#lang racket
;;----------------------------------------------ZAD 1----------------------------------------------
(define/contract (suffixes l)
  (let ((a (new-∀/c 'a)))
    (-> (listof a) (listof (listof a))))
   (if (null? l)
       '()
       (cons l (suffixes (cdr l)))))

;;----------------------------------------------ZAD 2----------------------------------------------
(define/contract (dist x y)
  (-> number? number? number?)
  (abs (- x y)))

(define/contract (average x y)
  (-> number? number? number?)
  (/ (+ x y) 2))

(define/contract (square x)
  (-> number? number?)
  (* x x))

(define/contract (sqrt x)
  (->i ((argument (>=/c 0)))
       (result (argument) (and/c (>=/c 0)
                                 (if (> argument 1)
                                     (<=/c argument)
                                     (>=/c argument)))))
  ;; lokalne definicje
  ;; poprawienie przybliżenia pierwiastka z x
  (define (improve approx)
    (average (/ x approx) approx))
  ;; nazwy predykatów zwyczajowo kończymy znakiem zapytania
  (define (good-enough? approx)
    (< (dist x (square approx)) 0.0001))
  ;; główna procedura znajdująca rozwiązanie
  (define (iter approx)
    (cond
      [(good-enough? approx) approx]
      [else                  (iter (improve approx))]))

  (iter 1.0))


;;----------------------------------------------ZAD 3----------------------------------------------
(define/contract (filter l p)
  (-> (and/c
       (let ((a (new-∀/c 'a)))
         (-> (listof a) (-> a boolean?) (listof a)))
       (->i ([l list?] [p procedure?])
            [result (l) (λ (r) (<= (length r) (length l)))])))
  (if (null? l)
      '()
      (if (p (car l))
          (cons (car l) (filter (cdr l) p))
          (filter (cdr l) p))))


;;----------------------------------------------ZAD 4----------------------------------------------
(define-signature monoid^
  ((contracted
    [elem? (-> any/c boolean?)] [neutral elem?]
    [oper (-> elem? elem? elem?)])))



;;----------------------------------------------ZAD 5----------------------------------------------