Re: The foundations of programming language theory

Xah Lee wrote:
[a lot]

Searching for some sense in what Xah Lee is saying (yeah, I know I
shouldn't do that...), it is certainly true that the design of languages
used for ordinary programming tasks doesn't much resemble mathematics.
This should not lead you to conclude that mathematical foundations are
useless in programming languages. It should lead to the recognition
that, in essence, there are many levels of working on programming
languages.

At some level (e.g., System F and other such languages), work in
programming languages is very tangibly a mathematics subject, and is
done by mathematicians (regardless of whether they happen to belong to
mathematics or computer science departments in their universities).
These completely theoretical languages then leak ideas and abstractions
into more concrete languages (say, Haskell and ML), which are actually
used by real people for purposes other than proving theorems about the
properties of themselves. At that point, you start seeing choices based
on far less mathematical ideas. Then ideas or concepts that thrive
there move to the mass market languages, where they are subjected to the
throes of uninformed public opinion, and it's basically a roll of the
dice to see what happens.

So if your goal is to create the next Java, then perhaps Mr. Lee is
correct; you shouldn't worry about math, other than to read about the
applications of that math in programming languages one layer back in
order to steal those ideas you need to build a compiler and related tool
set. And you should perhaps take an internship in an advertising firm.
But if you want to live a few layers in, then you're on the right track
in terms of looking at the fields mentioned in this thread.

--
Chris Smith
.

Relevant Pages

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