On 2007.12.18 21:07:25 -0500, Brad Larsen
Hi there list,
How would one go about creating a new type for a subset of the integers, for (contrived) example just the even integers? I was thinking of making a new type
newtype EvenInt = EvenInt Integer
but the problem with this is that it accepts any integer, even odd ones. So to prevent this, the module does not export the constructor for it---rather, the module exports a function `mkEvenInt' that creates an EvenInt if the given value is acceptable or raises an error otherwise.
What's the right way to do this? Thanks!
Brad Larsen
Well, I've had cause to do this in the past. Before I paste the following code, I'd like to emphasize that I wrote it a while when I was even more new to Haskell; that it compiles but hasn't been tested very much; and that I'm sure there are better ways to do it. What I wanted to do was to define a type for a subset of 'reals' (floats) which are either 0, or positive. The code looks like this:
{- For many equations and results, it is nonsensical to have negative results, > but we don't want to use solely natural numbers because then we lose precision. So we define a PosReal type which tries to define the subset of real numbers which are 0 or positive; this way the type system checks for negative results instead of every other function having conditionals checking for negative input or output. -} newtype PosReal = MakePosReal Float deriving (Show, Eq, Ord)
-- Basic numerical operations on positive reals instance Num PosReal where fromInteger = toPosReal . fromInteger x + y = MakePosReal (fromPosReal x + fromPosReal y) x - y = toPosReal ((fromPosReal x) - (fromPosReal y)) x * y = MakePosReal (fromPosReal x * fromPosReal y) abs x | x >= 0 = x | otherwise = x * (-1) signum x | x >= 0 = 1 | otherwise = (-1)
-- Define division on PosReals instance Fractional PosReal where x / y = toPosReal ((fromPosReal x) / (fromPosReal y)) fromRational x = MakePosReal (fromRational x)
-- Positive reals are truncated at 0 toPosReal :: Float -> PosReal toPosReal x | x < 0 = MakePosReal 0 | otherwise = MakePosReal x fromPosReal :: PosReal -> Float fromPosReal (MakePosReal i) = i
-- Define an instance to allow QuickCheck operations instance Arbitrary PosReal where arbitrary = liftM3 fraction arbitrary arbitrary arbitrary where fraction :: Integer -> Integer -> Integer -> PosReal fraction a b c = fromInteger a + (fromInteger b / (abs (fromInteger c) + 1))
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