Module 2: Higher-Order Functions

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Learning outcomes

• explain what a higher-order function is in Python;
• use map, filter, and lambda with confidence;
• write a function that receives or returns another function;
• trace a small function example step by step.

Prerequisites

Read Module 1 first. Make sure you are comfortable with Python values, lists, and function calls.

The idea in one sentence

A higher-order function is a function that works with other functions as values.

Everyday analogy

Think of a teacher who does not give one fixed answer. Instead, the teacher gives a rule such as "double every number" or "keep only even numbers." You then apply that rule to a whole list.

Syntax

def apply_twice(func, value):
    return func(func(value))

double = lambda x: x * 2

numbers = [1, 2, 3]
squared = list(map(lambda x: x * x, numbers))
even_numbers = list(filter(lambda x: x % 2 == 0, numbers))

Worked example

def square(x):
    return x * x

result = list(map(square, [1, 2, 3]))

Step by step:

1. map(square, [1, 2, 3]) sends each list item into square.
2. square(1) gives 1.
3. square(2) gives 4.
4. square(3) gives 9.
5. list(...) collects the results into [1, 4, 9].

Why this matters in practice

• In college notes, higher-order functions show how one idea can control many values.
• In real code, they are useful in data cleaning, report generation, validation, and repeated transformations.
• They help you write shorter code without repeating the same loop logic again and again.

Important concepts

Higher-order function

A higher-order function can:

• take a function as input;
• return a function as output;
• or do both.

Examples:

def apply(func, value):
    return func(value)

def make_multiplier(n):
    return lambda x: x * n

map

map applies a function to every item in an iterable.

list(map(str, [1, 2, 3]))

Result:

['1', '2', '3']

filter

filter keeps only the items that pass a test.

list(filter(lambda x: x > 2, [1, 2, 3, 4]))

Result:

[3, 4]

lambda

lambda creates a short anonymous function when a full def feels too heavy.

lambda x: x + 1

Technical meaning

Python treats functions as first-class values. That means functions can be stored in variables, passed into other functions, and returned from other functions. A higher-order function uses that property to make programs more reusable and expressive.

Memory rule

• map transforms
• filter selects
• lambda writes a small function quickly
• higher-order means "function with function power"

Quick check

• Why is map higher-order?
• What does lambda x: x + 1 do?
• What does list(filter(...)) return?
• Why is make_multiplier a higher-order function?

Short exam answer

A higher-order function is a function that takes another function as input or returns one as output. In Python, map, filter, and functions that return closures are common examples. They reduce repetition and make code easier to reuse.

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