Programming Scala, 3rd Edition

Chapter 18. Advanced Functional Programming

Let’s return to functional programming (FP) and discuss some more advanced concepts. You can skip this chapter if you are a beginner, but come back to it if you hear people using terms like algebraic data types, category theory, functors, monads, semigroups, and monoids.

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

Algebraic Data Types

There are two common uses for the acronym ADT, abstract data types and algebraic data types. Abstract data types are familiar from object-oriented programming (OOP). An example is Seq, an abstraction for all the sequential collections in the library.

In contrast, algebraic data types, for which we’ll use ADT from now on, are algebraic in the sense that they obey well-defined mathematical properties. This is important because if we can prove properties about our types, it raises our confidence that they are bug free.

Sum Types Versus Product Types

Scala types divide into sum types and product types. The names sum and product are associated with the number of instances possible for a particular type.

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

case class Person(name: Name, age: Age)   // or (Name, Age) tuples

You can have as many instances of Person as the allowed values for ...