Ketil Z Malde adds a comment concerning the query of Zhe Fu:
Is there any built-in functions in Haskell to implement diffential operation and partial diffential operation? Or can anyone give me some advices about how to implement them with Haskell? Thanks.
Jerzy Karczmarczuk has some interesting papers on his web site using a different approach to differentiation, maintaining, IIRC, a lazy list of all derivatives of functions. I don't have the URL ready, but a your favorite search engine should be able to help you out.
=== 1. First, I suggest to move this to Haskell-café. I leave the original address, though. 2. My work is about the "Automatic Differentiation" in Haskell. The paper http://users.info.unicaen.fr/~karczma/arpap/diffalg.pdf has been published in HOSC last year. But somebody might get interested in some geometric extensions thereof (differential forms) http://users.info.unicaen.fr/~karczma/arpap/ltforms.pdf Jerzy Karczmarczuk