Hal wrote:

# What are s-expressions? Is this symbolic math, as in symbolic
# differentiation and so on?

Once a pun a time, it was an ancient Lisp expressions, parenthetically 
speaking.

Simplistically speaking, think of using something like 

    s-exp = (a (b c) (d (e f (g)))) 

to represent a tree structure. This can be generalized to arbitrary 
directed graphs.

Here is an interesting application 
(http://www.toc.lcs.mit.edu/~rivest/sexp.html):

# S-expressions are a data structure for representing complex data.
# They are a variation on LISP S-expressions. (Lisp was invented by
# John McCarthy). 
# 
# We have adapted S-expressions for use in SDSI and SPKI. The work
# reported here is, however, application-independent. (That is, we
# will use S-expressions in the SPKI/SDSI work, but have developed it
# and presented it in an application-independent manner, so that
# others may most easily consider adopting it for other applications.) 

Conrad Schneiker
(This note is unofficial and subject to improvement without notice.)