7.1

Lab 4: Unions and recursion

Note: Whenever you design or write a function, you need to follow the design recipe.

1From unions to recursive unions

Recall unions of structures from class.

Exercise 1 Define three examples of railroad Wagons, according to the following data and structure definitions:
 ; A Wagon is one of: ;  - (make-passenger-wagon Company) ;  - (make-freight-wagon String Number) ; A Company is one of: ;  - "Alstom" ;  - "Bombardier" (define-struct passenger-wagon (model)) (define-struct freight-wagon (destination axles))
Your three examples should make use of every line of these data definitions.

Exercise 2 List the signatures for each of the courtesy functions for the passenger-wagon and freight-wagon structures.

Exercise 3 Write the template process-wagon for a function that processes a Wagon, and the template process-company for a function that processes a Company. Here’s a start:
 (define (process-wagon w) (cond [(passenger-wagon? w) (... FILL IN THIS BLANK)] [(freight-wagon? w) (... FILL IN THIS BLANK)])) (define (process-company c) (cond [(FILL IN THIS BLANK) ...] [(FILL IN THIS BLANK) ...]))
Each case of the template process-wagon should access all the fields of the input structure w, using courtesy functions you listed in Exercise 2.

Exercise 4 Point out where the data definition for Wagon refers to the data definition for Company. Does your template process-wagon refer to your template process-company in the corresponding place? It should.

Exercise 5 Design a function wagon-weight, which computes how many tons a Wagon weighs. An Alstom passenger wagon weighs 45 tons, and a Bombardier passenger wagon weighs 60 tons. Each axle of a freight wagon carries 6 tons of weight. Use the examples you defined in Exercise 1 in your tests, and follow the templates you wrote in Exercise 3. Those templates should guide you to design and use a helper function that computes the weight of a given passenger-wagon-model.

Exercise 6 Now we want to model a train of wagons on a railroad track. A shuttle is a train that that contains up to two wagons. In other words, a shuttle might have no wagons (so it is just an engine), or one wagon (attached to an engine), or two wagons (attached to an engine). Develop a data definition and corresponding structure definitions for a Shuttle. Here’s a start:
 ; A Shuttle is one of: ; - (FILL-IN-THIS-BLANK) ; - (FILL-IN-THIS-BLANK Wagon) ; - (FILL-IN-THIS-BLANK Wagon Wagon)
Don’t use any existing structures other than passenger-wagon and freight-wagon above. Instead, define your own structures.

Exercise 7 Write three examples of Shuttles. Your three examples should make use of every line of your data definition.

Exercise 8 List the signatures for each of the courtesy functions for the structures you defined in Exercise 6.

Exercise 9 Write the template process-shuttle for a function that processes a Shuttle. Here’s a start:
 (define (process-shuttle s) (cond [(FILL IN THIS BLANK) (... FILL IN THIS BLANK)] [(FILL IN THIS BLANK) (... FILL IN THIS BLANK)] [(FILL IN THIS BLANK) (... FILL IN THIS BLANK)]))
Like with process-wagon, each case of the template process-shuttle should access all the fields of the input structure s, using courtesy functions you listed in Exercise 8.

Exercise 10 Point out where the data definition for Shuttle refers to the data definition for Wagon. Does your template process-shuttle refer to your template process-wagon in the corresponding places? It should.

Exercise 11 Design the function shuttle-weight, which takes a Shuttle as input and computes how many tons the whole shuttle weighs. The engine weighs 130 tons. Use the examples you defined in Exercise 7 in your tests, and follow the template you wrote in Exercise 9. That template should guide you to define shuttle-weight using the function wagon-weight you designed in Exercise 5.

Exercise 12 Now we want to model a train that might be longer than a shuttle. A train might have no wagons (so it is just an engine), or it might contain a single wagon connected to the rest of the train. Develop a data definition and corresponding structure definitions for a TrainOfWagons. Here’s a start:
 ; A TrainOfWagons is one of: ; - (FILL-IN-THIS-BLANK) ; - (FILL-IN-THIS-BLANK Wagon TrainOfWagons)
Don’t use any existing structures other than passenger-wagon and freight-wagon above. Instead, define your own structures.

Exercise 13 Write three examples of TrainsOfWagons. Your three examples should make use of every line of your data definition.

Exercise 14 List the signatures for each of the courtesy functions for the structures you defined in Exercise 12.

Exercise 15 Write the template process-train-of-wagons for a function that processes a TrainOfWagons. Here’s a start:
 (define (process-train-of-wagons t) (cond [(FILL IN THIS BLANK) (... FILL IN THIS BLANK)] [(FILL IN THIS BLANK) (... FILL IN THIS BLANK)]))
Like with process-wagon, each case of the template process-train-of-wagons should access all the fields of the input structure t, using courtesy functions you listed in Exercise 14.

Exercise 16 Point out where the data definition for TrainOfWagons refers to the data definition for Wagon. Does your template process-train-of-wagons refer to your template process-wagon in the corresponding place? It should.

Exercise 17 Point out where the data definition for TrainOfWagons refers to itself. Does your template process-train-of-wagons refer to itself in the corresponding place? It should.

Exercise 18 Design the function train-weight, which takes a TrainOfWagons as input and computes how many tons the whole train weighs. Again, the engine weighs 130 tons. Use the examples you defined in Exercise 13 in your tests, and follow the template you wrote in Exercise 15. That template should guide you to define train-weight using the function wagon-weight you designed in Exercise 5 and the function train-weight itself.

2Extending the world

We would like to create a program using big-bang which initially draws a blank screen, but when you click the mouse (which produces the MouseEvent "button-down") it draws a circle at that position. When you click again, it should draw a new, larger circle at the new position, and the old circle should disappear.

Exercise 19 Design a data definition and structure definitions for representing the World in this program.

Exercise 20 Write three examples of Worlds.

Exercise 21 Write the template for processing the World data definition that you have defined.

Exercise 22 Design the appropriate to-draw and on-mouse functions for this big-bang program. Hint: you don’t need an on-tick function.

3Challenges

Now apply the lessons from the first part of the lab to your big-bang program.

Exercise 23 Modify the program from Exercise 22 so that instead of the old circle disappearing when you click the mouse, new circles appear each time, so that your world has more and more circles over time. This should be very similar to the program we wrote in class.

Exercise 24 Modify the program from Exercise 23 that instead of the circles staying where they start, they all move in some direction after being created.