solution to 2.57

diff --git a/src/sicp/ex2_57.clj b/src/sicp/ex2_57.clj
new file mode 100644 (file)
index 0000000..16c10ad
--- /dev/null
+++ b/src/sicp/ex2_57.clj
@@ -0,0 +1,77 @@
+(ns sicp.ex2_57
+  (:use [clojure.test]
+        [sicp.utils]))
+
+(defn exponentiation? [exp]
+  (= (first exp) '**))
+
+(defn base [exp]
+  (second exp))
+
+(defn exponent [exp]
+  (second (rest exp)))
+
+(defn variable? [x]
+  (symbol? x))
+
+(defn same-variable? [v1 v2]
+  (and (variable? v1)
+       (variable? v2)
+       (= v1 v2)))
+
+(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) (= (first x) '+)))
+
+(defn addend [s]
+  (second s))
+
+(defn augend [s]
+  (reduce make-sum 0 (rest (rest s))))
+
+(defn product? [x]
+  (and (list? x) (= (first x) '*)))
+
+(defn multiplier [p]
+  (second p))
+
+(defn multiplicand [p]
+  (reduce make-product 1 (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 -- derive " exp)))