On Wednesday 30 May 2007 07:04:31 Jon Harrop wrote:
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.
Sorry for replying to myself. :-) It occurs to me that laziness will eliminate the intermediate data structure between substitution and evaluation anyway, so that isn't such a concern in Haskell. However, I can't think how you might return physically identical results when possible in Haskell. Essentially, you need a higher-order map function: val id_map : ('a -> 'a) -> 'a t -> 'a t that returns its input when "f x = x" for every x. How might this be done? -- Dr Jon D Harrop, Flying Frog Consultancy Ltd. OCaml for Scientists http://www.ffconsultancy.com/products/ocaml_for_scientists/?e