2-57.scm

#lang scheme

(require "modules/sicp/sicp.rkt")

(provide make-sum
         addend
         augend
         make-product
         multiplier
         multiplicand
         exponent
         make-exponentiation
         base)

(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-sum a1 a2)
  (cond ((=number? a1 0) a2)
        ((=number? a2 0) a1)
        ((and (number? a1) (number? a2)) (+ a1 a2))
        (else (list '+ a1 a2))))

(define (sum? x)
  (and (pair? x) (eq? (car x) '+)))

(define (addend s) (cadr s))

(define (augend s)
  (let ((rest (cddr s)))
    (fold-right make-sum 0 rest)))

(define (make-product m1 m2)
  (cond ((or (=number? m1 0) (=number? m2 0)) 0)
        ((=number? m1 1) m2)
        ((=number? m2 1) m1)
        ((and (number? m1) (number? m2)) (* m1 m2))
        (else (list '* m1 m2))))

(define (multiplier p) (cadr p))

(define (multiplicand p)
  (let ((rest (cddr p)))
    (fold-right make-product 1 rest)))

(define (product? x)
  (and (pair? x) (eq? (car x) '*)))

(define (exponentiation? x)
  (and (pair? x) (eq? (car x) '**)))

(define (fold-right op initial sequence)
  (if (null? sequence)
      initial
      (op (car sequence)
          (fold-right op initial (cdr sequence)))))

(define (repeated x n)
  (if (= n 0)
      nil
      (cons x (repeated x (- n 1)))))

(define (** base exponent)
  (fold-right * 1 (repeated base exponent)))

(define (base s) (cadr s))
(define (exponent s) (caddr s))

(define (make-exponentiation base exponent)
  (cond ((=number? exponent 1) base)
        ((=number? exponent 0) 1)
        ((=number? base 1) 1)
        ((and (number? base) (number? exponent)) (** base exponent))
        (else (list '** base exponent))))

(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)
         (make-product  
          (exponent exp) 
          (make-exponentiation (base exp) 
                               (make-sum (exponent exp) -1))))
        (error "unknown expression type - DERIV" exp)))

(assert (deriv '(* x y (+ x 3)) 'x)
        '(+ (* x y) (* y (+ x 3))))
 
(assert (deriv '(+ y x) 'x) 1)