From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Sun, 19 Sep 2010 18:45:21 +0000 (+0530)
Subject: solution to 2.73
X-Git-Url: https://git.rkrishnan.org/pf/content/en/seg/cyclelanguage?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.
+|#
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