Terrence wrote:
> Yes, and they all say _what_ the verb does with absolutely
> no info on _where_ the result is taking place.
If you mean by this that the DoJ doesn't identify the C code that implements
this general rule, then you are right. The DoJ tries quite hard to divorce
specification from implementation. This is what makes your Scheme
implementation possible.
But if you mean the Dictionary doesn't define the general rule for padding
and fill, you are wrong. I know exactly what this rule is and where it is
specified. In fact, if you'd done the experiment I outlined in an earlier
message, taking the specifications of $ and ,: and > and seeking a
language intersection that accounts for this filling, then you would too (as
a side effect of the experiment, not a direct result).
So if I know what the rule is, and where it is specified, why didn't I just
send a link? Why would I recommend you experiment instead?
As you can probably tell from my posting history and our previous
discussions, I am personally interested in the theory of J. I like to know
the rules as specified, not derived. I like playing around in the
Dictionary. I even have a script dedicated to quoting precise parts of the
documentation. Why wouldn't I use it for you?
The short answer is because I have, before. In fact, I've sent you a link
to the very section you need right now. You've read it. I quote the
Dictionary at you, and you say it's unreadable.
When I started J, I thought the same thing. I publicly complained about it.
But now I say I like to play around in the Dictionary. What changed?
Well, it wasn't the Dictionary. I acquired an intuition for J through
experience. I played around, I experimented. I broke stuff. All those
obscure bugs you see I report? That's the result of "hey, what if...."
It is only my opinion, but I think you need to do the same thing. I
perceive repetition in your questions. You ask the same questions in
different contexts. I think that's merely because you haven't had enough
exposure. Once you see the same behavior in different contexts, you may
start thinking there's a general rule to cover it.
> Did you say *where* the filling occurs (i.e., in the verb's code
> or in the general dyad processing code)?
Here're some more examples:
A =: (1 2 $ 9)"_
B =: (3 4 $ 9)"_
A`B\ 'xx' NB. Try \. too.
A`B;.1 'xx' NB. Try _1 2 _2 too.
A`B`:0 'xx' NB. Try other y
These experiments demonstrate conclusively that it's not in the verb's code
or the general dyad processing code. But they won't tell you where to put
it in your Scheme reimplementation, either.
> No - in fact you couldn't because you used a verb with infinite rank for
> both arguments and no
> rationing occurred.
Alright, here's a more relevant experiment, then:
x =: 1 2 ,: _
y =: 3 4 $ 9
F =. <;.0"$ NB. Same ranks as $
G =. ];.0"$
x F y
+---+-------+
|9 9|9 9 9 9|
| |9 9 9 9|
| |9 9 9 9|
+---+-------+
x G y
9 9 0 0
0 0 0 0
0 0 0 0
9 9 9 9
9 9 9 9
9 9 9 9
Can this teach us anything? What is responsible for the fill in G ? What
is the difference between F and G ? Can the difference alone account
for the fill (not its motivation, but its definition)? Which primitive in
the definition of F specifies how the fill will work?
> The subject was specific and limited to partially infinite dyads.
That's missing the forest for the trees again. That's what I was trying to
make clear when I suggested that you do some experiments. Obviously that
wasn't clear. Sorry.
> Why would you provide different inputs to get the same outputs and
> consider
> that as proof that the internal processing is the same?
I thought that you understood the inputs were the same. You even pointed
out, in your original message:
> Shape will be called with 1 2 $ 9 and 3 4 $ 9 and the results are then
> filled....
Now, regarding induction: of course I could demonstrate any number of these
identical fillings and it wouldn't prove there is a general rule (except for
the intersection-of-specifications experiment). Even if we concluded with
some confidence there was such a rule, these experiments wouldn't tell us
what the rule was. We'd need different experiments to give us, again with
some confidence, a working definition.
My purpose wasn't to show you how to derive the rule, but to show you how to
exclude certain possibilities. How to cull your set of potential
explanations. I wanted to show you that your premise that fill had
something to do with "partially infinite dyads" was incorrect, and to pursue
a line of thinking that might lead you to a different conclusion.
> 2 + 2 = 4
> 1 * 4 = 4
Here's a fun though experiment wrt induction vs deduction:
(A) All men are mortal.
(B) Socrates is a man.
(C) Hence, Socrates is mortal.
This is a classic example of deduction. That is, if we know all men are
mortal is true. How do we know all men are mortal is true?
-Dan
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