Functional programming

As I understand it.

• Functional programming: Opposed to object-oriented programming, the return value of a function does not depend on the state of the object, ie. it will always be the same given the same argument.
• First-class functions: A language can either have first-class functions or not. It can: return a function, create an array of functions (source).
• Higher-order functions: Functions that can take functions as input (arguments) or output (return value).

These three are characteristically used by languages with first class functions.

• Anonymous functions: Functions defined without a name.

• Closure: When defining a function inside a function, the inner function has access to the arguments given to the outer function (source). Example in JavaScript:

  function makeCounter (a) {
  var b = a;
  return function (c) {
    b += c;
    return b;
  }
  }
  var x = makeCounter(1);
  x(2); //returns 3
  x(3); //returns 6
  makeCounter(1)(3); //returns 4
  

• Lambda expression: Most likely is an anonymous function, but not always. A shorter way to write functions. Comes from the concept of lambda calculus. \( \lambda x.x^{2} \) is the lambda expression for the function \( f(x) = x^{2} \). Lambda is usable in a language because the functions are first class (source).