Daniel-Nikpayuk_SICP-Solutions/Chapter 2/2.3/exercise-2.56 (deriv)/exercise.lsp
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;; Copyright 2015 Daniel Nikpayuk
;;
;; This file is part of SICP Solutions.
;;
;; SICP Solutions is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License
;; as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
;;
;; SICP Solutions is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty
;; of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License along with SICP Solutions. If not, see
;; <http://www.gnu.org/licenses/>.
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(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 (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 (sum? x) (and (pair? x) (eq? (car x) '+)))
(define (addend s) (cadr s))
(define (augend s) (caddr s))
(define (product? x) (and (pair? x) (eq? (car x) '*)))
(define (multiplier p) (cadr p))
(define (multiplicand p) (caddr p))

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(define (exponentiation? x) (and (pair? x) (eq? (car x) '**)))
(define (base e) (cadr e))
(define (exponent e) (caddr e))
(define (make-exponentiation e1 e2)
 (cond
  ((=number? e2 0) 1)
  ((=number? e2 1) e1)
  ((and (number? e1) (number? e2)) (expt e1 e2))
  (else (list '** e1 e2))
 )
)

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(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))))
        (else
         (error "unknown expression type -- DERIV" exp))))

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

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(deriv '(+ x 3) 'x)
(deriv '(** x 3) 'x)

