• Sethi: Chapter 1 (handout).
• SICP: Chapter 1 (on the web).

• R⁴RS (handout). This will be very useful for completing this assignment.

Try these questions out before section. First try to figure out the answers in your head. Then try typing them into the scheme interpreter.

1. Scheme variables and list constructs.

   Given the following definitions:

   (define x 10)
   (define y 44)
   (define foo '(1 2 3))
   (define bar '(a b c))
   

   what are the results of the following pieces of scheme code:
   1. x
   2. (cons x foo)
   3. (cons y bar)
   4. (list x y)
   5. (list x foo)
   6. '(x y)
   7. (car bar)
   8. (cdr bar)
   9. (+ x y)

2. Scheme flow control.

   What are the results of the following pieces of code?

   1. (if #f 5 10)
      

   2. (if (or #t #f)  5 10)
      

   3. (if #t 
          (if #f 2 3) 
          10
      )
      

   4. (define x 3)
      (cond ((= x 1)     44)
            ((= x 2)     (+ 5 50))
            ((= x 3)     (* 6 11))
            (else        (- 80 3))
      )
      

   5. (let ((x 5)
            (y 10)
           )
           (+ x y)
      )
      

3. Write predicate char-hex-letter? which returns true if its single argument is one of the letters that can be in a hexadecimal number, ``a'' through ``f'', in either upper or lower case). Write predicate char-hex? which returns true if its single argument is a hexadecimal character (letter or digit). For example:

   (char-hex-letter? #\b)          => #t
   (char-hex-letter? #\3)          => #f
   (char-hex? #\B)                 => #t
   (char-hex? #\3)                 => #t
   

These are some sample problems that we will be discussing in section. Use the error function for handling errors.

1. Write a function char-hex->number that converts a hexadecimal digit into a number (do not use the primitive string->number function). For example:

   (char-hex->number #\b)          => 11
   

2. Write a recursive function string-hex->number that takes a hexadecimal string and converts it into a number (do not use the primitive string->number function).

   (string-hex->number "3f")       => 63
   

3. Recursively define a function positive-only that takes a list and returns a list with the positive elements in it. For example:

   (positive-only '())             => ()
   (positive-only '(1 2 -3 4))     => (1 2 4)
   (positive-only '(-1 -2 -3))     => ()
   

Complete the following. You do not have to handle errors in input gracefully; however, if you want to you may use the error primitive function; e.g. (error "error in input"). Do not forget to turn in a print out of your source code as well as example executions of your code on test cases.

1. (5 points) Write a function, string-hex->char, that takes a hexadecimal string and returns the character that it represents. For example, the character ``a'' is represented as decimal 97 in ASCII which is 61 in hex.

   (string-hex->char "61")         => #\a
   

2. (5 points) Write a function, decode-hex-string, that takes a string and converts it as follows:

   • ``+'' gets converted to whitespace.
   • ``%XX'', where XX is a two digit hex number, gets converted to the character that it represents.
   • All other characters are unchanged.

   For example:

   (decode-hex-string "In+hex+5+%2b+5+is+%27a%27.")
         => "In hex 5 + 5 is 'a'."
   

3. (5 points) Write a function split that takes two arguments, a character ch and a string str. It breaks str up into a list of strings at each occurrence of ch. For example:

   (split #\space "this is a test")
          => ("this" "is" "a" "test")