Wouldn't it make more sense to get at the idea from another direction or
two? One obvious idea is to compare to a rational number:
compareRational :: a -> Rational -> Ordering
Neither this nor Ord can be supported by computable reals, so maybe there
should be a superclass for numbers that can be *approximated by* rationals
to an arbitrary precise degree.
On Wed, Dec 23, 2020, 8:06 PM David Feuer
Perhaps that's the answer, but it seems frankly bizarre to call a class Real if `Real s` actually means that `s` is a subset of the rational numbers.
On Wed, Dec 23, 2020, 8:02 PM Henning Thielemann < lemming@henning-thielemann.de> wrote:
On Wed, 23 Dec 2020, David Feuer wrote:
The Real class has one method: -- | the rational equivalent of its real argument with full precision
toRational :: a -> Rational
This is ... pretty weird. What does "full precision" mean? For integral and floating point types, it's fine. It's not at all meaningful for
1. Computable reals 2. Real algebraic numbers 3. Real numbers expressible in radicals 4. Rational numbers augmented with some extra numbers like pi 5. Geometrically constructable reals 6. Etc.
They cannot have Real instances, then. Right?