My guess is because irrationals can't be represented on a discrete computer (unless you consider a computaion, the limit of which is the irrational number in question). A single irrational might not just be arbitrarily long, but it may have an _infinite_ length representation! What you have described is arbitrary (not infinite) precision floating point. What IEEE has done is shoehorned in some values that aren't really numbers into their representation (NaN certainly; one could make a convincing argument that +Inf and -Inf aren't numbers). Perhaps it would make more sense to add constructors to the Rational type to represent these additional "values", ie, make Rational look like (edited from section 12.1 of the Report) data (Integral a) => Ratio a = a! :% a! | Nan | PosInf | NegInf deriving(Eq) type Rational = Ratio Integer This has the effect that pattern matching :% when the value is NaN etc. gives an error instead of doing bizarre things (by succeeding against non numeric values). This is an advantage or a disadvantage depending on your viewpoint. Unfortunately, that isn't how its defined in the Report, so it may not be an option. MR K P SCHUPKE wrote:
I would be very careful of adding non-rationals to the Rational type.
Why is there no Irrational class. This would make more sense for Floats and Doubles than the fraction based Rational class. We could also add an implementation of infinite precision irrationals using a pair of Integers for exponent and mantissa.
Keean. _______________________________________________ Glasgow-haskell-users mailing list Glasgow-haskell-users@haskell.org http://www.haskell.org/mailman/listinfo/glasgow-haskell-users