; CSE 341 lecture 18 (symbolic data) code

; A read-eval-print loop (REPL) that reads commands, runs them, and shows the result.
(define (repl)
  (display "type something: ")
  (let ((code (read)))
    (display (eval code)))
  (newline)
  (repl))


; differentiates the given function with respect to the given variable.
; differentiation rules:
;   dc/dx     = 0
;   dx/dx     = 1
;   d(u+v)/dx = du/dx + dv/dx
;   d(u*v)/dx = u(dv/dx) + v(du/dx)
(define (deriv func var)
  (cond ((number? func) 0)
        ((symbol? func) (if (eq? var func) 1 0)
        ((sum? func) 3)        (* unfinished *)
        ((product? func) 4)    (* unfinished *)
        (else 0))))            (* unfinished *)

; (sum? '(+ 2 4)) -> #t
; (sum? 42)       -> #f
(define (sum? lst)
  (and (list? lst) (eq? '+ (car lst))))

; (product? '(* 2 4)) -> #t
; (product? 42)       -> #f
(define (product? lst)
  (and (list? lst) (eq? '* (car lst))))

; test functions for deriv procedure
; d/dx 42 -> 0
(define f0 42)

; d/dx (x+3) -> 1
(define f1 '(+ x 3))

; d/dx (5x) -> 5
(define f2 '(* x 5))

; d/dz (z^2 + 5z) -> 2z + 5
(define f3 '(+ (* z z) (* 5 z)))

; d/dx (ax^2 + bx + c) -> 2ax + b
(define f4 '(+ (+ (* a (* x x)) (* b x)) c))