RE: Demystifying Continuations

[Guy Steele - Sun Microsystems Labs <address@hidden>]

   From: "David Simmons" <David.Simmons@smallscript.net>
   Date: Fri, 22 Mar 2002 13:39:37 -0800
   ...
   > But one can define continuations mathematically without resorting to
   the
   > kind of explanation you want.
   > Guy really hit the nail on the head here - as an implementor of a
   certain
   > type of language, you're steeped in ideas like reifiable cloneable
   > contexts, and that's the model that you want to translate
   continuations
   > into.  
   
   Anton,
   
   Perhaps I misunderstood his humor. I thought he was alluding to the fact
   the the terms I used were, in and of themselves, non-trivial concepts.
   Which in turn meant that my using those terms to explain continuations
   was perhaps no simpler or easier to understand than "explanations" I had
   complained about in my original missive.

Okay, I need to 'fess up here.  Indeed, I had originally intended
only this bit of humor about non-trivial concepts.  But I did not
object when Anton managed to extract a deeper meaning from my jest.

   ...   
   All in all, I find myself needing to disagree with you. I take the view
   more of a physicist wanting to know the first principles and build the
   ideas from there. That gives me much more latitude to explore new ideas
   and understand what is possible. It is the same approach that has
   allowed me to build a Smalltalk architecture that was richer than the
   classic Smalltalk-80 designs that had preceded it.

A laudable goal, but let me caution that we, like physicists,
should treat with some skepticism the assumption that one can
find "*the* first principles".  There is always the possibility
that one can find two or more stories or explanations, each of
which can be explained in terms of the others and which
seem equally sinple or low-level, at least for some areas
of application.  Two simple examples from physics:

(a) Which is the more fundamental, the time domain or the
frequency domain?  Given that they are interconvertible through
the Fourier transform, about the best one can say sometimes
is that one or the other is more convenient for some purposes.

(b) Which is the more fundamental concept, mass or momentum?
Think carefully, and be sure to consider both quantum mechanics
and general relativity.

So for computational science.  Which is more fundamental,
procedures or data structures?  Which is more fundamental,
lambda calculus or Turing machines?  You can take either as
a first principle and then derive the other and show their
equivalence.

--Guy