I want to be able to create a function to see if two types are equal. I have a type class called finite defined as follows,
class (Bounded a, Enum a) => Finite a
and want to be able to write a equality comparison function
equals :: (Finite a, Eq b) => (a -> b) -> (a -> b) -> Bool
for functions who's domain is of type Finite. For example, for a negation function:
neg :: Int8 -> Int8
neg n = -n
the return in the Main would be:
*Main> equals neg (\x -> x)
False
Basically what you need is to enumerate over all possible values for a, and check if the two functions produce the same result.
You can generate a list of all the items with [minBound ..], and you can use all :: Foldable f => (a -> Bool) -> f a -> Bool to check if for all items a certain predicate is satisfied.
You thus can implement such function with:
equals :: (Finite a, Eq b) => (a -> b) -> (a -> b) -> Bool
equals = all (…) [minBound ..]where I leave implementing the … part as an exercise. It should call f and g with the element of the list, and return True if and only if the two functions produce the same result.
[minBound], there are two dots, that is not an exercise, but simply a way to create a range list, so [minBound ..] :: Char will construct a list of all possible Characters.\x -> ... where x is an item from the list, and you need to map it to a bool that is true if both functions f and g produce the same resultmap is not a keyword: map is simply a function exported from the Prelude. The all will call the lambda-expression for all elements (or until it finds one item for which the lambda-expression returns False).