uses the ASCII keyboard. It’s completely arbitrary, but it
makes me keep the language small.
BC You speak about the arbitrariness in using the ASCII
keyboard. I heard one feature being described as this:
“When Arthur ran out of punctuation, he used a leading
underscore to denote system primitives.” When I read
that I thought to myself, “That’s a little ridiculous,” but
then I thought of all the goofy punctuation characters we
have in other languages: C uses nearly all of them; many
languages use the balance. And we use them in different
contexts and different ways.
AW Certainly it’s unfamiliar, and people say, “Oh, it looks
like line noise.” But even kids can learn this quickly.
BC Obviously, a point of pride for K is the ability to
phrase things concisely. Is there any length that is too
short, where you’ve actually squeezed too much information out in terms of its readability?
AW Yes, and I expect I cross that boundary a lot. But if
every line has up to seven operations, then I think that’s
manageable. In fact, we can remember seven things.
BC Right. People are able to retain a seven-digit phone
number, but it drops off quickly at eight, nine, ten digits.
AW If you’re Cantonese, then it’s ten. I have a very good
friend, Roger Hui, who implements J. He was born in
Hong Kong but grew up in Edmonton as I did. One day I
asked him, “Roger, do you do math in English or Cantonese?” He smiled at me and said, “I do it in Cantonese
because it’s faster and it’s completely regular.”
BC This raises an interesting question. When I heard
about your early exposure to APL, a part of me wondered if this was like growing up with tonal languages. I
think for most people who do not grow up with a tonal
language, the brain simply cannot hear or express some
of the tone differences because we use tone differently in
nontonal languages. Do you think that your exposure to
this kind of programming at such a young age actually
influenced your thinking at a more nascent level?
AW I think so, and I think that if kids got it even
younger, they would have a bigger advantage. I’ve
noticed over the years that I miss things because I didn’t
start young enough.
BC To ask a slightly broader question, what is the connection between computer language and thought? To
what degree does our choice of how we express software
change the way we think about the problem?
AW I think it does a lot. That was the point of Ken
Iverson’s Turing Award paper, “Notation as a Tool of
Thought.” I did pure mathematics in school, but later I
was a teaching assistant for a graduate course in computer
algorithms. I could see that the professor was getting
killed by the notation. He was trying to express the idea
of different kinds of matrix inner products, saying if you
have a directed graph and you’re looking at connections,
then you write this triple nested loop in Fortran or Algol.
It took him an hour to express it. What he really wanted
to show was that for a connected graph it was an or-dot-and. If it’s a graph of pipe capacities, then maybe it’s a
plus-dot-min. If he’d had APL or K as a notation, he could
have covered that in a few seconds or maybe a minute,
but because of the notation he couldn’t do it.
Another thing I saw that really killed me was in a class
on provability, again, a graduate course where I was grading the students’ work. In the ’70s there was a lot of work
on trying to prove programs correct. In this course the
students had to do binary search and prove with these
provability techniques that they were actually doing
binary search. They handed in these long papers that
were just so well argued, but the programs didn’t work.
I don’t think a single one handled the edge conditions
“If you can find a shorter,
more elegant program that
isn’t much slower than my code,
I want to hear about it.”
correctly. I could read the code and see the mistake, but I
couldn’t read the proofs.
Ken believed that notation should be as high level as
possible because, for example, if matrix product is plus-dot-times, there’s no question about that being correct.
BC By raising the level of abstraction, you make it easier
for things to be correct by inspection.
AW Yes. I have about 1,000 customers around the world
in different banks and hedge funds on the equity side
(where everything’s going fine). I think the ratio of comment to code for them is actually much greater than one.
I never comment anything because I’m always trying to
make it so the code itself is the comment.
BC Do you ever look at your own code and think, “What
the hell was I doing here?”
AW No, I guess I don’t.
BC Wow! I confess that I tend to write comments for my
future self. I know that when I come back to code I’ve