Re: [Caml-list] Why must types be always defined at the top level?

[Brian Hurt <bhurt@spnz.org>]

On Thu, 24 Jun 2004, Xavier Leroy wrote:

> There is a general need to have polymorphic operations that are 1- not
> defined on all instantiations of their types, and 2- can be defined
> differently on different instantiations.  Haskell type classes are an
> example of a *general* mechanism that addresses this need; GCaml's
> "extentional polymorphism" is another.

Ocaml modules are another way to implement this.  Wether it's a "good" way 
or not is open to debate.

> As to whether equality should be defined on floats, there are pros and
> cons.  My standpoint is that it's eventually better to stick to
> established standards (that is, IEEE float arithmetic) rather than try
> to reinvent a wheel likely to be even squarer than these standards.
> Prof. Kahan found it worthwhile to fully define equality over floats;
> I'll abide by his wisdom.

There are legitimate reasons to want floating point equality.  It's 
generally not what you want, but I had an example of needing it in Ocaml 
just the other day.

Basically, I was writting a root finding algorithm by range subdivision.  
Given a function f and a range [a,b] where sign(f(a)) != sign(f(b)),
find the root in that range, the x such that a <= x <= b, and f(x) = 0 (or 
as close as can come).  The function I ended up with was this:

let root_find f a b =
    let rec loop a b fa_is_neg =
        let c = (a +. b) /. 2. in
        if (c = a) || (c = b) then (* note the floating point equality *)
            (* We've bottomed out- pick a or b depending upon if
               f(a) or f(b) is closer to 0. *)
            if (abs_float (f a)) > (abs_float (f b)) then
                a
            else
                b
        else
            let fc_is_neg = ((f c) < 0.) in
            if (fa_is_neg == fc_is_neg) then
                loop c b fc_is_neg
            else
                loop a c fa_is_neg
    in
    loop a b ((f a) < 0.)
;;

Basically, I run the algorithm out until the distance between a and b is 
1ulp, then stop.

-- 
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                                - Gene Spafford 
Brian

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