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Re: various recent ll1 threads

   Date: Tue, 28 May 2002 12:26:02 -0400
   X-Authentication-Warning: everest.ascent.com: sundar set sender to sundar@everest using -f
   From: Sundar Narasimhan <sundar@ascent.com>
   To: a.schmolck@gmx.net
   CC: ll1-discuss@ai.mit.edu, Guy.Steele@sun.com
   Subject: Re: various recent ll1 threads
      > Interesting points, but contemplate
      >   / * - 2 3
      >       + 4 1
      >     + 11 3
      > or, with Lisp's parentheses,
      >   (/ (* (- 2 3)
      >         (+ 4 1))
      >      (+ 11 3))
      > In this case each operator tends to be quite close to its children.
      > If all you care about is "separation", then each operator is
      > separated from its first child by zero tokens and from its
      > second child by one token (because you scan horizontally
      > over to the first child, then vertically to the second child,
      > which may be some distance down but there will be no tokens
      > in the way!).
      > This two-dimensional effect is difficult to achoeve with infix.
      This is really interesting -- I've always thought that the main advantage of
      the classical mathematical notation is likely to be that it allows (by virtue
      of its irregularity) to build visually rich two dimensional structures, which
      I assume must be more congenial to the workings of our visual system.
      Although it was clear to me that this advantage doesn't transfer well into
      ASCII, it didn't occur to me that it might actually loose out in this respect
      to prefix (the above example also seems to demonstrate, however, that parens
      are a problem -- the parenless version is definitely easier to read). Which
      brings me onto the next question -- has someone come up with a more visual
      prefix-based notation for math that isn't "flat", has implicit operators
      (e.g. in LaTeX notation ^{2}3 rather than 3^{2}) etc.?
      > Yes, infix may win for small expressions.  Years of experience
      > have convinced me what prefix wins for large expressions.
      > --Guy Steele
   The finished product is easier to contemplate the way Guy has written
   the above of course, but what one needs to 'manipulate' is often
   different from what one needs to express the finished product -- in
   this case the arithmetic expression. Guy, do you realy 'work' in
   prefix while deriving equations like the above? I have never met a
   mathematician who used prefix for their calculations.

On the blackboard, using only + - / * expt sqrt, the answer is "no".
In an Emacs buffer, the answer is "yes", I do often use prefix form
for manipulation and generating expression derivations for proofs.
This may reflect the fact that Emacs has better tools for marking,
deleting, copying, and moving past prefix expressions than for infix
expressions.  I am sufficiently used to reading mathematical expressions
in both infix and Lisp forms that sometimes I don't find myself
consciously distinguishing them.  For example, several weeks ago
someone sent me some email containing the expression "(+ (* b b) (* 4 a c))"
and my mind merely said, "Ah, yes, the quadratic discriminant";
when I re-read the email the next day, I was actually surprised
to see it was in prefix form, because I had "misremembered" its content
as "b*b - 4*a*c".

On the blackboard I use a wild variety of notations,
and often scribble a hodgepodge of Java, Lisp, APL, regular
expressions, and mathematical notation---whatever seems most
convenient at the time.

--Guy Steele