Explain algebraic data types in Haskell and illustrate their usage.

In Haskell, algebraic data types (ADTs) are a powerful feature that allows you to define your own data structures by combining existing types in a structured and expressive manner. ADTs consist of two main components: sum types and product types. Let's explore the concept of ADTs in Haskell and illustrate their usage with examples. Sum Types: Sum types in Haskell are created by combining multiple types using the `|` (pipe) symbol to represent alternatives. Each alternative is called a constructor and represents a possible value of the sum type. Sum types are similar to the concept of union types in other programming languages. They allow you to model choices or different cases within a data type. Here's an example of defining a sum type in Haskell: ``` haskell`data Shape = Circle Float | Rectangle Float Float` ``` In the above example, we define a `Shape` data type that can be either a `Circle` or a `Rectangle`. The `Circle` constructor takes a single `Float` argument representing the radius,....