**Course Title:** Functional Programming with Haskell: From Fundamentals to Advanced Concepts **Section Title:** Basic Types, Functions, and Pattern Matching **Topic:** Defining and using functions: Lambda expressions, partial application **Overview** In this topic, we will delve into the world of functions in Haskell, exploring two essential concepts: lambda expressions and partial application. These concepts are crucial in functional programming, enabling you to write concise and reusable code. By the end of this topic, you will be able to define and use functions using lambda expressions and partial application, and understand their applications in real-world scenarios. **Lambda Expressions** A lambda expression is an anonymous function that can be defined inline within a larger expression. It is a shorthand way to create small, one-time-use functions. In Haskell, lambda expressions are defined using the following syntax: `λ parameters -> expression` Here, `λ` is the lambda symbol, `parameters` is a list of variables, and `expression` is the function body. Example: ```haskell doubleMe = \x -> x + x ``` In this example, we define a function `doubleMe` that takes a single argument `x` and returns its double. The `λ` symbol is represented by the backslash (`\`) character. You can also use lambda expressions as function arguments: ```haskell map (\x -> x * 2) [1, 2, 3, 4, 5] ``` This will apply the lambda expression to each element of the list, doubling all the numbers. **Partial Application** Partial application is a technique where you apply a function to only some of its arguments, resulting in a new function that takes the remaining arguments. This is useful when you want to create a specialized version of a function. In Haskell, you can partially apply a function by simply omitting some of the arguments. For example: ```haskell add x y = x + y addFive = add 5 ``` In this example, we define a function `add` that takes two arguments. We then partially apply `add` by fixing the first argument to `5`, resulting in a new function `addFive` that takes a single argument. You can also partially apply functions with multiple arguments: ```haskell tripleAdd x y z = x + y + z addTen = tripleAdd 10 ``` This will result in a new function `addTen` that takes two arguments. **Key Concepts and Takeaways** * Lambda expressions are shorthand ways to define small, one-time-use functions. * Partial application allows you to create specialized versions of functions by fixing some of the arguments. **Practical Applications** * **Data Processing**: Lambda expressions and partial application can be used to process large datasets. For example, you can define a lambda expression to filter out certain values and then partially apply it to a dataset. * **Event Handling**: Partial application can be used to create event handlers that are specialized for specific events. **External Resources** * [Learn You a Haskell for Great Good!](http://learnyouahaskell.com/chapters) (Chapter 3: "Functions" and Chapter 5: "Lambda Functions") * [Real World Haskell](http://book.realworldhaskell.org/read/functional-programming.html) (Chapter 3: "Defining Functions") **Questions and Comments** If you have any questions or need help with lambda expressions or partial application, feel free to leave a comment below. **Next Topic: Pattern Matching for Control Flow and Data Deconstruction** In the next topic, we will explore pattern matching, a fundamental concept in Haskell that enables you to control the flow of your programs and deconstruct data structures.

doubleMe = \x -> x + x

map (\x -> x * 2) [1, 2, 3, 4, 5]

add x y = x + y
addFive = add 5

tripleAdd x y z = x + y + z
addTen = tripleAdd 10