From: Ramakrishnan Muthukrishnan Date: Sun, 19 Sep 2010 18:45:21 +0000 (+0530) Subject: solution to 2.73 X-Git-Url: https://git.rkrishnan.org/components/com_hotproperty/flags/%22news.html/status?a=commitdiff_plain;h=01ac848490b37ffa83b6d4c424745dc8ca1ee486;p=sicp.git solution to 2.73 --- diff --git a/src/sicp/ex2_73.rkt b/src/sicp/ex2_73.rkt new file mode 100644 index 0000000..59acf92 --- /dev/null +++ b/src/sicp/ex2_73.rkt @@ -0,0 +1,71 @@ +#lang racket + +(define (deriv exp var) + (cond + [(number? exp) 0] + [(variable? exp) (if (same-variable? exp var) 1 0)] + [else ((get 'deriv (operator exp)) (operands exp) + var)])) + +(define (operator exp) (car exp)) +(define (operands exp) (cdr exp)) + +;; part a +#| + +The 'get' procedure fetches from the table, an appropriate lambda +function which takes as input, the operands and the variable. The +function will return the appropriate expressions for addition and +multiplication. + +In theory we can define dispatch functions for number? and variable?. +But for those functions, the dispatch functions will return a +constant regardless of the input operands. +|# + +;; part b +(define deriv-sum + (lambda (exp var) + (make-sum (deriv (addend exp) var) + (deriv (augend exp) var)))) + +(define deriv-prod + (lambda (exp var) + (make-sum (make-product (multiplier exp) + (deriv (multiplicand exp) var)) + (make-product (deriv (multiplier exp) var) + (multiplicand exp))))) + +(define (install-deriv-package) + ;; internal procedures + (define (make-sum a1 a2) (list '+ a1 a2)) + (define (make-product m1 m2) (list '* m1 m2)) + (define (addend s) (car s)) + (define (augend s) (cadr s)) + (define (multiplier p) (car p)) + (define (multiplicand p) (cadr p)) + ;; public procedures + (define (variable? x) (symbol? x)) + (define (same-variable? v1 v2) + (and (variable? v1) (variable? v2) (eq? v1 v2))) + (put 'deriv '+ deriv-sum) + (put 'deriv '* deriv-prod)) + +;; part c +(define deriv-exponentiation + (lambda (exp var) + (make-product (exponent exp) + (make-product (make-exponentiation (base exp) + (- (exponent exp) 1)) + (deriv (base exp) var))))) + +(define (make-exponent base exp) + (list '** base exp)) +(define (base x) (car x)) +(define (exponent x) (cadr x)) +(put 'deriv '** deriv-exponentiation) + +;; part d. +#| +If we modify get, we just modify put and nothing else. +|# \ No newline at end of file