[Haskell-cafe] Mathematica

[Dan Piponi]

There are two aspects to mathematica. There's the core language and
there is the library of functions made available to the user. The
library is many lifetimes of work so don't even think about doing more
than a fraction of a percent of it on your own! The core language is
more straightforward but it still has a fairly sophisticated
backtracking pattern matcher. To get the core language working you
need to implement at least some algebra - for example the pattern
matcher understands commutativity, associativity and the notion of an
identity for a binary function.

Many years ago I implemented a useful subset of the core language
myself using C and stack based continuation abuse for the
backtracking. (Good enough to be able to type in lots of standard
integrals from Abramowitz and Stegun and combine them with the all the
standard high school techniques for integration.) It took several
months of hacking in my spare time to get it working (back in the days
when I had a lot of spare time). I expect that in Haskell it would be
much easier, especially using a suitable non-determinism monad for the
pattern matching. The pattern matcher was probably the largest
component of the work.

Haskell has some great features that Mathematica doesn't and it'd be
nice to see those features in an algebra package. In particular: lazy
evaluation and static types. I'd probably also want dependent types.
Aldor/Axiom does the types part already.
--
Dan

On 5/11/07, Andrew Coppin <andrewcoppin at btinternet.com> wrote:
> Hi folks.
>
> How difficult would it be to implement Mathematica in Haskell?
>
> I mean, I really like Mathematica, but it costs over £2,000. I can't
> really afford to pay that much for something that's only really a "toy".
> (It's not like a *need* it for anything, I just like playing with it.)
>
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