Add solutions to exercises from section 1.1

ex-1.01.txt

@@ -0,0 +1,28 @@
+10 -> 10
+(+ 5 3 4) -> 12
+(- 9 1) -> 8
+(/ 6 2) -> 3
+(+ (* 2 4) (- 4 6)) -> 6
+(define a 3) -> a (3)
+(define b (+ a 1)) -> b (4)
+(+ a b (* a b)) -> 19
+(= a b) -> #f
+
+(if (and (> b a) (< b (* a b)))
+    b
+    a)
+-> 4
+
+(cond ((= a 4) 6)
+      ((= b 4) (+ 6 7 a))
+      (else 25))
+-> (+ 6 7 a) -> 16
+
+(+ 2 (if (> b a) b a))
+-> 6
+
+(* (cond ((> a b) a)
+         ((< a b) b)
+         (else -1))
+   (+ a 1))
+-> 16

ex-1.02.scm

@@ -0,0 +1,6 @@
+(/ (+ 5
+      4
+      (- 2 (- 3 (+ 6 (/ 4 5)))))
+   (* 3
+      (- 6 2)
+      (- 2 7)))

ex-1.03.scm

@@ -0,0 +1,9 @@
+#| BEGIN (Write your solution here) |#
+(define (sqr x) (* x x))
+(define (solution a b c)
+  (cond ((and (<= a b) (<= a c))
+         (+ (sqr b) (sqr c)))
+        ((and (<= b a) (<= b c))
+         (+ (sqr a) (sqr c)))
+        (else (+ (sqr a) (sqr b)))))
+#| END |#

ex-1.04.txt

@@ -0,0 +1,2 @@
+The if statement will select the appropriate function to execute, if b>0, it
+will add b, otherwise it will subtract it.

ex-1.05.txt

@@ -0,0 +1,4 @@
+If the interpreter uses normal-order evaluation, it will expand test into an
+"if", which will then evaluate to 0, if it uses applicative-order evaluation,
+it will first evaluate 0 and (p), while trying to evaluate (p), it will enter
+an infinite loop.

ex-1.06.txt

@@ -0,0 +1,3 @@
+The program will run into an infinite loop, because in every execution of
+square-iter, the improve function is called again, since this is an
+applicative-ordered language

ex-1.07.scm

@@ -0,0 +1,18 @@
+#| BEGIN (Write your solution here) |#
+(define (average a b)
+  (/ (+ a b) 2))
+
+(define (improve guess x)
+  (average guess (/ x guess)))
+
+(define (good-enough? guess x)
+  (< (abs (- (improve guess x) guess)) 0.0001))
+(define (sqrt-iter guess x)
+  (if (good-enough? guess x)
+      guess
+      (sqrt-iter (improve guess x)
+                 x)))
+
+(define (square-root x)
+  (sqrt-iter 1.0 x))
+#| END |#

ex-1.08.scm

@@ -0,0 +1,18 @@
+#| BEGIN (Write your solution here) |#
+(define (improve guess x)
+  (/ (+ (/ x guess guess)
+        (* 2 guess))
+     3))
+
+(define (good-enough? guess x)
+  (< (abs (- (improve guess x) guess)) 0.0001))
+
+(define (cbrt-iter guess x)
+  (if (good-enough? guess x)
+      guess
+      (cbrt-iter (improve guess x)
+                 x)))
+
+(define (cube-root x)
+  (cbrt-iter 1.0 x))
+#| END |#