Introduction to Functional Programming with Scheme (Part 1)

Scheme is a multi-paradigm language, developed in the 1970s by Guy L. Steele and Gerald Jay Sussman. Scheme is a minimal dialect of the LISP family, and although it supports both functional and procedural paradigms, Scheme is mainly functional. It is a language that is built with the purpose of learning about the core concepts of programming languages.

Procedural programming focuses on statements

Functional programming focuses on expressions

Expressions have values. A functional program is an expression who’s value is a sequence of instructions for the computer to carry out.

Statements don’t have values and instead modify the state of some conceptual machine.


In this tutorial we will learn a dialect of Scheme called Racket.

To follow along, feel free to download DrRacket, the IDE of Racket. I will proceed to call Scheme and Racket terms interchangeably.


In programming languages such as C, Java and others, the procedure call is f(x,y)

In Scheme the equivalent is (f x y)

The basic primitives of Scheme are:

  • Booleans: #t, #f
  • Characters: #\a, #\B
  • Numbers: 123, 1.23e+10, 3/4
  • Vectors: #( 1 2 3 4 5)
  • Strings: “Hello world!”
  • Symbols: symbol-a, symbol-b
  • Pairs: (x . z)
  • Lists: (1 2 3 4 5)

To write comments we use ;

Writing our first procedure

+ is a built-in procedure, hence, to add two numbers we can call (+ 1 2) which yields the expression 3

We can create our own procedure that adds two to a number

#lang racket

(lambda (x) (+ x 2))
; Output => #<procedure>Code language: PHP (php)

Now this lambda is an anonymous function that we can use directly instead of the above +

#lang racket

((lambda (x) (+ x 2)) 1) 
; Output => 3Code language: PHP (php)

We can do better, we can store the lambda in a variable:

#lang racket

(define add2
  (lambda (x) (+ x 2)))
;And then we can reference it
(add2 1)
; Output => 3Code language: PHP (php)

Lets make a define a procedure the calculate the cube of a number

#lang racket

(define cube
   (lambda (x) (* x x x)))
;And then we can reference it
(cube 3)
; Output => 27Code language: PHP (php)

We use a quote ‘ if we would like to stop the evaluation of a list, for example, if we would like to find if a number exists in a list:

#lang racket
(member 10 '(1 4 5 10 9 7))
; If we don't use quote ', we will get an error because the compiler will evaluate it as (f arg1 arg2 arg3) and not as a list
; Output => '(10 9 7) ; It returns the sublist from which the number 10 begins

(member 50 '(1 4 5 10 9 7))

; Output => #f ; False since 50 doesn't exist within the list
Code language: PHP (php)

Recursion in Scheme

The classical recursion Hello World is the factorial. Please note that if is a keyword, and not a procedure, (if cond a b) executes a if cond is true, otherwise b

(define (factorial n)
  (if (= n 0) ; Checking for the base case
      1 ; if the base case is true we return 1
      (* n (factorial (- n 1))))) ; otherwise we recurse passing n-1 as an argument
Code language: JavaScript (javascript)

With that, we conclude Part 1 of the Introduction to Functional Programming with Scheme.

You can find the above code on my github

I would like to express my gratitude for professors Matteo Pradella & Michele Chiari who taught me the course Principles of Programming Languages at PoliMi

In the upcoming parts, we will dive deeper into Scheme and its constructs

Brace yourself for even more parentheses 😀

Thanks for reading! and stay tuned.

Introduction to Higher Order Functions

A higher order function (HOF) is a function that takes one or more functions as arguments or return a function as a result, or both. They are supported by a wide range of programming languages including the most popular ones such as Python, C++ and JavaScript.

An example of Higher Order Functions that typically built-in within programming languages are:

  1. map
  2. fold
  3. filter

Although they are simple concepts, knowing how to use them can very much improve the way you write code :). So let’s get started!

In this tutorial we’ll use Python, without any loss of generalization the same concepts apply to any other language.

1. map

The signature of map function in Python is map(function, iterable,)

map operates on iterables (lists, tuples, strings or any sequence that can be iterated on with a for loop)

map is used to apply a function to each item in the iterable, or in other words to map each item to something else.

Example: Let’s say we have this list of numbers, and we would to return zero for each negative number, and return the square of each positive number.

Map function
import math

list_of_nums = [1, 5, 10, -5, 8, -4, 3]

def my_function(x):
    if x < 0:
        return 0
        return math.pow(x, 2)

new_list_of_nums = list(map(my_function, list_of_nums))


#Output: [1, 25, 100, 0, 64, 0, 9]

Code language: PHP (php)

2. reduce

reduce is the Pythonic version of foldl in Functional Programming, it can be used to apply operations that can accumulate the iterable, such as summing numbers, or concatenation of strings.

The reduce in Python is available in the functools module

The signature of reduce function in Python is reduce(function, iterable)

In reduce, the function we apply must have two arguments. This time we’ll use a lambda,

A lambda is an anonymous function that has the following syntax: lambda arguments : expression

In the following example, we are finding the sum of the first 100 natural numbers, the way this works is as follows it starts from the first item of the list from left to right:  ((((1+2)+3)+4)+5)...+100) = 5050

Reduce function
import functools

list_of_nums = list(range(1, 101))

sum_of_nums = functools.reduce(lambda x, y: x + y, list_of_nums)


#Output: 5050
Code language: PHP (php)

3. filter

The filter function as the name suggests, filters an iterable based on the boolean value returned by the function we pass.

The signature of filter function in Python is filter(function, iterable)

In the following example, we are filtering the list such that lowercase characters are removed.

Filter function

list_of_chars= ['A','B','c','D','e','F',]

filtered_list = list(filter(lambda x: x.isupper(), list_of_chars))


#Output: ['A', 'B', 'D', 'F']
Code language: PHP (php)

You can also find the code on my github.

Thanks for reading and happy coding!