# Symbols and Lists

Summary: In this laboratory, you will explore the basic operations for working with lists and symbolic values. You may want to refer to the reading on symbols and the reading on lists as you work on this lab.

Important Procedures: `append`, `car`, `cdr`, `cons`, `length`, `list`, `list-ref`, and `reverse`.

Contents:

## Exercises

Start DrScheme.

### Exercise 1: Two Simple Lists

a. Call the `cons` procedure to create a list that has the number 1 as its first and only element. The result of your call should be `(1)`.

b. Call the `cons` procedure to create a list that has the symbols `a` and `b` as its two elements. The result of your call should be `(a b)`.

### Exercise 2: Interpreting Compound `cons` Operations

a. Figure out (without using DrScheme) the result of the following expression.

```(cons 'alpha (cons 'beta (cons 'gamma (cons 'delta null))))
```

### Exercise 3: Non-Lists

a. Determine the result of the expression `(cons 'a 'b)`.

b. Determine the result of cons-ing `'d` to the front of the value you created in step a.

Neither of these values are lists! Make sure that you are able to distinguish them from lists when looking at results.

### Exercise 4: Using the `list` Procedure

Call the procedure `list`, supplying the numerals `17` and `43` as arguments. Describe the value returned by the procedure.

### Exercise 5: Building a List of Symbols

a. How would you call the `list` procedure to create a list containing the symbols `alpha`, `beta`, and `gamma`, in that order?

### Exercise 6: Empty Lists

How would you invoke the `list` procedure to create an empty list?

### Exercise 7: Repeated Elements

Determine by experiment whether it is possible to create a list in which the same element occurs more than once.

### Exercise 8: A Small `cdr`

a. What is the `cdr` of a one-element list?

### Exercise 9: Extracting Information from Empty Lists

It makes no sense to apply the `car` and ``` cdr``` procedures to an empty list, because there's no way to split off the first element of a list that has no elements. What happens if you try it anyway? Find out by having DrScheme evaluate a deliberately incorrect procedure call.

### Exercise 10: Extracting Information from Symbols

a. Does it make sense to apply `car` and `cdr` to values other than lists? Why or why not?

b. Determine what happens if you apply these procedures to symbolic values and numeric values.

### Exercise 11: Compound Lists

a. Create the list `(e)`.

b. Create the list `(d (e))`.

c. Create the list `(b c)`.

d. Create the list `(a (b c) (d (e)))`. You may use `list`, `cons`, or a combination of the two.

### Exercise 12: It's All Greek to Me

Use Scheme to give the name `Greek-letters` to the list constructed by the expression

```(list 'alpha 'beta (list 'gamma-1 'gamma-2) 'delta)
```

Then use the `length` procedure to confirm that it has four elements.

### Exercise 13: The Length of Emptiness

Determine the length of the empty list.

### Exercise 14: Checking Your Own Length

a. Create a list of length 5. I don't care what appears in the list, provided that it is in good taste.

b. Check your answer by having Scheme compute the length of that list.

### Exercise 15: Length of Compound Lists

a. Create the list `(a (b c) (d (e)))` and name it `letters`.

b. What do you think the length of `letters` should be?

c. Experimentally determine the length of `letters`.

d. Explain the result.

### Exercise 16: Reversing Lists

Use Scheme to compute the reversal of the list whose elements are the symbols `senior`, `third-year`, `second-year`, and `freshling`, in that order.

### Exercise 17: Reversing Compound Lists

a. If a list has another list as one of its elements (as in the case of `letters` above), should `reverse` reverse that inner list as well as the outer one?

b. Find out by experiment what Scheme does.

### Exercise 18: Joining Lists

a. Create a list named `symbols` with the elements `alpha` and `beta` as its elements.

b. Create a list named `numbers` with the numbers 1, 2, and 3 as its elements.

c. Use Scheme to find the result of joining together (with ``` append```) `symbols` and `numbers`.

d. How many elements does the resulting list have?

### Exercise 19: Listing Lists

a. Invoke the procedure `list`, applying it to `symbols` and `numbers` from the previous exercise.

b. How many elements does the resulting list have?

c. The answer to this question is different from the answer to the question at the end of the previous exercise. Why?

### Exercise 20: Cons-ing Lists

a. Write a call to the procedure `cons`, applying it to `symbols` and `numbers`.

b. How many elements does the resulting list have?

c. Why is the answer to this question different from the answers to the questions at the end of the previous two exercises?

### Exercise 21: Extracting Elements

Write a call to the `list-ref` procedure that will extract the fourth element of the list

```(38 72 apple -1/3 sample)
```

That is, you should extract the number -1/3.

### Exercise 22: Wrapup

Quit DrScheme and log out of the workstation.

## Extras

If you have extra time,

• Build the list `(a (b c) (d (e)))` using `cons` rather than quote or `list`.
• Build the list `(a (b (c (d (e ())))))` using `cons`.
• Without using Scheme, determine the length of that list.

## Notes

### Notes on Exercises 18, 19, and 20

The `append` procedure joins together the elements of a list to make a new list. Hence, when you append two lists together, the total number of elements in the new list is the sum of the number of elements in the lists.

The `list` procedure creates a new list whose elements are the parameters to `list`. Hence, if `list` takes two parameters, the length of the result is always two, regardless of what those parameters are.

The `cons` procedure builds a new list by placing its first parameter at the start of its second parameter (which is a list). Hence, the length of the result is one more than the length of the second parameter.

## History

Disclaimer: I usually create these pages on the fly, which means that I rarely proofread them and they may contain bad grammar and incorrect details. It also means that I tend to update them regularly (see the history for more details). Feel free to contact me with any suggestions for changes.

This document was generated by Siteweaver on Thu Sep 13 20:54:22 2007.
The source to the document was last modified on Sun Jan 28 21:52:19 2007.
This document may be found at `http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2007S/Labs/lists.html`.

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Samuel A. Rebelsky, rebelsky@grinnell.edu

Copyright © 2007 Samuel A. Rebelsky. 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.