction between
two bool_set values, i.e., in both cases the result is:
i/c  0  1  2  3
 0   0  0  0  0
 1   0  1  1  1
 2   0  1  2  2
 3   0  1  2  3

So if P1788 wishes the following to be true:

   -- The propagation of all decorations shall be handled uniformly, i.e.,
with conjunction/infimum or disjunction/supremum (but not some wild
combination of both)

   -- The IEEE 1788 definition of a tetrit shall be compatible with the
proposed C++ bool_set standard

Then the only choice is to accept the current definition of a tetrit, i.e.,
Motion 18, and standardize "defined and continuous" as opposed to
"discontinuous."

Sincerely,

Nate