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The University of Melbourne School of Computing and Information Systems
Semester 1, 2018 Sample Assessment
COMP90048 Declarative Programming
Reading Time: 15 minutes Total marks for this paper: 100 Writing Time: 2 hours
This paper has 12 pages.
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Writing instruments (e.g., pens, pencils, erasers, rulers). No other materials and no electronic devices are permitted.
Instructions to Invigilators:
Students will write their answers in the exam paper itself.
The exam paper must remain in the exam room and be returned to the subject coordinator.
Instructions to Students:
Write your enrolment (student) number in the box above. Answer questions directly on this exam paper in the box(es) provided. Use the flip sides of pages for rough work. The last 2 pages are provided in case you need more space for any answers. If you use this overflow space, put a note where the answer belongs saying where the rest of the answer is.
The marks for each question are listed at the beginning of the question. You should attempt all questions. Use the number of marks allocated to a question as a rough indication of the time to spend on it. We have tried to provide ample space for your answers; do not take the amount of space provided for an answer as an indication of how much you need to write.
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Examiners¡¯ use:
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Semester 1, 2018 Sample Assessment Declarative Programming
Question 1 [12 marks]
For each of the following Haskell expressions, give its type (which may be a function type, may include type variables, and may include type class constraints) or indicate that it represents a type error. You need not write anything other than the type, or that it is an error.
(a) (<)
(b) map (+3)
(c) foldr
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Declarative Programming
Semester 1, 2018 Sample Assessment
(d) Nothing
(e) zip [True,True,False]
(f) flip filter "hello"
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Semester 1, 2018 Sample Assessment Declarative Programming
Question 2 [12 marks]
For each of the following Haskell expressions, give its value, or explain why it will produce an error or fail to terminate. Assume the Data.List library is loaded, which defines the sort function.
(a) map (length < 3) [[1],[1,2,3]]
(b) filter (not.(==3)) [1,2,3]
(c) let e = head [] in 3
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Declarative Programming Semester 1, 2018 Sample Assessment
(d) map fst $ filter snd $ zip "abcde" [True,True,False,True]
(e) head $ sort $ zip [3,0,0,2,0] $ reverse [9,0,0,4,8]
(f) map snd $ sort $ zip "decl" [1..]
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Semester 1, 2018 Sample Assessment Declarative Programming
Question 3
Consider the following Haskell type for ternary trees:
data Ttree t = Nil | Node3 t (Ttree t) (Ttree t) (Ttree t)
[30 marks]
Suppose we have a Ttree of Doubles and we want a function to find the average of the numbers in the tree. Write a Haskell function which performs this task. If the Ttree is empty, your function should return 0.0. Include type declarations for all your functions. To obtain maximum marks, your code should use a single traversal over the tree and have O(N) worst case time complexity.
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Declarative Programming Semester 1, 2018 Sample Assessment
Question 4 [10 marks]
Give the formal semantics (meaning) of the following Prolog program. Recall that the formal semantics of a logic program is the set of ground unit clauses that would give the same answers to all queries as the program itself. English descriptions of the meanings of the programs will receive no credit.
p(a). p(b).
q(X,Y) :- p(X), p(Y).
r(a,c). r(d,b).
s(X,Y) :- q(X,Y), r(X,_), r(_,Y).
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Semester 1, 2018 Sample Assessment Declarative Programming
Question 5 [20 marks]
For this question, we will represent a set of integers as a binary tree in Prolog, using the atom empty to represent an empty tree or node, and tree(L,N,R) to represent a node with label N (an integer), and left and right subtrees L and R. Naturally, we also insist that N be strictly larger than any label in L and strictly smaller than any in R. We do not require that the tree be balanced. For example,
tree(tree(tree(empty, 1, empty),
2,
tree(empty, 3, tree(empty, 4, empty))),
5,
tree(tree(tree(empty,6,empty),
7,
tree(empty,8,empty)),
9,
tree(empty, 10, empty)))
is one possible representation of the set of numbers from 1 to 10. It might be visualized as
Write a predicate intset insert(N, Set0, Set) such that Set is the same as Set0, except thatNisamemberofSet,butmayormaynotbeamemberofSet0. Thatis,eitherNisa member of Set0 and Set = Set0, or N is not a member of Set0 and is a member of Set, and other than that, Set is the same as Set0. This predicate must work as long as N is bound to an integer and Set0 is ground.
Hint: Prolog¡¯s arithmetic comparison operators are <, >, =< (not <=), and >=. You can also use = and \= for equality and disequality.
Please write your answer on page 9.
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Declarative Programming
Semester 1, 2018 Sample Assessment
Answer to Question 5
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Semester 1, 2018 Sample Assessment Declarative Programming
Question 6 [16 marks] Following is a definition of a Prolog predicate to compute the sum of a list of numbers.
sumlist([], 0).
sumlist([N|Ns], Sum) :-
sumlist(Ns, Sum0),
Sum is N + Sum0.
Fill in the blanks in the following transformation of this code to be tail recursive.
sumlist(List, Sum) :-
sumlist(
sumlist([N|Ns], Sum0, Sum) :-
sumlist(
). ,
).
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Declarative Programming Semester 1, 2018 Sample Assessment
Overflow Answer Page 1
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Semester 1, 2018 Sample Assessment Declarative Programming
Overflow Answer Page 2
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¡ª End of Exam ¡ª
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