Purpose:

The goal of this problem set is to help you design functions that deal with arbitrarily large data.

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Drill:

HtDP: 9.5.4, 9.5.6, 10.1.7, 10.2.2, 10.2.3, 12.4 (large!)

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Required Problems:

Note: You may use DrScheme's HtDP Beginning Student Language (with list abbreviations) to solve the problems. If you are comfortable with using Intermediate Student Language (ISL) and facing the pitfalls that come with it, you are welcome to switch.

1. Design a program total-wage that computes the total wages a company pays in a single pay period from a list of wage records:

       (define-struct wage (name hours wage/hour))
       ;; LOW is one of: 
       ;;  -- (cons Wage empty)
       ;;  -- (cons Wage LOW)
       ;; Wage is (make-wage String Number Number)
   

   The company distributes overtime-pay if someone works for more than 40 hours per week. Overtime-pay means a 10% bonus for all hours over 40. The limit and the bonus are subject to wage negotiation.

   The design recipe demands a non-standard form of conditions for the main function. Why? How could you simplify the design?

   Furthermore the design guideline suggests the use of two distinct functions when applied to the data definition. Why?

2. Dolls are special in Russia. One is always nested inside another, and it (almost) never stops:

      ;; A Russian Doll (RD) is one of: 
      ;; -- (cons "body" empty)
      ;; -- (list Dress RD)
      ;; A Dress is a string (that describes a layer of dressing). 
   

   Yes, this is a proper data definition. Why?

   Design the function unwrap, which maps a RD to the list of Dresses.

   Design the function wrap, which maps a list of Dresses to a RD.

   Design the function image, which maps a RD to an Image. Your function should represent each layer of dress via a box that is larger than the representation of the inner RD and that is labeled with an appropriate text.

3. Design a program that renders an Expr as an image:

        (define-struct pls (x in?))
        ;; Expr is (make-pls 2LON Boolean)
        ;; interp. a pls struct represents an addition expression;
        ;; the boolean flag indicates whether it is an infix or 
        ;; a prefix expression. 
        ;; 2LON is one of: 
        ;; -- (cons Number (cons Number empty))
        ;; -- (cons Number 2LON)
        ;; interp. a 2LON is a list with at least two numbers
   

   Hint 1: The design guideline suggests the use of two distinct functions when applied to the data definition. Why? Hint 2: This problem is related to problem 1.3; re-read this problem for additional specifications.

4. Project: Re-design the editor from problem 1.4, but use a list-of-strings data representation for the state of the editor instead of the string-based one. Discuss the design trade-off in a paragraph of 20 to 30 words. (We will deduct points for each word in excess of 30.)