Haskell无法构造无限类型：a0 = [a0]

Question

I am attempting to solve the second problem on Project Euler using Haskell. The problem is fairly straight forward - sum the even fibonacci numbers less then 4000000. (Me being OCD, I'm implimenting a slightly modified function - one which allows an arbitraty limit).

My initial code was:

euler2 limit (num1:num2) 
    |(num1>limit) = 0
    |((num2>limit) && ((mod num1 2) == 0)) = num1
    |(num2>limit) = 0
    |(((mod num1 2) == 0) && ((mod num2 2) == 0)) = num1+num2+(euler2 limit [num1+num2,num1+num2+num2])
    |((mod num1 2) == 0) = num1+(euler2 limit [num1+num2,num1+num2+num2])
    |((mod num2 2) == 0) = num2+(euler2 limit [num1+num2,num1+num2+num2])
    |otherwise = euler2 limit [num1+num2,num1+num2+num2]
euler2 limit [] = euler2 limit [1,2]

Which produced the following error:

Occurs check: cannot construct the infinite type: a0 = [a0]
In the second argument of `(>)', namely `limit'
In the first argument of `(&&)', namely `(num2 > limit)'
In the expression: ((num2 > limit) && ((mod num1 2) == 0))

Now through some trial and error, I have realized that it is attempting to typecast num2 as a list, and this small change:

euler2 limit (num1:num2:[]) | (num1 > limit) = 0

fixes the problem. My question is why? What is going on and why was it refusing to cast num1 and num2 as Ints?

Answer 1

The type of (:) is

(:) :: a -> [a] -> [a]

If you have a pattern match

euler2 limit (num1:num2)

the names num1 and num2 are bound to the corresponding arguments of the constructor (:) (if the supplied argument is a nonempty list), thus num2 is a list whose elements have the type of num1 .

If you match on

(num1:num2:[])

that is implicitly parenthesized

(num1 : (num2 : []))

and now num2 : [] is matched with the list that is the second argument of the top-level (:) , and that match succeeds, binding num2 to the second list element, if the supplied argument is a list with exactly two elements.