# Laboratory: Pairs and Pair Structures

Summary: In this laboratory, you will further ground your understanding of what happens “behind the scenes” when Scheme deals with lists and other pair-based structures.

## Preparation

Make sure you have some blank pieces of paper (lined is okay) and something with which to write.

## Exercises

### Exercise 1: Some Pictures

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

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

Be prepared to share your pictures with me.

### 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 'a "null")`
• `(cons 'a "()")`
• `(cons null 'a)`
• `(cons null (cons null null))`

### Exercise 3: More Pictures

Draw a box-and-pointer representation of the value of the last two expressions 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?`. Attempt to confirm each 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: Is It A List?

You may recall that we told you that many kinds of data are defined recursively. For example, a list is either (1) null or (2) cons of anything and a list.

Using that recursive definition of lists, write a procedure, `(listp? val)`, that determines whether or not `val` is a list.

You may not use `list?` in your definition of `listp?`.

## For Those With Extra Time

If you were able to complete the primary exercises with time to spare, you might want to consider the following problems:

### Extra 1: Finding the Last element

Write a procedure, `(last pairthing)` that finds the “last” value in a list-like pairs structure. If the pair structure is actually a list, return the last element of the list. Otherwise, follow the cdrs until you find the last pair, and return the cdr of that pair.

In solving this problem you should only step through the list once.

### Extra 2: Rewriting `listp?`

Write `listp?` without using `if` or `cond`.

Samuel A. Rebelsky, rebelsky@grinnell.edu

Copyright (c) 2007-8 Janet Davis, Matthew Kluber, and Samuel A. Rebelsky. (Selected materials copyright by John David Stone and Henry Walker and used by permission.)

This material is based upon work partially supported by the National Science Foundation under Grant No. CCLI-0633090. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License. To view a copy of this license, visit `http://creativecommons.org/licenses/by-nc/2.5/` or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA.