The Java Execution Model (Continued)

4. Execution Trees as Nested Boxes

Earlier in the semester, we noticed the correspondence between trees and nested boxes. We can use this correspondence to represent execution trees in terms of nested boxes. Since nested boxes are easy to represent as nested tables within HTML, we can use HTML tables to represent the content of execution trees. For instance, below is the execution tree from the end of Section 2 represented as a table. Note how the variables can only be used in statements within the columns they appear.

H.paint(G);

this:

H

g:

G

H.drawHole(G, 50);

this:

H

g:

G

rad:

50

g.setColor(BLUE);

g.fillRect(10,30,100,100);

g.setColor(YELLOW);

g.fillOval(10,30,100,100);

H.drawHole(G, 25);

this:

H

g:

G

rad:

25

g.setColor(BLUE);

g.fillRect(35,55,50,50);

g.setColor(YELLOW);

g.fillOval(35,35,50,50);

Since the variable have already been "used" by the time of the final execution tree, we will sometimes abbreviate the above by omitting the variables, as in the following diagram:

H.paint(G);

H.drawHole(G, 50);

g.setColor(BLUE);

g.fillRect(10,30,100,100);

g.setColor(YELLOW);

g.fillOval(10,30,100,100);

H.drawHole(G, 25);

g.setColor(BLUE);

g.fillRect(35,55,50,50);

g.setColor(YELLOW);

g.fillOval(35,35,50,50);

5. Local Variables

The above example did not explain how to model the declaration of local variables. Recall that local variables may be introduced by statements like:

    int a = (x + width)/2;
    Polygon p = new Polygon();
    Color cb = c.brighter();

To illustrate the handling of local variables, let's modify the Hole1 class to make its structure clearer.

import 
java.awt.*;
import java.applet.Applet;
 
public class Hole2 
extends Applet {
 
  public void paint(Graphics g) 
{
    this.drawHole(g, 50);
    this.drawHole(g, 25);
  }
 
  public void drawHole(Graphics g, 
int rad) {
      // Draw a yellow circle with radius rad at point (60,80) inscribed in a blue 
square.
    this.drawHoleAt(g, 60, 80, rad);
  }
 
  public void drawHoleAt(Graphics g, 
int x, int y, 
int rad) {
      // Draw a yellow circle with radius rad at point (x,y) inscribed in a blue 
square.
    this.fillSquare(g, x-rad, y-rad, 2*rad, Color.blue);
    this.fillCircle(g, x, y, rad, Color.yellow);
  }
 
  public void fillSquare(Graphics g, 
int x, int y, 
int side, Color clr) {
     // Fill with color clr a square whose upper left corner is (x, y)
     // and whose side length is side.
    g.setColor(clr);
    g.fillRect(x, y, side, side);
  }
 
  public void fillCircle(Graphics g, 
int x, int y, 
int rad, Color clr) {
     // Fill with color clr a circle with center point (x, y) and radius rad.
    int side = 2* rad;
    g.setColor(clr);
    g.fillOval(x-rad, y-rad, side, side);
  }
}

The above Hole2 class draws the same logo as the Hole1 class, but uses the extra methods drawHoleAt, fillSquare, and fillCircle. fillCircle uses the declaration int side = 2 * rad to introduce a local variable side that is twice the radius rad. When the red control dot encounters a declaration like this, it adds a new variable name side to the set of variables of the local execution frame for fillCircle.The execution tree that results from sending a paint message to Hole2 instance H2 with argument G2 is shown below in table form. Pay particular attention to the extra side variables in the frame for fillCircle.

Click here for the final example table. (Be patient, it takes a minute or two for Netscape to build this table.)