; map and fold "higher-order" functions

; The function 'map' is a function that
; takes a function and a list as arguments,
; and applies (maps) the function over the
; elements of the list, returning a list. 
; It is written recursively as:

(define map
  (lambda (f ls)
    (if (null? ls)
        '()
        (cons (f (car ls)) (map f (cdr ls))))))

; Examples

(map car '((1 2 3) (1) (4 5))) 

(map cdr '((1 2 3) (1) (4 5)))

(map length '((1 2 3) (1) (4 5)))

(define (square x) (* x x))
(map square '(1 2 3 4 5))

;; or we can just write an inline lambda expression

(map (lambda (x) (* x x)) '(1 2 3 4 5))