Solutions to Exercises for November 23, 2018

Using the definitions

  iterate f x = x : iterate f (f x)

  tail (_:xs) = xs

  take n xs | n <= 0 || null xs = []
  take n (x:xs) = x : take (n-1) xs
  

The expression take 4 (iterate tail [1..3]) can be evaluated as follows:

  take 4 (iterate tail [1..3])
    = take 4 ([1..3] : iterate tail (tail [1..3]))
    = [1..3] : take 3 (iterate tail (tail [1..3]))
    = [1..3] : take 3 (tail [1..3] : iterate tail (tail (tail [1..3])))
    = [1..3] : tail [1..3] : take 2 (iterate tail (tail (tail [1..3])))
    = [1..3] : [2,3] : take 2 (iterate tail (tail [2,3]))
    = [1..3] : [2,3] : take 2 (tail [2,3] : iterate tail (tail (tail [2,3])))
    = [1..3] : [2,3] : tail [2,3] : take 1 (iterate tail (tail (tail [2,3])))
    = [1..3] : [2,3] : [3] : take 1 (iterate tail (tail [3]))
    = [1..3] : [2,3] : [3] : take 1 (tail [3] : iterate tail (tail (tail [3])))
    = [1..3] : [2,3] : [3] : tail [3] : take 0 (iterate tail (tail (tail [3])))
    = [1..3] : [2,3] : [3] : tail [3] : []
    = [1..3] : [2,3] : [3] : [] : []
    = [[1,2,3],[2,3],[3],[]]
  

Cmd, exec

NL

Calc