Title: Introduction to Scheme.

Instructions: Read Chapters 1-12 in Scheming on the Web and do the following exercises:

• Chapter 2, number 2.
• Chapter 3, number 1 (a-f).
• Chapter 4, number 2 (a-d).
• Chapter 6, numbers 1 and 3.
• Chapter 7, numbers 1, 3, and 5.
• Without using Scheme's built-in function REVERSE, write a recursive function MY-REVERSE that takes a list and returns a new list in which the top-level elements are in reverse order. Demonstrate your function on the list (A B C D) as well as a list of your own choosing.
• In this exercise, we'll explore "deep" processing of data. Again without using Scheme's built-in function REVERSE, write a recursive function DEEP-REVERSE that takes a list and returns a new list in which not only the top-level elements are in reverse order, but any sublists have been reversed as well. Any sub-sublists should be reversed, too, etc. Demonstrate your DEEP-REVERSE function on two examples, one of which is the list below and the other of which you make up yourself. Your example should contain at least one sublist with at least three elements.
  (THIS ILLUSTRATES (1 2 (3 4 5) 6 7) OK)
• Now let's work on a translation problem. Write a recursive function SPELL-NUMBERS that will take a list as its argument and process it as follows. The list will represent a sentence, such as (JOHN HAD 3 BAGS EACH CONTAINING 5 BALLS). Your procedure will return a new list in which each occurrence of a number has been replaced by its word equivalent. It should handle integers 0 through 10. In this example, the result would be (JOHN HAD THREE BAGS EACH CONTAINING FIVE BALLS). Demonstrate your function on this example and an example of your choice that involves five numbers.