Ok, I want to be explicit about all possible cases of verb and operand rank
for dyads.
First, if either verb rank is infinite, then no partitioning of the operands
is done: the operands are immediately handed off to the verb for completely
custom processing... true or false?
Next, we have to ask about the cases where both verb ranks are finite. Since
the data ranks will be finite as well, we can have 3 possible relations
between left operand and left verb rank: greater, equal or lessthan.
Likewise for the other verb rank, a total of 9 possible combinations
of comparison.
Stated algebraically, we must know what to do for:
left_operand_rank $LCMP left_verb_rank AND right_operand_rank RCMP
right_verb_rank
where $LCMP and $RCMP are any member of { >, = , < }
Henry's reply covered exactly one of these nine cases:
Henry Rich wrote:
>
> What can be modeled generally is what happens when the operands
> have rank higher than the rank of the verb. In that case, the
> operands are broken into cells, the verb is applied on each cell,
> and the results are padded with framing fills to produce an array.
>
That is the case where $LCMP and $RCMP are both >
I.e.,
left_operand_rank > left_verb_rank AND right_operand_rank > right_verb_rank
and of course the generic action is to break down both operands.
But we must know what to do for the other eight cases.
The table below lists all possible relations between the operands and verb
ranks for dyadic processing. Since I only have data on the case where
left_operand_rank > left_verb_rank AND right_operand_rank > right_verb_rank
I had to guess at the rest and would appreciate feedback on whether I was
correct.
The very first line represents:
left_operand_rank > left_verb_rank AND right_operand_rank >
right_verb_rank
hopefully the rest is self-explanatory.
If the table of combinations does not printout in this post, they exist
here:
http://schemelab.jottit.com/dyadproc
+-----+-----+---------+
| > | > | break |
| | |down |
| | |both |
+-----+-----+---------+
| | = | break |
| | |down |
| | |left |
+-----+-----+---------+
| | < | break|
| | |down left|
+-----+-----+---------+
| = | > |break |
| | |down |
| | |right |
+-----+-----+---------+
| | = | |
+-----+-----+---------+
| | < |break |
| | |down |
| | |right |
+-----+-----+---------+
| < | > |break |
| | |down |
| | |right |
+-----+-----+---------+
| | = | |
+-----+-----+---------+
| | < | |
+-----+-----+---------+
--
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http://www.nabble.com/dyad-verb-processing---take-2-tf4878127s24193.html#a13959534
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