Positive integer type

Question

In many articles about Haskell they say it allows to make some checks during compile time instead of run time. So, I want to implement the simplest check possible - allow a

Answer 1

This—or actually, the similar desire for a type of natural numbers (including 0)—is actually a common complaints about Haskell's numeric class hierarchy, which makes it impossible to provide a really clean solution to this.

Why? Look at the definition of Num:

class (Eq a, Show a) => Num a where
    (+) :: a -> a -> a
    (*) :: a -> a -> a
    (-) :: a -> a -> a
    negate :: a -> a
    abs :: a -> a
    signum :: a -> a
    fromInteger :: Integer -> a

Unless you revert to using error (which is a bad practice), there is no way you can provide definitions for (-), negate and fromInteger.