On Wed, 4 Mar 2009 01:11:18 -0500, Brian Hurt wrote: > > Try this. Let's reimplement Haskell's Fractional class, in Ocaml, and > then do Newton's method using this new Fractional class. [...] > > module type Fractional = sig > type t > val ( +. ) : t -> t -> t > val ( -. ) : t -> t -> t > val ( *. ) : t -> t -> t > val ( /. ) : t -> t -> t > val fabs : t -> t > (* other functions elided from brevity *) > end;;
Small point: you forgot the comparison functions — they are necessary for Ratio. > [...] once you realize that the definitions of Fractional, > FloatFractional, and RatioFractional all should be in the standard > library (and the latter two should be just called Float and Ratio). Well, they sort of are in the standard library already thanks to Delimited Overloading! http://pa-do.forge.ocamlcore.org/ With it, your code can simply be written as a macro: DEFINE NEWTON(M) = M.( let rec newton epsilon f df x = let x' = x - f x / df x in if abs(x - x') < epsilon then x' else newton epsilon f df x' in newton) let float_newton = NEWTON(Float) let ratio_newton = NEWTON(Ratio) (and with no performance lost at all for those concerned with clock cycles). I have released a new version of Delimited Overloading with that new example (ad-hoc-newton.ml). Enjoy, ChriS _______________________________________________ Caml-list mailing list. Subscription management: http://yquem.inria.fr/cgi-bin/mailman/listinfo/caml-list Archives: http://caml.inria.fr Beginner's list: http://groups.yahoo.com/group/ocaml_beginners Bug reports: http://caml.inria.fr/bin/caml-bugs
