Higher order functions

Higher order functions return functions as a result

def sumInts(a: Int, b: Int): Int =
if (a > b) 0 else a + sumInts(a + 1, b)

• Higher order functions also take other functions as parameters

def sum(f: Int => Int, a: Int, b: Int): Int =
if (a > b) 0
else f(a) + sum(f, a + 1, b)

def cube(x: Int): Int = x * x * x

We can write:

def sumInts(a: Int, b: Int) = sum(id, a, b)

Function types

Type A => B is the type of a function that takes an argument of type A and returns a result of type B

Anonymous functions

Anonymous functions are functions without names

(x: Int, y: Int) => x + y

(x: Int, y: Int) is the parameter of the function, and x + y is its body.

The type of the parameter can be omitted

Examples

Ex1: Write a function that takes the product of all the integers on a given interval

def productInts(a: Int, b: Int): Int = 
if (a > b) 1 
else a * productInts(a + 1, b) 

productInts(1, 4)

Ex2: Write a function that takes the product of the factorials of all the integers  on a given interval

def fact(x: Int): Int = 
 if (x == 0) 1 
 else x * fact(x - 1)

def productFactorials(a: Int, b: Int): Int =
 if (a > b) 1 
 else fact(a) * productFactorials(a + 1, b)

productFactorials(2, 3)

Ex3: Write a general function which generalizes both sum and product

def mapReduce(f: Int => Int, compose: (Int, Int) => Int, zero: Int, a: Int, b: Int): Int = {
 if(a > b) zero
 else compose(f(a), mapReduce(f, compose, zero, a + 1, b))
}

def sumCubes(a: Int, b: Int): Int = mapReduce(cube, sum, 0, a, b)

def cube(x: Int): Int = x * x * x

def sum(x: Int, y: Int): Int = x + y

def product(x: Int, y: Int): Int = x * y

sumCubes(2, 3)