Using Haskell's types to replace assert statements or if checks in other languages

Question

Sorry if the question is very elementary, I am still very new to Haskell. Lets say I have a function that can only work with two numbers that are in the golden ration (1.618), h

Answer 1

The best you can do practically is a run-time check. There could be some type-level calculus I don't know (see luqui's comment), but that's not pratical in Haskell.

You could use an assert, which is what you want to replace,

checker :: a -> b -> Bool
checker x y = x * 1.618 `approxEqual` y

unsafeMyfun :: a -> b -> c
unsafeMyfun x y = assert (checker x y) (doRealThingWith a b)

or return a Maybe a (or Either err a) to avoid exceptions which cannot be caught in pure functions,

myfun :: a -> b -> Maybe c
myfun x y = do
              guard $ checker x y
              return $ doRealThingWith x y

or use a custom contract type as in Tom's answer etc. In any way, it's not possible to check the constraint in compile time. In fact, due to the IO monad, any compile-time constraint cannot be precise.