304
Objectives CSSE You should learn
Assignment 5
to write more complicated recursive procedures in a functional style. to better understand and use let, lambda, letrec, and named let. to FOLLOW THE GRAMMAR! (see page 12 of EoPL)
At the beginning of your file, there should be a comment that includes your name and the assignment number. Before
the code for each problem, place a comment that includes the problem number. Please place the code for the problems in order by problem number. You may use solutions from previous assignments in your solutions for this assignment.
Turning in this assignment: It is easiest if you place all of your Scheme code for this assignment in one file. If you prefer
to place your code into more than one file, you need to create a .zip archive and submit it to the grading program. However, if you do this, the archive must contain a file called main.ss, which loads the other files. For more details, see the help page of the grading software. You should thoroughly test your procedures, but what you turn in should only include the definitions of the required procedures and any auxiliary procedures that they use. Do not include your test code in the file that you submit unless you comment (or quote) it out. I suggest keeping your test code in a separate file called 5-test.ss, in which you can include (load "5.ss"). You may choose any names that you wish for helper procedures that you write, but the required procedures must have exactly the specified names and they must work for the specified number and types of arguments.
Where submit your code. Submit your code to the server located at: https://plc.cs.rose-hulman.edu , where you can also see
whether your code passes our test cases. Be sure to choose assignment A5 before submitting.
Restriction on Mutation. No mutation or I/O allowed! This includes: do not use set!, and the only use of "define"
should follow this pattern: (define <some_variable> (lambda ...))
Abbreviations for the textbooks:
EoPL TSPL
- Essentials of Programming Languages, 2nd Edition - The Scheme Programming Language, 3rd Edition
No argument error-checking is required. Unless specified otherwise, you may assume that all arguments have the
correct form.
Reading Assignment:
See the Schedule page
Problems to think about:
I do not think you need to take the time to write out solutions to these problems, but you should consider them. EoPL Exercises 1.6 and 1.7, page 16 ; 1.8 and 1.9, page 18.
Written problems to turn in (at the beginning of class):
#W1 (10 points) EoPL, Exercise 1.4, page 8 (your proof must use mathematical induction) #W2(15 points) Consider the following grammar for a language L whose terminal symbols are a and b: <S> ::= <A><A> <A> ::= <A><A><A> | b<A> | <A>b | a (a) Describe in simple English (i.e. with no recursion or iteration in your description) the language L generated by this grammar, assuming that <S> is the start symbol. (b) Prove (using mathematical induction) that every string of terminals that can be generated by this grammar is a string in the language you described in part (a). (c) Describe algorithm an that, given a string w in L, produces a sequence of productions that can be used to create a derivation of w from <S>.
CSSE 304 Assignment 5
Page 1
04/27/09
Programming problems to submit to the grading program (by 8:05 AM):
Read the instructions and naming conventions at the beginning of Exercise 1.15 on p 24. They apply to all parts of Exercises 1.15, 1.16, and 1.17. #1 (10 points) exists? EoPL 1.15.5, page 25. #2 (10 points) vector-index EoPL 1.15.6, p 25. #3 (10 points) product EoPL 1.15.8, page 25. Note that the product of the empty set with any other set is empty. #4 (10 points) vector-append-list EoPL 1.15.10, page 25. For this problem only, you may use mutation: namely vector-set! #5 (15 points) rotate (rotate the first element of the returned list. (rotate '(a b c d)) (rotate '(shortlist)) (rotate '()) los) returns a list that is similar to los, except that the last element of los becomes Be sure that you rotate in the correct direction! (d a b c) (shortlist) ()
#6 (15 points) flatten EoPL 1.16. 4, page 26. #7 (10 points) merge EoPL 1.16.5, page 26. #8 (10 points) path EoPL 1.17.1, page 27. Your code can assume that this is only called for successful searches). Note that the symbol right should be produced by the code 'right . left is similar. #9 (20 points) qsort. (qsort pred ls)is a Scheme procedure whose arguments are a predicate which takes two arguments x and y, and returns #t if x is "less than" y, #f otherwise. a list whose items can be compared using this predicate. qsort should produce the sorted list using a QuickSort (note: write your own; do not use Schemes sort function) algorithm. For example: (qsort < '(4 2 4 3 2 4 1 8 2 1 3 4)) (1 1 2 2 2 3 3 4 4 4 4 8) (qsort (lambda (x y) (< (abs (- x 10)) (abs (- y 10)))) '(5 1 10 8 16 17 23 -1)) (10 8 5 16 17 1 -1 23) If you arent sure how QuickSort works, see http://en.wikipedia.or...