[Haskell-beginners] Further constraining types

[Daniel Fischer]

On Friday 05 August 2011, 04:52:03, Christopher Howard wrote:
> But this means the type of square would have to be changed to
> 
> square :: Int -> Maybe (Positive Int)
> 
> ...which is unacceptable. (I know square will always return an 
> positive integer, not that it might do so!)

As for Int, that's not true:

Prelude> 4000000000^2 :: Int
-2446744073709551616

The square of an Integer will be nonnegative (or kill your process by OOM), 
but to decide whether something could return a (Positive Foo) instead of a 
(Maybe (Positive Foo)), you have to take Foo's semantics into account in 
addition to the abstract mathematical properties of the algorithm.

(Tangential to your point, but nevertheless.)