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?
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