Haskell restricting integer values via enumeration

Question

I want to do something like this:

data Bit = 0 | 1

But since the right hand side has to be a valid data constructor (?) I would have to use something like

data Bit = Zero | One

This isn't particularly good since I want to use the actual values 0 and 1. What's the best solution to my conundrum?

Answer 1

You might enjoy this cheeky Num instance I wrote some time ago:

instance Num Bool where
    (+) = (/=)
    (*) = (&&)
    negate = id
    abs = id
    signum = id
    fromInteger = odd

For example, in ghci:

> (3 + 5) * 6 :: Bool
False

You should be able to use something similar, suitably modified to support your data Bit = O | I rather than data Bool = False | True.