This problem set continues the study of complex data and first class functions. Some of the problems cover functions that process two arguments from classes with complex (self-referential) data definitions, others deal with functions that take functions as arguments.

--- You must follow the design recipe. The graders will look for data definitions, contracts, purpose statements, tests, and properly organized function definitions. For the latter (as before), you must design templates. You do not need to include the templates with your homework, however. If you do, comment them out.

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HtDP Problems:

Do not use equal? for these problems, you will not get points if you do.

17.8.4: Assume that the lists do not contain duplicates
17.8.7,
17.8.8: Use the definitions of BT/BST from Sect. 14.2 (~pg. 199).

19.1.5, 19.1.6, 19.2.2, 19.2.4

Problem A1:

Scheme has lots of great abstract functions for processing lists (pg. 313, Sect. 21.2).

Given the following data definitions:

;; A Grade is: (make-grade Symbol Number)
(define-struct grade (letter num))

;; The Symbol in a Grade represents
;;    'A  >= 90
;;    'B  >= 80
;;    'C  >= 70
;;    'D  >= 60 
;;    'F  < 60

;; A (listof Grades) ...
(define grades 
  (list (make-grade 'D 62) (make-grade 'C 79) (make-grade 'A 93) (make-grade 'B 84) 
        (make-grade 'F 57) (make-grade 'F 38) (make-grade 'A 90) (make-grade 'A 95)
        (make-grade 'B 82) (make-grade 'A 91) (make-grade 'A 94) (make-grade 'B 84)
        (make-grade 'C 71) (make-grade 'F 58) (make-grade 'F 42) (make-grade 'B 86)
        (make-grade 'A 95) (make-grade 'F 53) (make-grade 'F 43) (make-grade 'F 52)
        (make-grade 'C 76) (make-grade 'A 90) (make-grade 'F 55) (make-grade 'C 74)
        (make-grade 'A 92) (make-grade 'B 86) (make-grade 'F 43) (make-grade 'C 73)))

Design the requested functions to manipulate Grades. You must use the given list as one of your tests. Use the Intermediate Student language in DrScheme.

Note: if you do not use the Scheme function mentioned, you will not recieve credit for the sub-problem!

1. Design the function log->lon that converts a (listof Grade) into a (listof Number) that contains just the numerical grade, using the Scheme function map.
2. Using foldr, design the function best-grade that finds the highest Grade in a (listof Grade).
3. Design a function just-As that returns a list of only the 'A grades, using filter.
4. Use andmap to design the function all-pass? that checks to see if all the Grades in a given list are not 'F. (** Return a Boolean!)
5. Finally design the function bonus that adds 5 to all of the Grades in a given list, and updates the letter portion of the Grade if it changes. Use map to design it your function... it must return a (listof Grade)!