I'm looking for simple examples of using TeX as a programming language, not LaTeX, and ideally these examples only use the primitive TeX commands. Why? Because the members of a local computer club take turns talking about offbeat languages, and it will be my turn soon. The audience ranges from programming neophytes to people with a sophisticated understanding of computer science. I'm trying to come up with examples that everyone can understand, and that also demonstrate how TeX "works."
I'm aware of a few examples along these lines, not all of which are as primitive as I would like:
Count the number of elements of each size in a list
Position of largest element in a list
Count number of elements in a list
Find the number of elements in a list that occurs most often
Macros with binary trees as arguments
How to produce a list of prime numbers in LaTeX
How to make the last word in a sequence the first
\rand inside \forloop creates identical values
Stack datastructure using LaTeX
Delete and element from a comma delimited list
As long as we're making a list, it's worth including things on the fun/crazy end of the spectrum too. I'm aware of:
BaSiX -- An Interpreter Written in TeX
Lists in TeX's Mouth (lambda calculus in TeX)
An AVR Emulator written in pure LaTeX
Finally, are there certain design patterns or paradigms that are particular to TeX (or macro-based languages in general)? Other languages have things like lambdas, or they may be strongly, weakly, dynamically or statically typed. Some languages lean on encapsulation or being object-oriented, and there's a whole universe of design patterns that fall under the umbrella of "object-oriented." TeX seems to be off in its own world.
\foois replaced by it's definition at point-of-use), and expansion (i.e. that some things work by expansion, others by execution, and we sometimes need to keep everything in the input stack to work expandably).