Editing Declarative programming (section)

===Lisp===
[[Lisp (programming language) |Lisp]] is a family of programming languages loosely inspired by mathematical notation and [[Alonzo Church]]'s [[lambda calculus]]. Some dialects, such as [[Common Lisp]], are primarily imperative but support functional programming. Others, such as [[Scheme (programming language)|Scheme]], are designed for functional programming.

In Scheme, the [[factorial]] function can be defined as follows:

<syntaxhighlight lang=scheme>
(define (factorial n)
    (if (= n 0)                     
        1                             ;;; 0! = 1
        (* n (factorial (- n 1)))))   ;;; n! = n*(n-1)!
</syntaxhighlight>

This defines the factorial function using its recursive definition. In contrast, it is more typical to define a procedure for an imperative language.

In lisps and lambda calculus, functions are generally [[first-class citizen]]s. Loosely, this means that functions can be inputs and outputs for other functions. This can simplify the definition of some functions.

For example, writing a function to output the first n [[square number]]s in [[Racket (programming language)|Racket]] can be done accordingly:

<syntaxhighlight lang=scheme>
(define (first-n-squares n)
    (map (lambda (x) (* x x))          ;;; A function mapping x -> x^2
         (iota n)))                    ;;; Lists the first n naturals
</syntaxhighlight>

The [[Map (higher-order function) |map]] function accepts a function and a list; the output is a list of results of the input function on each element of the input list.