On Sun, Jun 28, 2009 at 15:24, Andrew Coppin
I just wrote a small module for dealing with half-integers. (That is, any number I/2 where I is an integer. Note that the set of integers is a subset of this; Wikipedia seems to reserve "half-integer" for such numbers that are *not* integers.)
module HalfInteger where
data HalfInteger i
instance (Eq i) => Eq (HalfInteger i) instance (Ord i) => Ord (HalfInteger i) instance (Integral i) => Show (HalfInteger i) instance (Integral i) => Num (HalfInteger i)
half :: (Num i) => HalfInteger i
fromNum :: (Integral i, RealFrac x) => x -> HalfInteger i toNum :: (Integral i, Fractional x) => HalfInteger i -> x
isInteger :: (Integral i) => HalfInteger i -> Bool
Note carefully that the set of half-integers is *not* closed under multiplication! This means that for certain arguments, there are two reasonable products that could be returned. (E.g., 1/2 * 1/2 = 1/4, so 0 or 1/2 would be a reasonable rounding.) I haven't put a lot of effort into the rounding details of (*) or fromNum; which answer you get is kind of arbitrary. (However, addition and subtraction are exact, and for multiplications where an exact result is possible, you will get that result.)
The Show instance outputs strings such as
fromInteger 5 fromInteger 5 + half fromInteger (-5) - half
depending on the isInteger predicate.
Now, the question is... Is this useful enough to be worth putting on Hackage?
Out of curiosity, what are *you* using it for? Thomas