(define (subst x v e)
  (match e
    [(op s l r)         (op s (subst x v l)
                        (subst x v r))]
    [(const n)          (const n)]
    [(variable y)       (if (eq? x y)
                        (const v)
                        (variable y))]
    [(derivative s exp) (derivative s (subst x v (∂ exp)))]
    [(let-expr y e1 e2)
     (if (eq? x y)
         (let-expr y
                   (subst x v e1)
                   e2)
         (let-expr y
                   (subst x v e1)
                   (subst x v e2)))]))

;; (gorliwa) ewaluacja wyrażenia w modelu podstawieniowym

(define (eval e)
  (match e
    [(const n)           n]
    [(op '+ l r)         (+ (eval l) (eval r))]
    [(op '* l r)         (* (eval l) (eval r))]
    [(derivative '∂ exp) (eval (∂ exp))]
    [(let-expr x e1 e2)  (eval (subst x (eval e1) e2))]
    [(variable n) (error n "cannot reference an identifier before its definition ;)")]))