In Kotlin, a higher-order function is a function that can take one or more functions as parameters and/or return a function as its result. It treats functions as first-class citizens, allowing them to be assigned to variables, passed as arguments, and returned from other functions.

Here are some key points about higher-order functions :

1. Functions as Parameters :
   * Higher-order functions can receive other functions as parameters. These functions are typically referred to as "function types" or "lambda expressions" and can be invoked within the higher-order function.
   * Function parameters can specify the expected function type using a syntax similar to `(parameterName: FunctionType)`.
   Example :

     fun performOperation(operation: (Int, Int) -> Int) {
         val result = operation(5, 3)
         println("Result: $result")
     }​

2. Functions as Return Types :
   * Higher-order functions can return functions as their results. The returned function can be invoked later, outside the scope of the higher-order function.
   * The return type of the higher-order function includes the function type that will be returned.
   Example :

     fun getOperation(): (Int, Int) -> Int {
         return { a, b -> a + b }
     }
​

3. Lambda Expressions and Function References :
   * Higher-order functions often work with lambda expressions or function references. Lambda expressions are a concise way to define anonymous functions, while function references refer to existing named functions.
   * Lambda expressions can be used inline when calling higher-order functions, while function references provide a way to pass named functions as arguments.
   Example :

     val multiply: (Int, Int) -> Int = { a, b -> a * b }

     performOperation { a, b -> a + b }
     performOperation(multiply)​

4. Function Composition and Transformation :
   * Higher-order functions enable powerful functional programming techniques such as function composition and transformation of functions.
   * Function composition allows you to combine multiple functions into a single function, where the output of one function is the input of the next.
   * Function transformation involves modifying the behavior of a function by wrapping it in another function.
   Example :

     fun compose(f: (Int) -> Int, g: (Int) -> Int): (Int) -> Int {
         return { x -> f(g(x)) }
     }​

Higher-order functions in Kotlin enable functional programming paradigms and allow for more expressive and flexible code. They promote code reuse, modularity, and the separation of concerns. Higher-order functions, combined with lambda expressions or function references, open up possibilities for concise and powerful programming constructs.