{-
Equational reasoning:

sum [1..5]
== expand .. 
sum [1,2,3,4,5]
== expand sum
1 + 2 + 3 + 4 + 5
== def of +
15

-}

{-
Wrong version:

N = a ’div’ length xs
    where
       a = 10
      xs = [1,2,3,4,5]

-}

n = a `div` length xs
    where
       a = 10
       xs = [1,2,3,4,5]

-- Define the function last using the combinators introduced in the lecture

last' xs = head (reverse xs)

last'' xs = head (drop (length xs - 1) xs)

last''' xs = xs !! (length xs - 1)

-- All other interactive examples are covered in the slides!