Teaching Programming

[Stefan Behnel]

superpollo, 04.05.2010 17:55:
> since i have some kind of computer literacy (as opposed to most of my
> colleagues), some years ago i was kindly asked to try and solve a
> "simple" particular problem, that is to write a program that generates
> math exercises (q+a) from an example taken from the textbook. for
> instance, this:
>
> %%TITLE:Sample worksheet
> %%
> %%SCHEMA:\lim_{x \to <A>}
> %%SCHEMA:\frac
> %%SCHEMA:{x^3-<A-B>x^2-<AB>x}
> %%SCHEMA:{x^3-<A>x^2+<C>x-<AC>}\\
> %%
> %%ANS:FRAC
> %%ANSNUM:<A^2+AB>
> %%ANSDEN:<A^2+C>
> %%
> %%AMIN:1
> %%AINC:1
> %%AMAX:2
> %%BMIN:3
> %%BINC:1
> %%BMAX:4
> %%CMIN:2
> %%CINC:1
> %%CMAX:3
>
> should generate this latex source document:
>
> \documentclass[a4paper,10pt,twocolumn,fleqn]{article}
> \title{Sample worksheet}
> \pagestyle{empty}
> \usepackage[italian]{babel}
> \usepackage{amsmath}
> \usepackage{amssymb}
> \usepackage{cancel}
> \usepackage{mathrsfs}
> \usepackage[dvips]{graphicx}
> \usepackage{eurosym}
> \usepackage{pstricks}
> \usepackage{pst-eucl}
> \usepackage{pst-poly}
> \usepackage{pst-plot}
> \frenchspacing
> \begin{document}
> \section*{\center{\framebox{Sample worksheet}}}
> \noindent
> \begin{enumerate}
> \item
> \begin{multline*}
> \lim_{x \to 1}
> \frac
> {x^3+3x^2-4x}
> {x^3-x^2+2x-2}\\
> \end{multline*}
> \item
> \begin{multline*}
> \lim_{x \to 2}
> \frac
> {x^3+x^2-6x}
> {x^3-2x^2+2x-4}\\
> \end{multline*}
> \item
> \begin{multline*}
> \lim_{x \to 2}
> \frac
> {x^3+2x^2-8x}
> {x^3-2x^2+2x-4}\\
> \end{multline*}
> \item
> \begin{multline*}
> \lim_{x \to 1}
> \frac
> {x^3+2x^2-3x}
> {x^3-x^2+2x-2}\\
> \end{multline*}
> \item
> \begin{multline*}
> \lim_{x \to 1}
> \frac
> {x^3+2x^2-3x}
> {x^3-x^2+3x-3}\\
> \end{multline*}
> \item
> \begin{multline*}
> \lim_{x \to 1}
> \frac
> {x^3+3x^2-4x}
> {x^3-x^2+3x-3}\\
> \end{multline*}
> \item
> \begin{multline*}
> \lim_{x \to 2}
> \frac
> {x^3+x^2-6x}
> {x^3-2x^2+3x-6}\\
> \end{multline*}
> \item
> \begin{multline*}
> \lim_{x \to 2}
> \frac
> {x^3+2x^2-8x}
> {x^3-2x^2+3x-6}\\
> \end{multline*}
> \end{enumerate}
> \subsection*{\center{Answers}}
> \begin{enumerate}
> \item
> \begin{displaymath}
> \frac{5}{3}
> \end{displaymath}
> \item
> \begin{displaymath}
> \frac{5}{3}
 > [...]

I'm not exactly sure I understand the mapping between the two formats, but 
it seems to me that you'll need a proper math expression parser (with a 
strong emphasis on *parser*) for this. Math expressions are not exactly 
trivial (recursion, prefix/infix/postfix notations, functions), which is 
why 'real' programmers don't write parsers for them but download tested, 
working code for that from somewhere.


> another thing is that for some features i intended to include i found
> convenient to use python (since it's the language i feel i am more at
> ease with), so i had to cope with template lines like this:
>
> %%SCHEMA:<PYCODE1:import math ; print int(math.sqrt($A**2-2.*$A*$B))>

You should assure that the math module is always imported, and otherwise 
restrict the expressiveness to expressions (terms that result in a value), 
not arbitrary statements (executable commands that do things without 
returning anything).


> to make a long story short: the whole program is now 4775 lines of bash
> code,

Argh!


> *but* it was and it is a wonderful experience to learn to program

It does sound like you almost completely skipped over two very important 
programming lessons, though: reading code is harder than writing it (i.e. 
maintenance cost matters), and the best code is the code that you don't 
need to write (and debug and maintain).

Stefan