discriminant in typed racket.rkt

#lang typed/racket

(require racket/cmdline)


(: square (-> Real Real))
(define (square x)
  (* x x))


(: sqrt (-> Real Real))
(define (sqrt x)
  (: good-enough? (-> Real Boolean))
  (define (good-enough? guess)
    (< (abs (- (square guess) x)) 0.001))

  (: average (-> Real Real Real))
  (define (average x y)
    (/ (+ x y) 2))

  (: improve (-> Real Real))
  (define (improve guess)
    (average guess (/ x guess)))

  (: sqrt-iter (-> Real Real))
  (define (sqrt-iter guess)
    (if (good-enough? guess) guess
        (sqrt-iter (improve guess))))

  (if (< x 0) 0 (sqrt-iter 1)))

(: discriminant (-> Real Real Real Real))
(define (discriminant a b c)
  (- (square b) (* 4 a c)))

(: discriminant-solutions (-> Real Real Real (Listof Real)))
(define (discriminant-solutions a b c)
  (let ((discriminant-result (discriminant a b c)))
    (if (negative? discriminant-result)
        (list )
        (let ((discriminant-result-root (sqrt discriminant-result))
              (double-a (* 2 a)))
          (list (/ (- (- b) discriminant-result-root) double-a)
                (/ (+ (- b) discriminant-result-root) double-a))))))

;; (sqrt 25.0)
;; 2 solutions:
(discriminant-solutions 2.0 4.0 -7.0)
;; 1 solution:
(discriminant-solutions 1.0 6.0 9.0)
;; incorrect (no solutions)
(discriminant-solutions 2.0 4.0 7.0)