**Course Title:** Functional Programming with Haskell: From Fundamentals to Advanced Concepts **Section Title:** Algebraic Data Types and Pattern Matching **Topic:** Working with `Maybe`, `Either`, and other standard types. In this topic, we will explore some of the most commonly used algebraic data types in Haskell, including `Maybe`, `Either`, and others. These types are essential for building robust and error-free applications. **What is `Maybe`?** `Maybe` is a type that represents a value that may or may not exist. It is defined as follows: ```haskell data Maybe a = Nothing | Just a ``` `Nothing` represents the absence of a value, while `Just a` represents a value of type `a`. **Using `Maybe`** Here's an example of using `Maybe` to represent a function that may or may not return a value: ```haskell safeDivide :: Int -> Int -> Maybe Int safeDivide _ 0 = Nothing safeDivide x y = Just (x `div` y) ``` In this example, `safeDivide` returns `Nothing` if the denominator is 0, and `Just` the result of the division otherwise. **What is `Either`?** `Either` is a type that represents a value that can be one of two possible types. It is defined as follows: ```haskell data Either a b = Left a | Right b ``` `Left a` represents a value of type `a`, while `Right b` represents a value of type `b`. **Using `Either`** Here's an example of using `Either` to represent a function that returns an error message or a value: ```haskell divide :: Int -> Int -> Either String Int divide _ 0 = Left "Cannot divide by zero!" divide x y = Right (x `div` y) ``` In this example, `divide` returns a `Left` value with an error message if the denominator is 0, and a `Right` value with the result of the division otherwise. **Other Standard Types** In addition to `Maybe` and `Either`, Haskell provides several other standard algebraic data types, including: * `Bool`: a type that represents a boolean value * `Ordering`: a type that represents an ordering (less than, equal to, or greater than) * `List`: a type that represents a list of values **Key Concepts** * Algebraic data types can be used to represent complex data structures in a concise and elegant way. * `Maybe` and `Either` are two of the most commonly used algebraic data types in Haskell. * `Maybe` is used to represent a value that may or may not exist. * `Either` is used to represent a value that can be one of two possible types. **Practical Takeaways** * Use `Maybe` to represent functions that may or may not return a value. * Use `Either` to represent functions that return an error message or a value. * Familiarize yourself with the standard algebraic data types provided by Haskell. **Example Code** Here's some example code that uses `Maybe` and `Either`: ```haskell module Main where import Data.Maybe import Data.Either safeDivide :: Int -> Int -> Maybe Int safeDivide _ 0 = Nothing safeDivide x y = Just (x `div` y) divide :: Int -> Int -> Either String Int divide _ 0 = Left "Cannot divide by zero!" divide x y = Right (x `div` y) main :: IO () main = do print $ safeDivide 10 2 -- prints Just 5 print $ safeDivide 10 0 -- prints Nothing print $ divide 10 2 -- prints Right 5 print $ divide 10 0 -- prints Left "Cannot divide by zero!" ``` **External Resources** * [Haskell Documentation: Maybe](https://hackage.haskell.org/package/base-4.14.0.0/docs/Data-Maybe.html) * [Haskell Documentation: Either](https://hackage.haskell.org/package/base-4.14.0.0/docs/Data-Either.html) **What's Next?** In the next topic, we will cover **Advanced pattern matching techniques**. Do you have any questions or feedback about this topic? Please leave a comment below.