What is the difference between a function and a lambda?

Question

I'm a little bit confused about 'function' and 'lambda'. I've seen some examples showing that the scheme keyword lambda works very similarly to the JavaScript keyword function, but I really don't know how they are related.

I'm told that 'function' and 'method' can be used interchangeably when speaking about objects in .net. I'm wondering if 'lambda' and 'function' similarly mean the same thing. I wonder if 'lambda' has some esoteric meaning, seeing that the Greek letter lambda (λ) appears in so many avatars on this site. To make things even more confusing, in .net, the functional parts of C# refer to function expressions passed to another function as 'lambda expressions', so the word really seems to be all over the place.

I'm also vaguely familiar with the term 'lambda calculus'.

What is the difference between a function and a lambda?

Answer 1

The word "lambda" or "lambda expressions" most often refers to anonymous functions. So in that sense a lambda is a kind of function, but not every function is a lambda (i.e. named functions aren't usually referred to as lambdas). Depending on the language, anonymous functions are often implemented differently than named functions (particularly in languages where anonymous functions are closures and named functions are not), so referring to them with different terms can make sense.

The difference between scheme's lambda keyword and Javascript's function keyword is that the latter can be used to create both anonymous functions and named functions while the former only creates anonymous functions (and you'd use define to create named functions).

The lambda calculus is a minimal programming language/mathematical model of computation, which uses functions as its only "data structure". In the lamdba calculus the lambda-symbol is used to create (anonymous) functions. This is where the usage of the term "lambda" in other languages comes from.

Answer 2

A lambda is simply an anonymous function - a function with no name.

Answer 3

Answered Here: http://stackoverflow.com/questions/16501/what-is-a-lambda-function

Basically Lambda is an anonymous function.

Answer 4

In C# Anonymous function is a general term that includes both lambda expressions and anonymous methods (anonymous methods are delegate instances with no actual method declaration).

Lambda expressions can be broken down to expression lambda and statement lambda

Expression lambda:

(int x, string y) => x == y.Length 

Statement lambda is similar to expression lambda except the statement(s) are enclosed in braces:

(int x, string y) => {
         if (x == y.Length) {
             Console.WriteLine(y);
         }
}

In JavaScript the anonymous method is declared like this:

var add = function(x, y){
    return x + y;
};

When we talk about lambda expressions in JavaScript that basically just means using a function as an argument in a call to another function.

var calculate = function(x, y, operation){
    return operation(x, y);
}

calculate(10, 15, add); // 25

Answer 5

Clearly the last example of an anonymous function in javascript is not anonymous as its name is "add". I think of lambda expressions as the half-way point between very simple procedural programming and object orientation. Simply you can pass values or pointers -- lambda lets you pass procedure (code blocks) -- objects are the full encapsulation of values and methods. C allows you to pass function pointers. And of course java, javascript and c# handle completely anonymous (having no name) functions.

The add function above is lambda expressed but is certainly not anonymous.