Updates to week 2

lectures/progfun1-2-5.md

@@ -47,7 +47,7 @@ This definition introduces two entities:
  - A \red{constructor} `Rational` to create elements of this type.
 
 Scala keeps the names of types and values in \red{different namespaces}.
-So there's no conflict between the two defintions of `Rational`.
+So there's no conflict between the two definitions of `Rational`.
 
 Objects
 =======
@@ -106,11 +106,11 @@ Implementing Rational Arithmetic
           r.numer * s.denom + s.numer * r.denom,
           r.denom * s.denom)
 
-      def makeString(r: Rational) =
-        r.numer + "/" + r.denom
+      def makeString(r: Rational): String =
+        s"${r.numer}/${r.denom}"
 
 \begin{worksheet}
-      \verb@makeString(addRational(new Rational(1, 2), new Rational(2, 3)))@ \wsf       7/6
+      \verb@makeString(addRational(Rational(1, 2), Rational(2, 3)))@ \wsf       7/6
 \end{worksheet}
 
 
@@ -137,12 +137,12 @@ Here's a possible implementation:
       def numer = x
       def denom = y
       def add(r: Rational) =
-        new Rational(numer * r.denom + r.numer * denom,
-                     denom * r.denom)
+        Rational(numer * r.denom + r.numer * denom,
+                 denom * r.denom)
       def mul(r: Rational) = ...
       ...
-      override def toString = numer + "/" + denom
-    }
+      override def toString = s"$numer/$denom"
+    end Rational
 
 \red{Remark}: the modifier `override` declares that `toString`
 redefines a method that already exists (in the class `java.lang.Object`).
@@ -153,9 +153,9 @@ Calling Methods
 
 Here is how one might use the new `Rational` abstraction:
 
-      val x = new Rational(1, 3)
-      val y = new Rational(5, 7)
-      val z = new Rational(3, 2)
+      val x = Rational(1, 3)
+      val y = Rational(5, 7)
+      val z = Rational(3, 2)
       x.add(y).mul(z)
 
 Exercise