134 lines
3.3 KiB
Racket
134 lines
3.3 KiB
Racket
#lang sicp
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(define (deriv exp var)
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(cond ((number? exp) 0)
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((variable? exp)
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(if (same-variable? exp var) 1 0))
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((sum? exp)
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(make-sum (deriv (addend exp) var)
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(deriv (augend exp) var)))
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((product? exp)
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(make-sum
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(make-product (multiplier exp)
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(deriv (multiplicand exp) var))
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(make-product (deriv (multiplier exp) var)
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(multiplicand exp))))
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((exponentiation? exp) ;;(make-product (exponent exp) (deriv (base exp) var))
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(let ((e (exponent exp))
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(b (base exp)))
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(make-product e
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(make-product
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(make-exponentiation b (- e 1))
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(deriv b var)))))
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(else
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(error "unknown expression type -- DERIV" exp))))
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;; representing algebraic expressions
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(define (variable? x) (symbol? x))
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(define (same-variable? v1 v2)
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(and (variable? v1) (variable? v2) (eq? v1 v2)))
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;;(define (make-sum a1 a2) (list '+ a1 a2))
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;;(define (make-product m1 m2) (list '* m1 m2))
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(define (more-than-2-terms x) (pair? (cdddr x)))
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;;(define (sum? x)
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;; (and (pair? x) (eq? (car x) '+)))
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;;
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;;(define (addend s) (cadr s))
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;;
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;;(define (augend s)
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;; (if (more-than-2-terms s)
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;; (cons '+ (cddr s))
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;; (caddr s)))
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;;
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;;(define (product? x)
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;; (and (pair? x) (eq? (car x) '*)))
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;;
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;;(define (multiplier p) (cadr p))
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;;
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;;(define (multiplicand p)
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;; (if (more-than-2-terms p)
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;; (cons '* (cddr p))
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;; (caddr p)))
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;: (deriv '(+ x 3) 'x)
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;: (deriv '(* x y) 'x)
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;: (deriv '(* (* x y) (+ x 3)) 'x)
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;; With simplification
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;;(define (make-sum a1 a2)
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;; (cond ((=number? a1 0) a2)
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;; ((=number? a2 0) a1)
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;; ((and (number? a1) (number? a2)) (+ a1 a2))
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;; (else (list '+ a1 a2))))
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(define (=number? exp num)
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(and (number? exp) (= exp num)))
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;;(define (make-product m1 m2)
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;; (cond ((or (=number? m1 0) (=number? m2 0)) 0)
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;; ((=number? m1 1) m2)
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;; ((=number? m2 1) m1)
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;; ((and (number? m1) (number? m2)) (* m1 m2))
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;; (else (list '* m1 m2))))
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;; Exercise 2.56
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(define (make-exponentiation b p)
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(cond ((=number? p 0) 1)
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((=number? p 1) b)
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((and (number? b) (number? p)) (expt b p))
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(else (list '** b p))))
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(define (base e) (cadr e))
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(define (exponent e) (caddr e))
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(define (exponentiation? x) (and (pair? x) (eq? (car x) '**)))
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;; Exercise 2.58
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(define (make-sum a1 a2)
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(cond ((=number? a1 0) a2)
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((=number? a2 0) a1)
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((and (number? a1) (number? a2)) (+ a1 a2))
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((product? a2) (list a1 '+ (multiplier a2) '* (multiplicand a2)))
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(else (list a1 '+ a2))))
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(define (make-product m1 m2)
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(cond ((or (=number? m1 0) (=number? m2 0)) 0)
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((=number? m1 1) m2)
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((=number? m2 1) m1)
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((and (number? m1) (number? m2)) (* m1 m2))
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(else (list m1 '* m2))))
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(define (sum? x)
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(and (pair? x) (eq? (cadr x) '+)))
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(define (addend s) (car s))
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;; Special case of multiplication distributing across addition. It
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;; should be possible to rewrite augend and/or multiplicand to deal
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;; with this case
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(define (augend s)
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(if (product? (cddr s))
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(cddr s)
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(caddr s)))
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(define (product? x)
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(and (pair? x) (eq? (cadr x) '*)))
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(define (multiplier p) (car p))
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(define (multiplicand p) (caddr p))
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