section23.bak

#lang sicp

; Symbolic data: work with arbitrary symbols as data

(define a 1)
(define b 2)
;(list a b)
;(list 'a 'b)
(define false #f)
(define true #t)
(define abc (list '(a b c)))
;(list '123)
;(list nil)
;(list '())

(define (memq symbol symbols)
  (cond ((null? symbols) false)
        ((eq? symbol (car symbols)) symbols)
        (else (memq symbol (cdr symbols)))))

;(memq 'apple '(x (apple sauce) y apple pear))

; 2.53
; (a b c)
; ((george))
; ((y1 y2))
; (y1 y2)
; #f
; #f
; (red shoes blue socks)

(define (list-equal? list1 list2)
  (cond ((and (null? list1)
              (null? list2)) true)
        ((or (null? list1)
             (null? list2)) false)
        ((not (eq? (car list1)
                   (car list2))) false)
        (else (list-equal? (cdr list1)
                           (cdr list2)))))

;(list-equal? '(this is a list) '(this is a list))
;(list-equal? '(this is a list) '(this (is a) list))

; 2.55
; when you quote a quote, "quote" is itself now part of the symbol.
; the first character in a quoted quote is '.
; thus, the first element, the car, is '


; taking some derivatives
; ax2 + bx + c should be derived to 2ax + b
(define (variable? x) (symbol? x))
(define (same-variable? v1 v2)
  (and (variable? v1) (variable? v2) (eq? v1 v2)))
(define (=number? exp num)
  (and (number? exp) (= exp num)))
(define (make-expr-prefix op v1 v2)
  (list op v1 v2))
(define (numbers? a b)
  (and (number? a) (number? b)))


; sums, addition
(define (make-sum a1 a2)
  (cond ((=number? a1 0) a2)
        ((=number? a2 0) a1)
        ((numbers? a1 a2)
         (+ a1 a2))
        (else (make-expr-prefix '+ a1 a2))))
(define (sum? x) (and (pair? x) (eq? (car x) '+)))
(define (addend s) (cadr s))
(define (augend s) (caddr s))

; products multiplication
(define (make-product m1 m2)
  (cond ((or (=number? m1 0) (=number? m2 0)) 0)
        ((=number? m1 1) m2)
        ((=number? m2 1) m1)
        ((numbers? m1 m2) (* m1 m2))
        (else (make-expr-prefix '* m1 m2))))
(define (product? x) (and (pair? x) (eq? (car x) '*)))
(define (multiplier p) (cadr p))
(define (multiplicand p) (caddr p))


(define (make-exponentiation base exponent)
  (cond ((=number? base 1) 1)
        ((=number? exponent 1) base)
        ((=number? exponent 0) 1)
        ((numbers? base exponent)
         (expt base exponent))
        (else (make-expr-prefix '** base exponent))))
(define (exponentiation? x) (and (pair? x) (eq? (car x) '**)))
(define (base x) (cadr x))
(define (exponent x) (caddr x))

;(make-exponentiation 1 1)
;(make-exponentiation 2 1)
;(make-exponentiation 5 0)
;(make-exponentiation 4 3)
;(make-exponentiation 'b 1)
;(make-exponentiation 'b 2)
;(exponentiation? '(** x 1))
;(make-exponentiation 'a 3)
;(exponentiation? (make-exponentiation 'a 3))


(define (deriv exp var)
  (cond ((number? exp) 0)
        ((variable? exp) (if (same-variable? exp var) 1 0))
        ((sum? exp) (make-sum (deriv (addend exp) var)
                              (deriv (augend exp) var)))
        ((product? exp)
         (make-sum
          (make-product (multiplier exp)
                        (deriv (multiplicand exp) var))
          (make-product (deriv (multiplier exp) var)
                        (multiplicand exp))))
        ((exponentiation? exp)
         (let ((old-e (exponent exp))
               (old-b (base exp)))
           (make-product
            (make-product old-e
                          (make-exponentiation old-b (make-sum old-e -1)))
            (deriv old-b var))))
        (else
         (error "unknown expression type: DERIV" exp))))

;(deriv '(* (* x y) (+ x 3)) 'x)
;(deriv '(+ x 3) 'x)
;(deriv '(* x y) 'x)
(deriv '(** x 4) 'x)