Lab 2. High 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).

Create a new Scala worksheet to write your solutions

2.1.1 Write a function apply that takes an integer and return the result of the applied function on the given integer. Start from the code stub below:

def apply(n: Int, f: Int => Int): Int = {
   ???
}

2.1.2 Write a function doubler that returns a function that doubles the input it receives (an integer). Start from the code stub below:

def doubler(): Int => Int = {
   ???
}

2.2.1 Define the function foldWith 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 to 3 will be 1+2+3=6. foldWith 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  = ???
  ??
}

2.2.2 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 = ???

2.2.3 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)$ . Use the apply and foldWith methods

def foldMap(op: (Int,Int) => Int, f: Int => Int)(start: Int, stop: Int): Int = ???

2.3.1 Modify the function below so that it's curry and use it to calculate 5*3

def multiply(x:Int, y:Int): Int => x * y

2.3.2 Modify the function below so that it's curry and use it to compare 3 numbers and return the maximum

def compare(x: Int, y: Int, z: Int): Int =
{
  if x > y && x > z then 
    x
  else if y > x && y > z then
    y
  else
    z
}

The graph of a function can undergo different geometric transformation such as scaling, shifting, rotating, mirroring and so on. The result of those transformation will also be a function that looks similarly to the original. In this exercice we will particularly work with lines. A line is a linear equation of the form $ f(x) = a*x + b$

2.4.1 Implement a function that shifts a line on Oy axis by a certain amount $ \Delta y$

def shiftOY(line: Double => Double, delta_y: Double): Double => Double = {
   ???
}

2.4.2 Implement a function that shifts a line on Ox axis by a certain amount $ \Delta x$

def shiftOX(line: Double => Double, delta_x: Double): Double => Double = {
   ???
}

2.4.3 Implement a function that checks if two lines intersect at an integer value from a given interval

def intersect(line1: Double => Double, line2: Double => Double)(start: Int, stop: Int): Boolean = {
   ???
}