In Haskell, is there infinity :: Num a => a?

Question

I\'m trying to implement a data structure where if I had the use of infinity for numerical comparison purposes, it would simply things greatly. Note this isn\'t maxBound/min

Answer 1

Try something like this. However, to get Num operations (like + or -) you will need to define Num instance for Infinitable a type. Just like I've done it for Ord class.

data Infinitable a = Regular a | NegativeInfinity | PositiveInfinity deriving (Eq, Show)

instance Ord a => Ord (Infinitable a) where
    compare NegativeInfinity NegativeInfinity = EQ
    compare PositiveInfinity PositiveInfinity = EQ
    compare NegativeInfinity _ = LT
    compare PositiveInfinity _ = GT
    compare _ PositiveInfinity = LT
    compare _ NegativeInfinity = GT
    compare (Regular x) (Regular y) = compare x y    

main =
    let five = Regular 5
        pinf = PositiveInfinity::Infinitable Integer
        ninf = NegativeInfinity::Infinitable Integer
        results = [(pinf > five), (ninf < pinf), (five > ninf)]
    in
        do putStrLn (show results)

Answer 2

Take a look at my RangedSets library, which does exactly this in a very general way. I defined a "Boundary" type so that a value of type "Boundary a" is always either above or below any given "a". Boundaries can be "AboveAll", "BelowAll", "Above x" and "Below x".