iterate' :: (a -> a) -> a -> [a] I am trying going to go ahead and write my own iterate function. But before I do I want to be clear on types. Looking at :: (a -> a) -> a -> [a] The first part is (a -> a) Now because it is in parentheses it is a function? I can call iterate like this: take 5 $ iterate (*2) 5 So (*2) is a possible function. Does the brackets mean it is a function, the left hand a is indicating a general type and the right hand a means the return type must be the same as the function type. Eg in the case of (*2) the 2 is an Int so the function returns and Int? Is my understanding correct? How could this be better explained? The last bit is easier to understand. a -> [a] meaning a singleton of general type and [a] means a list of same type.