I only just subscribed to this mailing list and I am a complete Haskell newbie, so forgive me if this is too OT. I noticed a recent thread about writing a Mathematica implementation in Haskell. I think this is an excellent idea and would be a great project for a Haskell newbie. I wrote a toy Mathematica implementation in OCaml while I waited to be viva'd for my PhD. It garnered so much interest that Wolfram Research bought it from me for £4,500 and gave me several free copies of Mathematica. Regarding the specific points made: 1. Numerical libraries: you should be able to reuse existing libraries like GMP, BLAS, LAPACK, FFTW and so on. These are often much faster than Mathematica's. For example, FFTW was about 4x faster than Mathematica's FFT the last time I benchmarked it. However, they do not support interval arithmetic. 2. GUI: I would take our existing vector graphics software: http://www.ffconsultancy.com/products/smoke_vector_graphics/ http://www.ffconsultancy.com/products/fsharp_for_visualization/ and rewrite it in Haskell as the foundation. This would far exceed anything that Mathematica has to offer, in part because Mathematica's graphics are still evaluated via the completely generic rewrite engine which is extremely slow. Our code already implements high-performance hardware-accelerated vector graphics and it is probably one of the first things I would consider porting to Haskell (if there is any commercial interest in such a library). 3. The language: the hardest part of reimplementing Mathematica is inferring what it means (there are no formal evaluation semantics). Once you've done that it is just a case of implementing an extensible term rewriter and putting in about 20 core rules. The pattern matcher is well under 100 LOC and you can do various things to make it more efficient. There are two tricks that vastly improve performance of the rewriter: return physically identical results whenever possible, and perform substitution and evaluation at the same time rather than as two separate passes. 4. Libraries: You should have no trouble exceeding the capabilities of Mathematica by pulling in existing libraries. For example, Mathematica provides no wavelet transforms, no time-frequency transforms, no function minimization over an arbitrary number of variables etc. Having worked in numerical computing for many years, I can say that Mathematica is an excellent tool for prototyping and for doing disposable analyses but many people reach for conventional languages when Mathematica's capabilities run dry. You should easily be able to implement a rewriter for the language that is ten times faster and doesn't leak. Incidentally, my implementation of Mathematica in OCaml took four days, and it was one of my first OCaml programs. -- Dr Jon D Harrop, Flying Frog Consultancy Ltd. OCaml for Scientists http://www.ffconsultancy.com/products/ocaml_for_scientists/?e