Explain the concept of partial application in functional programming.

Partial application in functional programming is the process of fixing a number of arguments to a function, producing another function of smaller arity.

In more detail, functional programming is a programming paradigm where functions are first-class citizens. This means that functions can be passed as arguments to other functions, returned as values from other functions, and assigned to variables. One of the powerful techniques in functional programming is partial application.

Partial application is a technique where you create a new function by pre-setting, or 'fixing', some of the arguments to a function. The result is a new function where those arguments are no longer required. This new function is of smaller arity, meaning it takes fewer arguments than the original function.

For example, consider a simple function that adds two numbers together. Using partial application, you could create a new function that has one of the numbers already set. This new function would only require one argument, the second number to be added to the fixed number.

This technique is particularly useful when you have a function that takes multiple arguments, and you know some of the values you want to use ahead of time. By using partial application, you can simplify your code and make it more readable. It also allows you to create more specialised functions from more general ones.

In essence, partial application allows you to control the complexity of your functions and your code. It's a powerful tool in the functional programmer's toolkit, and understanding it can greatly enhance your ability to write clean, efficient, and effective code.