#lang racket

(define (factorial n)
  (if (zero? n)
      1
      (* n (factorial (- n 1)))))
;(factorial 5)
;(map factorial (range 1 11))

(define (factorial-adv n)
  (apply * (range 2 (+ n 1))))

;(map factorial-adv (range 1 11))

; expresie = (f e1 e2 .. en)
;(+ 6 (- (* 5 2) 3) 1)

; (define identificator expresie)
(define PI 3.14159265)
(define r 5)
(define area (* PI r r))


; functii anonime: (lambda lista-parametri corp)
; λx.x - in Calcul Lambda
;(lambda (x) x)

;λx.λy.(x y) - in Calcul Lambda

;(λx.x λx.y) - in Calcul Lambda

;(  (λ (x y)
;    (/ (+ x y) 2)) 6 12)

; (define (f x y ... ) corp)
(define (arithmetic-mean x y)
  (/ (+ x y) 2))

(define (sum-of-squares x y)
  (+ (sqr x) (sqr y)))
;(sum-of-squares (+ 1 2) (* 3 5))

; perechi
; constructor: cons
; selectori: car, cdr
;(cons (cons 1 2) 'a)
;(cons + 3)
;(car (cons (cons 1 2) 5))
;(cdr '(4 . b))

; liste
; constructori: null, cons, list
; selectori: car, cdr
; alte operații: null?, length, append
;(car (list 1 'a +))
;(cdr '(2 3 4 5))
;(null? '())
;(length (list))
;(append (cons 1 '(2)) '(a b))

; (if conditie rez-then rez-else)
;(if (null? '(1))
;    "lala"
;    (- 7 1))

; (cond (cond1 rez1) (cond2 rez2) ... )
(define L '(1 2 3))
(define val
  (cond
    ((null? L)             0)
    ((null? (cdr L)) (/ 1 0))
    (else             'other)))
;val

; Traducere din axiome
; sum([])  = 0
; sum(x:l) = x + sum(l)
(define (sum L)
  (if (null? L)
      0
      (+ (car L) (sum (cdr L)))))
;(sum '(1 2 3))


; Exemplu: my-take
; L = '(1 2 3 4 5 6 7)       
; n = 4                      
; r = '(1 2 3 4)

; L1 = '(2 3 4 5 6 7)
; n1 = 3
; r1 = '(2 3 4)

; axiome:
; take([], n) = []
; take(L, 0) = []
; take(x:L, n) = x:take(L, n-1)
(define (my-take L n)
  (if (or (null? L) (zero? n))
      '()
      (cons (car L) (my-take (cdr L) (sub1 n)))))

;(my-take (range 2 10) 20)
;(my-take (range 2 10) 3)