First-Class, Higher-Order, and First-Order Functions

First-Class Functions, Higher-Order Functions, and First-Order Functions are three technical terms that look very similar and are easily confused. This article will thoroughly introduce what these three terms mean and compare their relationships.

First-Class Functions: Functions as Values

First-Class Functions are an important concept in programming language design, referring to a programming language treating functions as “first-class citizens,” giving them the same rights and capabilities as other data types.

In other words, when functions in a programming language can be treated like any other variable for input or output, we say that programming language has first-class functions.

Specifically, functions with first-class capabilities have the following abilities:

1. Can be assigned to variables

2. Can be passed as parameters

3. Can be returned as values

4. Can be created at runtime

5. Can be stored in data structures

Using JavaScript as an example, we can refer to the following code for more concrete examples:

// 1. Can be stored in variables
const greet = function (name) {
  return `Hello, ${name}!`;
};

// 2. Can be passed as parameters
function executeFunction(fn, value) {
  return fn(value);
}

// 3. Can be returned as values
function createMultiplier(factor) {
  return function (number) {
    return number * factor;
  };
}

// 4. Can be created at runtime
const dynamicFunction = new Function("x", "y", "return x + y");

// 5. Can be stored in data structures
const operations = {
  add: (a, b) => a + b,
  multiply: (a, b) => a * b,
};

Most modern programming languages support first-class functions, such as JavaScript and Python. This makes functions extremely flexible, enabling powerful programming patterns like Higher-Order Functions, Callbacks, and Closures.

Higher-Order Functions: Functions that Operate on Functions

Higher-Order Functions are simply functions that take functions as parameters or return functions.

Their core characteristics are:

1. Functions are first-class citizens: can be passed as values

2. Pattern abstraction: extracting repetitive logic

3. Composability: combining small functions into complex functionality

This is a core concept of functional programming—a mindset that makes your code more modular, reusable, and composable.

First-Order Functions: Basic Functions

First-Order Functions refer to ordinary functions that “do not accept functions as parameters and do not return functions.”

This is a concept relative to Higher-Order Functions.

Specific examples:

// First-Order Functions - only handle basic data types
function add(a, b) {
  return a + b;
}

function square(x) {
  return x * x;
}

function getName(user) {
  return user.name;
}

Relationship and Comparison of the Three

In summary:

1. First-Class Functions are a language feature, not a function classification. They allow functions to be manipulated as values and are the foundation for implementing Higher-Order Functions.

2. Higher-Order Functions accept functions as parameters or return functions, built upon the characteristics of First-Class Functions, providing powerful abstraction capabilities.

3. First-Order Functions are ordinary functions that don’t involve function operations, representing the most basic form of functions and typically concrete implementations of business logic.

The key to understanding these three concepts is: First-Class Functions are a language feature, Higher-Order Functions are a design pattern, and First-Order Functions are basic implementations. In actual development, they complement each other and together form the core of modern JavaScript/TypeScript development.