Yet to me, literate programming is certainly the most important thing
that came out of the TeX project. Not only has it enabled me to write
and maintain programs faster and more reliably than ever before, and
been one of my greatest sources of joy since the 1980s -- it has
actually been indispensable at times. Some of my major programs, such
as the MMIX meta-simulator, could not have been written with any other
methodology that I've ever heard of. The complexity was simply too
daunting for my limited brain to handle; without literate programming,
the whole enterprise would have flopped miserably.
If people discover nice ways to use the newfangled multithreaded
machines, I would expect the discovery to come from people who
routinely use literate programming. Literate programming is what you
need to rise above the ordinary level of achievement.
I believe that Axiom's complexity is large enough to demand literate
programming. There are several reasons.
First, computational mathematics requires people to be exceptional at
mathematics and programming. This is a small subset of already small
sets. We might as well add another subset of those who can communicate
their ideas in writing.
Second, there are many design decisions that are necessary to reduce
a mathematical idea to implementation. Some of these design decisions
are mathematically arbitrary (e.g. branch cuts) or computationally
arbitrary (e.g. sparse versus dense) or programatically arbitrary
(e.g. all Spad versus Spad-and-lisp). These design decisions need to
be documented so people who maintain and modify the program know why
the decisions were made. Without this knowledge it would be trivial
to accidently destroy important optimizations.
Third, nobody is an expert in the range of mathematics that Axiom can
and will implement. It is important to present some portions of the
theory associated with domains so people have a clue about the ideas
being encoded. Imagine what would happen if all of the math textbooks
only contained equations but no human-readable text. You might be able
to "read" a calculus textbook but not an infinite group theory textbook.
Fourth, a million line program is too large to put into your head. You
need to have some background on the data structures, control flow, any
special tricks (e.g. funcalls through the symbol-plist), database
design, communication protocols (e.g. between Axiom and Hyperdoc and
Graphics), parsing structures, and a million other details. At best,
the code tells you HOW it does something but not WHY, not what it
depends on, not what depends on it, etc.
Fifth, a program this large and this long-lived will eventually no
longer have the authors around to ask questions. Several of the Axiom
authors are already dead and most are not associated with it anymore.
Some of those authors are the world's expert in their subject matter.
That is a steep hill to climb if you want to understand the code,
especially if you have to debug or modify it.
Sixth, in the 30 year horizon view, we need to pursue a new level of
excellence. As Knuth said:
"Literate programming is what you need to rise above
the ordinary level of achievement"
For all these reasons, and more, Axiom needs to be literate.
Tim Daly
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