What is a "function" in the context of functional programming?

In the context of functional programming, a function is typically understood in a mathematical sense, rather than as a block of code that can be called. It is a deterministic, side-effect-free mapping from inputs to outputs, meaning that for any given input, the function will always produce the same output without modifying external state or causing side effects45.

Key Characteristics of Functions in Functional Programming:

1. Determinism: The output of a function depends only on its input arguments and not on any external state or side effects35.
2. No Side Effects: Functions do not modify external variables, input/output streams, or any other external state35.
3. Referential Transparency: Functions can be replaced with their output values without affecting the program's behavior3.
4. First-Class Citizenship: Functions can be passed as arguments to other functions, returned from functions, and stored in data structures, just like any other data type15.
5. Higher-Order Functions: Functions can take other functions as arguments or return functions as output35.

These characteristics allow functional programming to emphasize declarative programming, where the focus is on specifying what the program should accomplish rather than how it should accomplish it35.