What is a lambda (function)?

Question

For a person without a comp-sci background, what is a lambda in the world of Computer Science?

Pat · Accepted Answer · 2013-08-12 16:40:09Z

Lambda comes from the Lambda Calculus and refers to anonymous functions in programming.

Why is this cool? It allows you to write quick throw away functions without naming them. It also provides a nice way to write closures. With that power you can do things like this.

Python

def adder(x):
    return lambda y: x + y
add5 = adder(5)
add5(1)
6

JavaScript

var adder = function (x) {
    return function (y) {
        return x + y;
    };
};
add5 = adder(5);
add5(1) == 6

Scheme

(define adder
    (lambda (x)
        (lambda (y)
           (+ x y))))
(define add5
    (adder 5))
(add5 1)
6

C# 3.5 or higher

Func> adder = 
    (int x) => (int y) => x + y; // `int` declarations optional
Func add5 = adder(5);
var add6 = adder(6); // Using implicit typing
Debug.Assert(add5(1) == 6);
Debug.Assert(add6(-1) == 5);

// Closure example
int yEnclosed = 1;
Func addWithClosure = 
    (x) => x + yEnclosed;
Debug.Assert(addWithClosure(2) == 3);

As you can see from the snippet of Python and JavaScript, the function adder takes in an argument x, and returns an anonymous function, or lambda, that takes another argument y. That anonymous function allows you to create functions from functions. This is a simple example, but it should convey the power lambdas and closures have.

This is by by far the best yet simplest description of lambda I have ever seen. Yet you managed to not lose any of the key ideas bravo. +1 — faceless1_14, Aug 10 '09 at 13:36

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What is a lambda (function)?