Higher-Order Functions (HOF)

Building on the idea that functions are first-class values, we can now explore a powerful consequence: Higher-Order Functions (HOFs). These are functions that operate on other functions, either by taking them as input or returning them as output. This section introduces the basic patterns of HOFs.

The 3 Basic Higher-Order Function (HOF) Patterns

As we just discussed, the core idea of First-Class Functions means we can:

• Pass functions into other functions as arguments.

• Have functions return new functions as their result.

These two capabilities define what makes a function a Higher-Order Function (HOF). We can visualize the basic patterns that emerge from this definition using the following diagram:

Let’s break down these patterns based on the definition:

1. Value |> Function = Function

Returns a Function as its output.

2. Function |> Function = Value

Takes a Function as input.

3. Function |> Function = Function

Takes and Returns a Function as input and also returns a function as output.

These three patterns illustrate the fundamental ways functions can be used as first-class values, enabling the powerful techniques found in functional programming.