3. Higher-order functions

Objectives:

• implement and use higher-order functions. A higher-order function takes other functions as parameter or returns them
• implement curry and uncurry functions, and how they should be properly used (review lecture).

3.1. Define the function foldRange which uses an operation op to reduce a range of integers to a value. For instance, given that op is addition (+), the result of folding the range 1, 3 will be 6. foldRange should be curried (it will take the operation and return another function which expects the bounds).

def foldWith (op: (Int,Int) => Int)(start: Int, stop: Int): Int = {
  def tail_fold(crt: Int, acc: Int): Int  = ???
  ??
}

3.2. Define the function foldConditional which extends foldWith by also adding a predicate p: Int ⇒ Int. foldConditional will reduce only those elements of a range which satisfy the predicate.

def foldConditional(op: (Int,Int) => Int, p: Int => Boolean)(start: Int, stop: Int): Int = ???

3.3. (!) Let $ count_k(n) = k + 2k + 3k + \ldots x*k$ , with $ x*k \leq n$ be the sum of all multiples of $ k$ within the range 1,n. Write a function alldivs which computes the sum: $ count_1(n) + count_2(n) + \ldots + count_k(n)$ . (Hint, use foldConditional).

def alldivs(n: Int): Int = ???

3.4. Write a function foldMap which takes values $ a_1, a_2, \ldots, a_k$ from a range and computes $ f(a_1)\;op\;f(a_2) op \ldots f(a_k)$ .