Work Note 18, DM509, fall 2008

Exercises December 12

• [H07] exercises 10.1, 10.2, 10.3, 10.4, 12.1, 12.2, 12.3, 12.4, 12.5.
• Continue exercise 12.5 by also computing the index of the first Fibonacci number greater than 1000.
• Using the type definition

  data Tree a = Leaf a | Node (Tree a) a (Tree a)

  define a function

  depths :: Tree a -> [Int]

  that computes the number of nodes at each level in the tree, i.e., depth with argument

  Node (Leaf 1) 2 (Node (Leaf 3) 4 (Leaf 5))

  should return [1, 2, 2].
• A twin prime is a pair of primes, the values of which differ by two, e.g., (17,19) is a twin prime. Use primes from the book to define the infinite list of all twin primes.