Add Matrix exampel

aspUnify.tex

@@ -77,6 +77,48 @@ Java has adopted more and more type inference features over time.
 Currently Java only has local type inference.
 We want to bring type inference for Java to the next level.
 
+Our type inference algorithm for Java should be able to retrieve missing type annotations
+in a Java program.
+The main difference from existing type inference algorithms for Java is that we also allow method types to be omitted in the input program.
+
+\begin{figure}
+\begin{lstlisting}
+public class Matrix extends Vector<Vector<Integer>> {
+   
+    public Matrix(vv) {
+        Integer i;
+        i = 0;
+        while(i < vv.size()) {
+            this.add(vv.elementAt(i));
+            i=i+1;
+        } 
+    }
+
+    public mul(m) {
+        var ret = new Matrix();
+        var i = 0;
+        while(i < size()) {
+            var v1 = this.elementAt(i);
+            var v2 = new Vector<Integer>();
+            var j = 0;
+            while(j < v1.size()) {
+                var erg = 0;
+                var k = 0;
+                while(k < v1.size()) {
+                    erg = erg + v1.get(k)
+                             * m.get(k).get(j);
+                    k++; }
+                v2.addElement(erg);
+                j++; }
+            ret.addElement(v2);
+            i++; 
+         }
+        return ret;
+    }
+}
+\end{lstlisting}
+\end{figure}
+
 \section{Subtyping}
 \begin{mathpar}
 \inferrule[Refl]{}{