Haskell (:) and (++) differences

Question

I'm sorry for a question like this. I'm not too sure about the difference of the : and ++ operator in Haskell.

x:y:[] = [x,y]   

also

[x] ++ [y] = [x,y] 

as for the reverse function which arose this question for me,

reverse ::[a]->[a] reverse [] = [] reverse (x:xs) = reverse(xs)++[x] 

Why doesn't the following work?

reversex ::[Int]->[Int] reversex [] = [] reversex (x:xs) = reversex(xs):x:[] 

giving a type error.

Answer 1

The : operator is known as the "cons" operator and is used to prepend a head element to a list. So [] is a list and x:[] is prepending x to the empty list making a the list [x]. If you then cons y:[x] you end up with the list [y, x] which is the same as y:x:[].

The ++ operator is the list concatenation operator which takes two lists as operands and "combine" them into a single list. So if you have the list [x] and the list [y] then you can concatenate them like this: [x]++[y] to get [x, y].

Notice that : takes an element and a list while ++ takes two lists.

As for your code that does not work.

reversex ::[Int]->[Int] reversex [] = [] reversex (x:xs) = reversex(xs):x:[] 

The reverse function evaluates to a list. Since the : operator does not take a list as its first argument then reverse(xs):x is invalid. But reverse(xs)++[x] is valid.