Anonymous function

In computer science and mathematics, an anonymous function is a function with no name. Usually, a function is written like: ${\displaystyle f(x)=x^{2}-x+42}$. It can be written anonymously as ${\displaystyle x\rightarrow x^{2}-x+42}$. Anonymous functions exist in most functional programming languages and most other programming languages where functions are values.

Each of these examples show a nameless function that multiplies two numbers.

Uncurried (not curried):

(lambda x, y: x * y)

Curried:

(lambda x: (lambda y: x * y))

When given two numbers:

>>>(lambda x: (lambda y: x * y)) (3) (4)
12

Curried:

\x -> \y -> x * y

\x y -> x * y

When given two numbers:

>>> (\x -> \y -> x * y) 3 4
12

The function can also be written in point-free (tacit) style:

(*)

Uncurried:

fn (x, y) => x * y

Curried:

fn x => fn y => x * y

Point-free:

(op *)

Uncurried:

(x, y) => x * y

function (x, y) {
  return x * y;
}

Curried:

x => y => x * y

function (x) {
  return function (y) {
    return x * y;
  };
}

Uncurried:

(lambda (x y) (* x y))

Curried:

(lambda (x) (lambda (y) (* x y)))

Point-free:

*

Uncurried:

[](int x, int y)->int
{
	return x * y;
};

Curried:

[](int x)
{
	return [=](int y)->int
	{
		return x * y;
	};
};

Uncurried:

_1 * _2

Note: What you need to write boost lambda is to include <boost/lambda/lambda.hpp> header file, and using namespace boost::lambda, i.e.

#include <boost/lambda/lambda.hpp>
using namespace boost::lambda;

• Lambda calculus
• Closure
• Function
• Functional programming language

• Anonymous Functions in Math and CS

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