**Course Title:** Functional Programming with Haskell: From Fundamentals to Advanced Concepts **Section Title:** Algebraic Data Types and Pattern Matching **Topic:** Defining custom data types (algebraic data types) **Introduction** In the previous topics, we explored the basics of Haskell, including its syntax, types, functions, and recursion. Now, it's time to dive deeper into one of Haskell's most powerful features: algebraic data types (ADTs). ADTs enable us to define custom data types, allowing us to model complex data structures and relationships. In this topic, we'll learn how to define and work with custom data types in Haskell. **What are algebraic data types?** Algebraic data types are a way to define custom data types using a combination of existing types and constructors. Think of constructors as functions that create new values of a type. ADTs provide a way to define new types by combining existing types using the following: * **Sum types**: The type is a sum of its constructors. * **Product types**: The type is a product of its constructors. **Defining custom data types** In Haskell, we use the `data` keyword to define custom data types. Let's consider a simple example: ```haskell data Color = Red | Green | Blue ``` Here, we define a new type `Color` with three constructors: `Red`, `Green`, and `Blue`. The `Color` type is an example of a sum type, as it's a sum of its constructors. Let's define another example: ```haskell data Cartesian = Point Float Float ``` Here, we define a new type `Cartesian` with a single constructor `Point`. The `Cartesian` type is an example of a product type, as it's a product of its constructors. **Data constructors** Data constructors are functions that create new values of a type. In the `Color` example above, `Red`, `Green`, and `Blue` are all data constructors. We can use data constructors to create new values of the type: ```haskell myColor = Red myPoint = Point 3.5 2.8 ``` **Pattern matching** We can use pattern matching to deconstruct values of custom data types. For example: ```haskell printColor :: Color -> String printColor Red = "Red" printColor Green = "Green" printColor Blue = "Blue" ``` In this example, we define a function `printColor` that takes a `Color` value and returns a string representation of the color. We use pattern matching to deconstruct the `Color` value and return the corresponding string. **Recursive data types** We can define recursive data types using ADTs. Let's consider an example: ```haskell data Tree a = Empty | Leaf a | Node a (Tree a) (Tree a) ``` Here, we define a recursive data type `Tree` that represents a binary tree with nodes of type `a`. **Type parameters** We can define type parameters for custom data types. For example: ```haskell data Maybe a = Nothing | Just a ``` Here, we define a custom data type `Maybe` with a type parameter `a`. The `Maybe` type represents a value that may or may not be present. **Conclusion** In this topic, we learned how to define custom data types using algebraic data types in Haskell. We covered sum types, product types, data constructors, pattern matching, recursive data types, and type parameters. With this knowledge, you can define custom data types to model complex data structures and relationships in your Haskell programs. **Practical Takeaways** * Define custom data types using the `data` keyword. * Use sum types and product types to define new types. * Define data constructors to create new values of a type. * Use pattern matching to deconstruct values of custom data types. If you have any questions or need further clarification, please leave a comment below. For more information on algebraic data types, refer to the [Haskell Wiki](https://wiki.haskell.org/Algebraic_data_type). **Next Topic:** In the next topic, we'll explore working with `Maybe`, `Either`, and other standard types. Please proceed to the next topic: '[Working with `Maybe`, `Either`, and other standard types](link_to_next_topic)'