2500 F '12
The Hand In
Set 1
Set 2
Set 3
Set 3h
Set 4
Set 4h
Set 5
Set 5h
Set 6
Set 6h
Set 7
Set 7h
Set 8
Set 9
Set 8h
Set 10
Set 9h
Set 11
Set 12
Set 10h

Problem Set 10

Due date: 11/14 @ 11:59pm

Programming Language: Intermediate Student Language with lambda

The goal of this problem set is to practice using DrRacket's loop functions. In addition we will look into local and lambda (λ) a bit more.

Problem A1:

Given the following sorting function:

;; sort-a : [Listof Number]  ->  [Listof Number] 
;; to construct a list with all items from alon in increasing order
(define (sort-a alon)
  (local ((define (insert an alon)
            (cond [(empty? alon) (list an)]
                  [( < an (first alon)) (cons an alon)]
                  [else (cons (first alon) 
                              (insert an (rest alon)))])))
         (cond [(empty? alon) empty]
               [else (insert (first alon) (sort-a (rest alon)))])))
Design an abstracted version of the sort-a function which consumes the comparison as an additional argument and uses a loop function. Use this function to design sort-ascending and sort-descending, which sort a [Listof Number] in ascending and descending order, respectively.

Problem A2:

Decide which of the following phrases are legal lambda-expressions:
  1. (lambda (x y) (x y y))
  2. (lambda () 10)
  3. (lambda (x) x)
  4. (lambda (x y) x)
  5. (lambda x 10)
Explain why they are legal or illegal.

Problem A3:

In an arithmetic sequence, a0, a1, a2,..., an, an+1,..., each successor term an+1 is the result of adding a fixed constant to an. For example, the sequence 8, 13, 18, 23, ... has a starting point of 3 and the constant is 5. From these two facts, called starting point and summand, respectively, all other terms in the sequence can be determined.
  1. Develop the recursive function a-fives, which consumes a natural number and recursively determines the corresponding term in the above series.
    (a-fives 0) -> 8
    (a-fives 1) -> 13 
  2. Develop the function seq-a-fives, which consumes a natural number n and creates the sequence of the first n terms according to a-fives. Hint: Use build-list.

Problem A4:

DrRacket has lots of great abstract functions for processing lists (pg. 313, Sect. 21.2, or the online version).

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 '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.

For each you may use a local function or an anonymous (lambda) function.

Note: if you do not use the DrRacket loop 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.
  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 your function... it must return a [Listof Grade]!

last updated on Sun Dec 2 14:52:34 EST 2012generated with Racket