Rational sequence

Ferenc Wagner wferi@afavant.elte.hu
Tue, 22 Oct 2002 14:07:27 +0200

"Simon Peyton-Jones" <simonpj@microsoft.com> writes:

> The Report says that the Enum instance for Ratio uses the
> same rule as for Float/Double,

Now I can see that the revised Report contains more about
this than the one on haskell.org.  But I still can't see the
statement you cited above.  Where should I look?

On the other hand, I found that 'the instance for Ratio t
simply "lifts" the corresponding operations over t.'  What
does this mean with respect to Enum?

> namely that [a..b] means takeWhile (<= (b+1/2)) [a, a+1,
> a+2, ...]
> You may say that the "<=" should be "<" but that's what
> the Report says.

Well, neither makes more sense to me.  For an imprecise type
I don't expect precise behaviour.

> I'm not sure what your rule should be, though.  (What
> about [2%4, ...  20%4]?)

Rationals are represented precisely, so that well defined
precise mathematical rules apply to them:

[2%4..20%4] == [1%2..10%2] == [1%2,3%2,5%2,7%2,9%2],

that's to say

[a..b] = takeWhile (<= b) [a, a+1, a+2, ...]

Those fuzzy 1/2-s are inserted solely to 'overcome' the
imprecise floating point representation, and make 'simple
stupid' programs work and programming newbies happy, aren't
they?  For serious work they don't count, only create one
more peculiarity to observe.  Please correct me if I'm

And please don't feel offended, I suppose that our opinions
differ on this point, as shown by a previous thread.  Still
I don't think things like this promote Haskell, or make it
more acceptable for anyone.

> Anyway, it's a bit late to change the Report

As I told above, I can't see anything to change, except
implementation.  If it's only my stupidity, then sorry for
the nitpicking.