Assignments

The following table indicates assignments and due dates for Computer Science 302. Unless otherwise indicated,

assignments related to program verification are due weekly, usually on Fridays,
other assignments are usually due on Mondays, although a few Wednesday assignments are likely
extensions to due dates will be granted only in advanced,
textbook references are to course textbooks,
Additional exercises are stated later on this page.
collaboration is allowed on some assignments and not on others; specific rules of collaboration are shown for each assignment.

Due Date	Text	Chapter	Collaboration	Problems	Answer Format and Notes
January 23	Gries	1	No	1.3,1.4	in writing
	Gries	2	No	2.5, 2.6cegk	in writing
January 26	Gries	2	Yes	2.6fhjl	in writing
	Mitchell	1-2	Yes	2.1	in writing
			Yes	Problem 1 (below)	in writing
January 28	Mitchell	3	Yes	3.2, 3.3	class presentation; group assignment 0
January 30	Gries	4	No	4.1.3, 4.2.6a-bjkm, 4.4.2, 4.5.2ac	in writing
February 4	Mitchell	4	yes	4.1-4.4, 4.6	in writing; group assignment 1
February 6	Gries	5-6	No	5.1.1ace, 5.1.2bfg, 5.2.2, 5.2.3, 6.2.1deg	in writing
February 11	Michell	4	Yes	Problem 2 (below)	in writing; group assignment 2
February 18	Michell	4	Yes	4.8, (4.9 or 4.10), 4.13	in writing; group assignment 3
February 25	Michell	5	No	ML Programming Assignment 1	program and tests
February 27	Gries	7	No	7.1acef, 7.2(1,3,5), 7.4, 7.5	in writing
	Gries	8	No	8.1, 8.3, 8.6	in writing
March 8	Gries	9	No	9.1.1ace, 9.2.2, 9.2.3bdf, 9.2.4ace, 9.3.1ace	in writing
	Gries	10	No	10.1, 10.3, 10.5, 10.6, 10.8	in writing
March 10	Mitchell	5-6	Yes	ML Programming Assignment 2	program and tests
	Mitchell	6	Yes	6.1, 6.2, 6.5, 6.6, 6.7	in writing, group assignment 4
March 12	Gries	11	No	11.1, 11.8, 11.9, 11.10, 11.12	in writing
	Gries	14	No	14.1abd	in writing
March 31	Mitchell	7	Yes	Problem 3 (below)	in writing, group assignment 5
April 2	Gries	15	No	15.1.3, 15.1.4, 15.2.2, 15.2.3, 15.2.4	in writing
April 7	Gries	15-16	Yes	Problem 4 (below)	in writing, group assignment 6
April 9	Gries	16	No	16.2.2, 16.2.3	in writing
	Gries	16	No	16.3.1, 16.3.5, 16.3.7	in writing
April 14	Mitchell	8	Yes	8.8 and any 3 of 8.1, 8.2, 8.4, 8.5	in writing, group assignment 7
April 16	Gries	16	No	16.5.2, 16.5.5, 16.5.9	in writing
April 16	Gries	16	No	Problem 5 (below)	in writing , group assignment 8
April 23	Gries	16	No	16.5.2 (proof required)	in writing
				16.5.5 (1 pass through data, proof required)
				16.5.9 (simple arithmetic only, no logs, assume array large enough without declaration, proof required)
April 28	[Prolog]		Yes	Problem 6, Problem 7 (below)
April 30	[Prolog]		No	Problem 8, Problem 9 (below)
Due Date	Text	Chapter	Collaboration	Problems

Additional Exercises

Problem 1: Find a partial function that has all three of the following three properties:

the function is well-defined for at least 2 values,
the function is undefined for at least 2 values, and
the function does not terminate for at least 2 values.

Note: In the preferred solution to this problem, "at least 2 values" would be replaced by "an infinite number of values" in each case above.

Problem 2: Give the BNF grammar and the corresponding denotational semantics for the Roman numerals between 1 and 99 (inclusive).

Problem 3: Write a program with just two procedures which prints the single integer shown in the following table, based on the type of parameter passage and scoping rules:

Desired Result	Description
1.	Parameter passage is by value and with static scoping rules.
2.	Parameter passage is by value-result and with static scoping rules.
3.	Parameter passage is by reference and with static scoping rules.
4.	Parameter passage is by name and with static scoping rules.
5.	Parameter passage is by value and with dynamic scoping rules.
6.	Parameter passage is by value-result and with dynamic scoping rules.
7.	Parameter passage is by reference and with dynamic scoping rules.
8.	Parameter passage is by name and with dynamic scoping rules.

Thus, if the program were interpreted as parameter passage by value-result with dynamic scoping rules, then the program should print the number 6.

Problem 4: Develop a binary search program with the following conditions:

Preconditions: integers m, N are given with 0 ≤ m < N

integer array a[0..N] is defined and initialized
array segment a[0..m] is in non-descending order
that is, a[k] ≤ a[k+1] for each 0 ≤ k < m

item is an initialized integer variable

Postconditions: integer variable i satisfies the following:

((0 ≤ i ≤ m) cand (item = a[i])) or ((0 ≤ i ≤ m+1) and (item > a[0..i-1]) and (item < a[i..m]))

Notes:

Loop invariants for each group will be assigned in class
Your work should explicitly clarify whether it matters which midpoint computation is used (e.g., (left + right) div 2 or (left + right + 1) div 2) ), and if so which one is needed.
Final work should include both a program and a proof of correctness in a form that could be used by another group for a subsequent assignment.

Problem 5: A class handout gives seven solutions that were turned in to solve the binary search program (Problem 4). This problem asks you to:

Analyze two submitted solutions, work to develop a proof of correctness for each, and complete either your own correctness proof or an explanation of why such a proof cannot be done from the submitted material. If additional information could be added to what is given to support a proof, then you should specify what this material would be.
Translate each solution to a running program in a language of your choice, and provide thorough testing of each program. In the case that you conclude that the submitted program is not correct, you should demonstrate the errors with selected test cases.

Assignments for reviewing code are as follows:

Group 0,3,6: Programs 0, 1
Group 1,2,4: Programs 1, 6
Group 5,10,12: Programs 3, 4
Group 7,9,13: Programs 3, 6
Group 8,11,17: Programs 2, 5
Group 14,15,19: Programs 0, 2
Group 16,18: Programs 4, 5

Problem 6: Define Prolog relations to determine if a list has an even number of elements.

Problem 7: Define Prolog relations to determine if a list:

is a permutation of another.
is formed by merging two lists.

Problem 8: Write a Prolog program that succeeds if the intersection of two given list parameters is empty.

Problem 9: Draw Prolog search trees for the query:


?- reverseList([a, b, c, d], W).

where reverseList is defined by the rules:

a.  
reverseList([ ], [ ]).
reverseList([A|X], Z) :- reverseList(X, Y),append(Y, [A], Z).

b.  
reverseList(X, Z) :- rev(X, [ ], Z).
rev([ ], Y, Y).
rev([A|X], Y, Z) :- rev(X, [A|Y], Z).

This document is available on the World Wide Web as

http://www.math.grin.edu/~walker/courses/302.sp04/assignments.html

created December 20, 2003 last revised April 18, 2004
For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.

Preconditions:	integers `m, N` are given with `0 ≤ m < N`
	integer array `a[0..N]` is defined and initialized
	array segment `a[0..m]` is in non-descending order that is, `a[k] ≤ a[k+1]` for each `0 ≤ k < m`
	`item` is an initialized integer variable

Postconditions:	integer variable `i` satisfies the following:
	`((0 ≤ i ≤ m) cand (item = a[i])) or ((0 ≤ i ≤ m+1) and (item > a[0..i-1]) and (item < a[i..m]))`