This question is primarily aimed at people who are familiar with
Mathematica.

Is there any general purpose computer language (preferably with a
freely available implementation) that is based on the same (or similar)
principles as Mathematica, namely expression evaluation and pattern
matching? I mean a language that would allow for a relatively simple
implementation of the example in section 2.3.14 of the Mathematica book
(http://documents.wolfram.com/mathematica/book/section-2.3.14) and can
also handle large and complicated datasets.

If there is such a language, how does it compare to Mathematica (what
are the main differences and similarities)?

Please be gentle with your answers, as, unlike most people here, I
haven't "officially" studied computer science (I am a physics student).

Szabolcs

Szabolcs wrote:

"Szabolcs" gmail.com> writes:

That level of pattern matching is more part of the algebra system than
a general language. You could look at Prolog or Mozart, or some other
algebra system like Macsyma. Anyway sci.math.symbolic may be a better
place to ask.

In article <1161794321.465694.158300@e3g2000cwe.googlegroups.com>,
"Szabolcs" gmail.com> wrote:

When I taught a symbolic math grad course more than a decade ago, we used
Maple, because the sources were essentially open, and one could write ones
own symbolic routines. Book: Heck, "Introduction to Maple". The Wikipedia
now says that Axiom is open source and for free:

Thanks for all the replies! (I am taking a look at the suggested
languages right now.)

I'm not specifically looking for an algebra system, but for any general
purpose language that has similar capabilities to Mathematica (not in
the terms of built-in functions aimed for doing algebraic computations,
such as Factor or Integrate, but language features: the possibility to
use very general patterns, ReplaceAll, the availability of powerful
list manipulation functions etc.). Probably the example from the
Mathematica book was not a good one because it is mathematically
oriented. I do not aim to solve one specific problem. I'd just like to
experiment with such systems and broaden my knowledge.

Szabolcs

"Szabolcs" gmail.com> writes:

You should read Structure and Interpretation of Computer Programs if
you haven't.

http://mitpress.mit.edu/sicp/

In article <7xslhc44qp.fsf@ruckus.brouhaha.com>, Paul Rubin
<http://phr.cx@NOSPAM.invalid> wrote:

And if one is interested in Prolog style resolution, there is a MiniProlog
that comes with Hugs <http://haskell.org/hugs/>.

Szabolcs wrote:

Just for fun, here's a Prolog implementation of that problem...

integrate(Y+Z, X, A+B) :- integrate(Y,X,A), integrate(Z,X,B).
integrate(C*Y, X, C*A) :- freeQ(C,X), integrate(Y,X,A).
integrate(C,X,C*X) :- freeQ(C,X).
integrate(X,X,X^2).
integrate(X^N,X,X^N1/N1) :- freeQ(N,X), N =\= -1, N1 is N + 1.
integrate(1/(A * X + B),X,log(A*X+B)/A) :- freeQ(A,X),freeQ(B,X).
integrate(exp(A*X+B),X,exp(A*X+B)/A) :- freeQ(A,X), freeQ(B,X).
integrate(E,X,integrate(E,X)).

freeQ(C,X) :- \+ bound(C,X).

Paul Rubin schreef:

See also http://maxima.sourceforge.net/

(beware, the ScienTek-Macsyma-site is currently "owned")

Szabolcs wrote:

No, it's okay.
To be sure, the task should be simple one for any decent functional
language. Let me sketch it in Haskell:

-- we need a type for mathematical expressions