Why is there no conditional statements in the last line of this code?

Question

In the following code you have to write a function to check if a list is sorted or not.

isOrd :: [Int] -> Bool
isOrd [] = True
isOrd [_] = True
isOrd (x:y:xs) = x<=y && isOrd (y:xs)

I would like to know why there is no need to write if/then/else or case for the last line? Why don't we need to check if it's True or False?

Answer 1

What if/then/else would you propose writing? The one I would imagine would look something like this:

isOrd (x:y:xs) = if x<=y && isOrd (y:xs)
                 then True
                 else False

But we know that if x then True else False is always just a particularly long-winded way to write x. So there's not really any need for a specific conditional branch here: we can just return the condition itself.

Answer 2

That is checked by the (&&) :: Bool -> Bool -> Bool function: if the left operand is False, it returns False. If the left operand is True, it returns the right operand.

Indeed, the function is implemented as ^[src]:

(&&)                    :: Bool -> Bool -> Bool
True  && x              =  x
False && _              =  False

It thus will check the first operand, and based on that either return False, or recurse on the rest of the function.