Question

I am trying to understand how to write functions using tail recursion in Haskell. In my example below, the function takes in a list and outputs the maximum value in the list. My intention is to use the c variable to store the current max. I was wondering if someone can explain how using tail recursion would work for this instance?

    myMax [] c = error "max of empty list"
    myMax [x] c = x
    myMax (x:xs) c = 
                if x > myMax xs then c = x
                else myMax xs c

--currently getting a parse error

Answer 1

There are a couple things to think about here. First You don’t want the user to have to enter some beginning value, so we want a function that takes only a list as its parameter. Since you want a tail recursive implementation we do need a function that takes a second parameter though, so we’ll create an inner function named go which takes the current max and the remaining list.

myMax [] = error "Empty List"
myMax (x:xs) = go x xs  -- Initialize current max to head of list.
  where
    -- go takes the current max as the first argument and the remaining list
    -- as the second.
    -- m is the current max, if there are no more elements it is the max.
    go m [] = m 
    -- Otherwise we compare m to the current head.
    -- If the head (y) is greater than m it becomes the current max.
    go m (y:ys) = if m > y then go m ys else go y ys

Note that we never changed the value of any variable here. We update the current max value
by passing it as a parameter to the next step in the function. This is critical to understand in Haskell because mutating variables is not allowed.