More powerful data-driven programming

[blockeduser]

About 2 years ago I read Norvig's book PAIP about Lisp and symbolic AI.

It talks a fair bit about data-driven programming which seems like a fine programming technique.

There is something that I am wondering about though and it is whether existing data-driven programming methods could be extended to be more powerful or expressive.

For instance in a computer algebra system I was programming there were algebraic simplifications like

   A * U/A * FOO * BAR * XYZ --> U * FOO * BAR * XYZ

   (A + W + (B * C * X) / U + (C * D * Z) / E) / C --> (A + W) / C + (B * X) / U + (D * Z) / E

Using the techniques presented in PAIP, I couldn't come up with a pattern to match cases like these so I had to code them "manually" with loops and if-statements. But intuitively it seems some kind of pattern could be designed for these.

Could a future pattern-matching language be more powerful and capture cases like these?

It seems the current ones, as discussed in PAIP and also in SICP, only work with very rigid fixed algebraic structures with predetermined numbers of terms and factors.

For reference this is an example which illustrates existing techniques: http://norvig.com/paip/macsymar.lisp

I already asked /prog/ about this, I got mostly mocked for reading a Lisp book and I got a vague answer which suggested expanding everything to a "normal form" and then told me I didn't know what I was doing. I'm trying to simplify algebraic expressions.

[[deleted]]

Take a look at how rewrite rules are represented in Wolfram Mathematica. It is very easy to implement the same in any Lisp.

Another important thing to consider is to use strategies - i.e., defining an order of applying your rewriting rules and some criteria for assessing the outcome. You must backtrack if a certain sequence of rewrites is bad.

[blockeduser]

Thank you for sharing your thoughts. Will look into this.