^^Funzione matematica.

La funzione vista in ambito insiemistico

Funzione da un insieme ad un altro.

La funzione vista in ambito informatico

Computable function, funzione calcolabile.

The traditional way of defining a function (in mathematics)

es: f(x) = 2x2 + 3x - 2

equation left side: name of the function and its formal parameter

right side: the defining expression.

 

This method of definition makes it impossible to specify the name f of the function independently of the name x of the formal parameter.

The λ-calculus way of defining a function

To separate them, Church adopted the greek letter λ as a marker of the defining

lambda expression

f = λx(2x2 + 3x - 2)

formal parameter ≡ bound variable  the symbol x that appears after λ

body (of the expression) the remainder part

In this equation, the name f of the function appears by itself on the left, and its definition is a separate expression on the right.

In computer science, the clear separation of the name of a function from its defining expression enables a lambda expression to be used anywhere that a function name could be used. This feature is especially useful for applications that create new functions dynamically and pass them as arguments to other functions that evaluate them.

ref: jfsowa/math