Polymorphic and Overloaded Types

We have already touched upon polymorphic types in our triple function when we made it work with both integers and floating-point numbers. We used Num a in the function's type signature to specify that it can accept both number types as arguments. The Num is a class constraint and a is the type variable in our function signature. triple :: Num a => a -> a reads as "for any type a that is an instance of the class Num, the function triple has the type signature a -> a".

Any type that has a class constraint is called an overloaded type, and hence our triple function is an overloaded function. We can even also specify a type variable without the class constraint, in which case that type is completely polymorphic and any type can fill the arguments' place. For example, this is used in several list functions we used earlier, as their results do not depend on the types of elements that fill the lists. For example, the head (which returns the first element of a list) and tail (which returns the list excluding the first element) functions must work regardless of what type the elements in the list are. Therefore, their type signatures are:

head :: [a] -> a
-- a list of type a's returns a type a, whatever type a is for that list

tail :: [a] -> [a]
-- a list of type a's returns a type [a], whatever type a is for that list