Chapter 16. Advanced Functional Programming

Let’s return to functional programming and discuss some advanced concepts. You can skip this chapter if you’re a beginner, but come back to it if you hear people using terms like Algebraic Data Types, Category Theory, and Monads.

The goal here is to give you a sense of what these concepts are and why they are useful without getting bogged down into too much theory and notation.

Algebraic Data Types

There are two common uses of the “ADT” acronym, abstract data types and algebraic data types, which is confusing. The former meaning is common in the object-oriented programming world. It includes our familiar friends like Seq, an abstraction for any of the sequential collections. In contrast, algebraic data types comes from the functional programming world. It may be less familiar, but it’s equally important.

The term algebraic data type arises because the kinds of data types we’ll discuss obey algebraic, i.e., mathematical properties. This is important because if we can prove properties about our types, it raises our confidence that they are bug-free and it promotes safe composition to create more complex data structures and algorithms.

Sum Types Versus Product Types

Scala types divide into sum types and product types.

Most of the classes you know are product types. When you define a case class, for example, how many unique instances can you have? Consider this simple example:

case class Person(name: Name, age: Age)

You can have as many ...

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