From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Sun, 5 Sep 2010 16:41:43 +0000 (+0530)
Subject: A partially working solution for 2.58b. Still need expression
X-Git-Url: https://git.rkrishnan.org/?a=commitdiff_plain;h=85c0a6f69117ef5e69bf1d573e4bf4c6340103a6;p=sicp.git

A partially working solution for 2.58b. Still need expression
simplification.
---

diff --git a/src/sicp/ex2_58b.clj b/src/sicp/ex2_58b.clj
new file mode 100644
index 0000000..9d2ffc9
--- /dev/null
+++ b/src/sicp/ex2_58b.clj
@@ -0,0 +1,180 @@
+(ns sicp.ex2_58b
+  (:refer-clojure :exclude (number?))
+  (:use [clojure.test]
+        [sicp.utils]))
+
+;;; differentiation of infix expressions
+;;    part b. Assume standard algebraic form.
+;;
+(defn third [x]
+  (if (= (count x) 3)
+    (second (rest x))
+    (rest (rest x))))
+
+(defn same-op? [op x]
+  (= op x))
+
+(defn peek-op [expr]
+  (second expr))
+
+(defn- first-expr* [expr op]
+  (cond (and (nil? (peek-op expr)) (empty? expr)) nil
+        (and (same-op? op (peek-op expr))
+             (= op '*)) (cons (first expr) (cons (second expr) (first-expr* (rest (rest expr)) op)))
+        :else (list (first expr))))
+
+(defn first-expr [expr]
+  (let [op (second expr)]
+    (when (not (nil? op))
+      (first-expr* expr op))))
+
+(defn- rest-expr* [expr op]
+  (cond (empty? expr) nil
+        (and (same-op? op (peek-op expr)) (= op '*)) (rest-expr* (rest (rest expr)) op)
+        :else (rest (rest expr))))
+
+(defn rest-expr [expr]
+  (let [op (second expr)]
+    (when (not (nil? op))
+      (rest-expr* expr op))))
+
+(defn- op-expr* [expr op]
+  (cond (empty? expr) nil
+        (same-op? op (peek-op expr)) (op-expr* (rest (rest expr)) op)
+        :else (if (= op '*) (peek-op expr) op)))
+
+(defn op-expr [expr]
+  (let [op (second expr)]
+    (when (not (nil? op))
+      (op-expr* expr op))))
+
+(defn exponentiation? [exp]
+  (= (second exp) '**))
+
+(defn base [exp]
+  (first exp))
+
+(defn exponent [exp]
+  (third exp))
+
+(defn variable? [x]
+  (if (and (list? x)
+           (= (count x) 1))
+    (symbol? (first x))
+    (symbol? x)))
+
+(defn same-variable? [v1 v2]
+  (cond (list? v1) (and (variable? v1)
+                        (variable? v2)
+                        (= (first v1) v2))
+        (list? v2) (and (variable? v1)
+                        (variable? v2)
+                        (= v1 (first v2)))        
+        :else (and (variable? v1)
+                   (variable? v2)
+                   (= v1 v2))))
+
+(defn number? [exp]
+  (if (and (list? exp)
+           (= (count exp) 1))
+    (clojure.core/number? (first exp))
+    (clojure.core/number? exp)))
+
+(defn =number? [exp num]
+  (and (number? exp)
+       (= exp num)))
+
+(defn make-sum [a1 a2]
+  (cond (=number? a1 0) a2
+        (=number? a2 0) a1
+        (and (number? a1) (number? a2)) (+ a1 a2)
+        :else (list a1 '+ a2)))
+
+(defn 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)))
+
+(defn sum? [x]
+  (and (list? x) (= (op-expr x) '+)))
+
+(defn addend [s]
+  (first-expr s))
+
+(defn augend [s]
+  (rest-expr s))
+
+(defn product? [x]
+  (= (second x) '*))
+
+(defn multiplier [p]
+  (first p))
+
+(defn multiplicand [p]
+  (rest (rest p)))
+
+(defn make-exponentiation [b n]
+  (cond (=number? b 1) 1
+        (=number? b 0) 0        
+        (=number? n 1) b
+        (=number? n 0) 1
+        (and (number? b) (number? n)) (Math/pow b n)
+        :else (list b '** n)))
+
+(defn 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-product (make-exponentiation (base exp)
+                                                                               (- (exponent exp) 1))
+                                                          (deriv (base exp) var)))
+        :else (str "unknown expression type -- deriv " exp)))
+
+
+(deftest test-deriv-and-helpers
+  (let [e1 1
+        e2 '(x)
+        e3 '(x + 1)
+        e4 '(x * y)
+        e5 '(x * x)
+        e6 'x
+        e7 '(x + 2 * x + 2)
+        e8 '(x * y + 1)]
+    (are [p q] [= p q]
+         (first-expr e3) '(x)
+         (op-expr e3)    '+
+         (rest-expr e3)  '(1)
+         (first-expr e4) '(x * y)
+         (op-expr e4)    nil
+         (rest-expr e4)  ()
+         (first-expr e7) '(x)
+         (op-expr e7) '+
+         (rest-expr e7) '(2 * x + 2)
+         (first-expr e8) '(x * y)
+         (op-expr e8) '+
+         (rest-expr e8) '(1))))
+
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