Laboratory: Pairs and pair structures

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: Some pictures
  • Exercise 2: Some pairs
  • Exercise 3: More pictures
  • Exercise 4: Are they pairs?
  • Exercise 5: Counting pairs
• Notes
  • Notes on Exercise 5

Exercises

Exercise 0: Preparation

Start DrScheme.

Exercise 1: Some pictures

Draw box-and-pointer diagrams for each of the following lists:

• ((x) y z)
• (x (y z))
• ((a) b (c ()))

Exercise 2: Some pairs

Enter each of the following expressions into Scheme. In each case, explain why Scheme does or does not use the dot notation when displaying the value.

• (cons 'a "Walker")
• (cons 'a null)
• (cons null 'a)
• (cons null (cons null null))

Exercise 3: More pictures

Draw a box-and-pointer representation of the value of each expression in the previous exercise.

Exercise 4: Are they pairs?

What do you think that pair? will return for each of the following? How about list?. Confirm you answer experimentally and explain any that you found particularly tricky.

• (cons 'a 'b)
• (cons 'a (cons 'b 'c))
• (cons 'a null)
• null
• (list 'a 'b 'c)
• (list 'a)
• (list)

Exercise 5: Counting pairs

Define and test a procedure named cons-cell-count that takes any Scheme value and determines how many boxes would appear in its box-and-pointer diagram. (The data structure that is represented by such a box, or the region of a computer's memory in which such a structure is stored is called a cons cell. Every time the cons procedure is used, explicitly or implicitly, in the construction of a Scheme value, a new cons cell is allocated, to store information about the car and the cdr. Thus cons-cell-count also tallies the number of times cons was invoked during the construction of its argument.)

For example, the structure in the following box-and-pointer diagram contains seven cons-cells, so when you apply cons-cell-count to that structure, it should return 7. On the other hand, the string "sample" contains no cons-cells, so the value of (cons-cell-count "sample") is 0.

Use cons-cell-count to find out how many cons cells are needed to construct the list (0 (1 (2 (3 (4))))). Draw a box-and-pointer diagram of this list to check the answer.

Notes

Notes on Exercise 5

If, for some reason, you are having troulbe creating the list

(0 (1 (2 (3 (4)))))

, try

(list 0 (list 1 (list 2 (list 3 (list 4)))))