Assignment 1 on Logical Programming

COMP 348: Principles of Programming Languages
Assignment 1 on Logical Programming
Summer 2020, sections AA and AB

Contents
1 General Information 2
2 Introduction 2
3 Ground rules 2
4 Your Assignment 2
4.1 Fact Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4.2 Queries, Unication, and Resolution . . . . . . . . . . . . . . . . . . . . . . . 6
4.3 Implementation Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5 What to Submit 12
6 Grading Scheme 13
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1 General Information

.
Weight: 5% of the overall grade.
2 Introduction
In this assignment you will be practicing logical programming using Prolog language. This
assignment consists of three parts: 1) Fact representation, 2) Queries, Unication, and
Resolution, and 3) Implementation Exercises.
Note that Part 1 of the assignment is due on May 10th and is to be submitted separately.
See section 5 for more details.
3 Ground rules
You are allowed to work on a team of 3 students at most (including yourself). Each team
should designate a leader who will submit the assignment electronically. ONLY one copy of
the assignment is to be submitted.
This is an assessment exercise. You may not seek any assistance from others while expecting
to receive credit. You must work strictly within your team). Failure to do so will
result in penalties or no credit.
4 Your Assignment
Your assignment is given in three parts, as follows. 1) Fact representation, which is to
be submitted separately, 2) Queries, Unication, and Resolution, and 3) Implementation
Exercises, all of which will be demoed by the whole team.
1
see submission notes (deadline for 1 is Sunday, May 10th at Noon)
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4.1 Fact Representation
Provide a knowledge-base of clauses specifying your class schedule in prolog, as demonstrated
in the following.
team([<<student-ids>>...]).
student_info('<<student-id>>', '<<first-name>>', '<<last-name>>').
takes_course('<<student-id>>', '<<course-name>>',
'<<course-number>>', '<<course-section>>').
course_schedule('<<course-name>>', '<<course-number>>',
'<<course-section>>', '<<dow>>', '<<from-time>>', <<to-time>>').
ˆ dow is day of week: `sun', `mon', `tue', `wed', `thu', `fri', and `sat'.
ˆ from-time and to-time are class start and end in military format, i.e. 0845 (8:45am),
1445 (2:45pm), etc.
ˆ course-name, course-number, and course-section are all in lower case: e.g.. comp 348
aa
Below is a sample knowledge-base for a group of two: John Doe and Jane Doe. Note that
in this question, using single quote (') is mandatory.
team(['4000123', '4000228']).
student_info('4000123', 'John', 'Doe').
student_info('4000228', 'Jane', 'Doe').
takes_course('4000123', 'comp', '348', 'aa').
takes_course('4000123', 'comp', '348', 'aaae').
takes_course('4000228', 'comp', '348', 'ab').
takes_course('4000228', 'comp', '348', 'abaf').
takes_course('4000228', 'comp', '346', 'cc').
course_schedule('comp', '348', 'aa', 'mon', '1445', '1715').
course_schedule('comp', '348', 'aa', 'wed', '1445', '1715').
course_schedule('comp', '348', 'aaae', 'mon', '1345', '1405').
course_schedule('comp', '348', 'aaae', 'wed', '1345', '1405').
course_schedule('comp', '348', 'ab', 'tue', '1315', '1545').
course_schedule('comp', '348', 'ab', 'thu', '1315', '1545').
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course_schedule('comp', '348', 'abaf', 'tue', '1615', '1705').
course_schedule('comp', '348', 'abaf', 'thu', '1615', '1705').
course_schedule('comp', '346', 'cc', 'tue', '1830', '2100').
course_schedule('comp', '346', 'cc', 'thu', '1830', '2100').
John is taking one course (comp 348 aa + the tutorial aaae) and Jane is taking two courses
(comp 348 ab + the tutorial abaf we well as comp 346 cc with no tutorial). Note that
both courses are scheduled on multiple days.
Q 1. Provide the knowledge-base of ALL courses for ALL members of the team. Create a
le named `schedule-studid.pl' where studid is the id of the leader of the team. Include
all clauses in the le. Write every clause in a single line. One le per group. Submit this
separately (see submission notes).
Q 2. Run the following query and report the result:
team(X), member(S, X),
findall(S, takes_course(S, _, _, _), LL),
length(LL, NN),
write(S), write(' has only taken '), write(NN),
write(' courses and tutorials in summer 2020.'), nl, fail.
Is the above information correct?
The above must be submitted in stage 1 (see submission notes for details).
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Q 3. Create below mentioned rules to query the designation information from your knowlegebase.
Hint: Use the cut operator where applicable.
all_sections(CNAM, CNUM, L) :- ...
/* L contains a list of all sections of course CNAME, CNUM,
i.e. calling all_sections('comp', '348', L) will result in L=['aa', 'ab'];
no duplicates */
has_taken(S, [CNAM|[CNUM|[SEC|[]]]]) :- ...
/* true if student S takes the course CNAM CNUM SEC,
e.g. takes('4000123', ['comp', '348', 'aa']) */
has_taken2(S, [CNAM|[CNUM|[]]]) :- ...
/* true if S takes any sections of the course CNAM CNUM,
e.g. takes('4000123', ['comp', '348']) */
all_subjects(S, L) :- ...
/* L contains all the courses subjects that have been
taken by student S, i.e. ['comp', 'soen']; no duplicates */
all_courses(S, L) :- ...
/* L contains all the courses that have been taken by
student S, i.e. all_courses('4000123', L) will result in
L=[['comp', '348', 'aa'], ['comp', '348', 'ab']] */
all_courses2(S, L) :- ...
/* similar to all_courses but without section info;
no duplicates */
Q 4. Modify the code in Q2 to count only the courses regardless of their sections (i.e. comp
348 aa and aaae will be counted as one)
Q 5. Compare the result for all_courses2('4000123', L) vs. all_courses2(4000123,
L). Explain the dierence.
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4.2 Queries, Unication, and Resolution
Q 6. Unication: Indicate which of the following pairs of terms can be unied together? If
they can't be unied, please provide the reason for it. In case of error, indicate the error. If
they can be unied successfully, wherever relevant, provide the variable instantiations that
lead to successful unication. (Note that `=' indicates unication)
1. food(bread, X) = Food(Y, soup)
2. Bread = soup
3. Bread = Soup
4. food(bread, X, milk) = food(Y, salad, X)
5. manager(X) = Y
6. meal(healthyFood(bread), drink(milk)) = meal(X,Y)
7. meal(eat(Z), drink(milk)) = [X]
8. [eat(Z), drink(milk)] = [X, Y | Z]
9. f(X, t(b, c)) = f(l, t(Z, c))
10. ancestor(french(jean), B) = ancestor(A, scottish(joe))
11. meal(healthyFood(bread), Y) = meal(X, drink(water))
12. [H|T] = [a, b, c]
13. [H, T] = [a, b, c]
14. breakfast(healthyFood(bread), egg, milk) = breakfast(healthyFood(Y), Y, Z)
15. dinner(X, Y, Time) = dinner(jack, cook( egg, oil), Evening)
16. k(s(g), Y) = k(X, t(k))
17. equation(Z, f(x, 17, M), L*M, 17) = equation(C, f(D, D, y), C, E)
18. a(X, b(c, d), [H|T]) = a(X, b(c, X), b)
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Q 7. Queries: Assume we have the following database in a Prolog program:
course(hit_transfer, mechanical).
course(web_design,computer).
course(design_methods, fine-arts).
course(poetry, literature).
course(leadership, management).
course(biology,medicin).
lab_number(mechanical,15).
lab_number(fine_arts,10).
lab_number(X, Z) :-course(X, Y), lab_number(Y, Z).
field(mechanical,engineering).
field(computer, engineering).
field(fine-arts, art). field(literature, social).
field(management, buisiness).
field(X, Y) :- course(X, Z), field(Z, Y).
student(anna, hit_transfer).
student(daniel, hit_transfer).
student(adrian, web_design).
student(ava, design_methods).
student(jack, poetry).
student(lee, leadership).
student(X, Y) :- field(Z, Y), student(X, Z).
student(X):- student(X,_).
Determine the type of each of the following queries (ground/non-ground), and explain what
will Prolog respond for each of these queries (write all the steps of unications and resolutions
for each query)?
1. ? field(hit_transfer,engineering).
2. ? lab_number(fine_arts,X).
3. ? field(computer, literature).
4. ? course(X,Y).
5. ? student(adrian).
6. ? student(anna, engineering).
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7. ? student(X, engineering).
8. ? student(X,fine-arts), course(fine_arts, Y).
9. ? field(_,X).
10. ? lab_number(_,X), field(X,Y).
11. ? lab_number(X,15), field(X,Y).
12. ? student(X), !, student(X,_). % note to cut here
13. ? student(X), student(X,_), !.
14. ? course(X,_), \+ student(_,X). % \+ is for negation (not)
Q 8. Unication, Resolution, and Backtracking: Assume, you are working with the
following knowledge base:
house_elf(dobby).
witch(hermione).
witch(mcGonagall).
witch(rita_skeeter).
wizard(dobby).
magic(X):- house_elf(X).
magic(X):- wizard(X).
magic(X):- witch(X).
Write the details of steps of search (unication, resolutions, and back tracking) and also the
answer for each of the following queries:
? magic(Hermione).
? magic(hermione).
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4.3 Implementation Exercises
Q 9. Assume, you are working with the following knowledge base::
family(
person(john, cohen, date(17,may,1990), unemployed),
person(lily, cohen, date(9,may,1990), unemployed),[] ).
family(
person(john, armstrong, date(7,may,1988), unemployed),
person(lily, armstrong, date(29,may,1961), unemployed),[]).
family(
person(eric, baily, date(7,may,1963), works( bbc, 2200)),
person(grace, baily, date(9,may,1965), works( ntu, 1000)),
[ person(louie, baily, date(25,may,1983), unemployed) ] ).
family(
person(eric, baily, date(7,may,1963), works( acc, 21200)),
person(grace, baily, date(9,may,1965), works(ntnu, 12000)),
[ person( louie, baily, date(25,may,1983), unemployed) ]).
family(
person(eric, fox, date(27,may,1970), works(bbc, 25200)),
person(grace, fox, date(9,may,1971), works(ntbu, 13000)),
[ person(louie, fox, date(5,may,1993), unemployed) ]).
family(
person(tom, cohen, date(7,may,1960), works( bcd, 15200)),
person(ann, cohen, date(29,may,1961), unemployed),
[ person(pat, cohen, date(5,may,1983), works(bcd, 15200)),
person(jim, cohen, date(5,may,1983), works(bcd, 15200))]).
family(
person(bob, armstrong, date(12,oct,1977), works(ntnu, 12000)),
person(liz,armstrong, date(6,oct,1975), unemployed),
[ person(bob, armstrong, date(6,oct,1999), unemployed),
person(sam,armstrong, date(8,oct,1998), unemployed) ]).
family(
person(tony, oliver, date(7,may,1960), works( bbc, 35200)),
person(anny, oliver, date(9,may,1961), unemployed),
[ person(patty, oliver, date(8,may,1984), unemployed),
person(jimey, oliver, date(5,may,1983), unemployed) ]).
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family(
person(jack, fox, date(27,may,1940), unemployed),
person(jane, fox, date(9,aug,1941), works( ntu, 13050)),
[ person(andy, fox, date(5,aug,1967), works(com, 12000)),
person(kai, fox, date(5,jul,1969), unemployed) ]).
husband(X) :- family( X, _, _).
wife(X) :- family( _, X, _).
child(X) :- family( _, _, Children), member(X, Children).
exists(Person) :- husband(Person); wife(Person); child(Person).
dateofbirth(person(_, _, Date, _), Date).
salary(person(_, _, _, works(_, S)), S).
salary(person(_, _, _, unemployed), 0).
a) Write a prolog rule totalIncome/2 to compute the total income of a family.
b) Write a prolog query to print total income of each family.
c) Write a prolog query to print family details of each family that has income per family
member less than 2000.
d) Write a prolog query to print family details of each family where children's total income
is more than their parents.
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Q 10. The following circuit represents a half-adder where A and B are the inputs, and S
and C represent the Sum and Carry bits, respectively.
a) Implement the above circuit in prolog.
b) Write the query to calculate the outputs for S and C for A = 0 and B = _. Provide the
output.
Q 11. Write a Prolog query with arity 2 to return the rst n numbers of a Lucas sequence
in a list.
https://brilliant.org/wiki/lucas-numbers/
The Lucas sequence has the same recursive relationship as the Fibonacci sequence, where
each term is the sum of the two previous terms, except that the rst two numbers in the
sequence are: 2, and 1. The rst few elements of the sequence are: 2, 1, 3, 4, 7, 11, 18, ...
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5 What to Submit
This assignment is submitted in two stages.
Stage 1 - Fact Representation
The rst part of the assignment (1) is submitted by Sunday, May 10th at Noon. It has
to be completed by ALL members of the team in one submission le. The knowledge-base
le must contain all the facts for all the members of the team, all merged in one single le.
You submission includes one single le namely `schedule-studid.pl' where studid is the id
of the leader of the team. Failure to submit may result in 0 mark for the whole assignment
for the whole team. Make sure there is no syntax error. Make sure the query in (2) succeeds.
Test before submission. Do not include the query nor result of 2 in this submission.
Stage 2 - Whole Assignment
The whole assignment (including 1 and 2) is submitted by the due date under the corresponding assignment box. Your instructor will provide you with more details.
Submission Notes
Note: The following applies to stage 2 (Whole Assignment Submission).
Clearly include the names and student IDs of all members of the team in the submission.
Indicate the team leader.
IMPORTANT: You are allowed to work on a team of 3 students at most (including yourself).
Any teams of 4 or more students will result in 0 marks for all team members. If your work on
a team, ONLY one copy of the assignment is to be submitted. You must make sure that you
upload the assignment to the correct assignment box on Moodle. No email submissions are
accepted. Assignments uploaded to the wrong system, wrong folder, or submitted via email
will be discarded and no resubmission will be allowed. Make sure you can access Moodle
prior to the submission deadline. The deadline will not be extended.
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Naming convention for uploaded le: Create one zip le, containing all needed les for your
assignment using the following naming convention. The zip le should be called a#_studids,
where # is the number of the assignment, and studids is the list of student ids of all team
members, separated by (_). For example, for the rst assignment, student 12345678 would
submit a zip le named a1_12345678.zip. If you work on a team of two and your IDs are
12345678 and 34567890, you would submit a zip le named a1_12345678_34567890.zip.
Submit your assignment electronically on Moodle based on the instruction given by your
instructor as indicated above:
https://moodle.concordia.ca
Please see course outline for submission rules and format, as well as for the required demo
of the assignment. A working copy of the code and a sample output should be submitted
for the tasks that require them. A text le with answers to the dierent tasks should be
provided. Put it all in a le layout as explained below, archive it with any archiving and
compressing utility, such as WinZip, WinRAR, tar, gzip, bzip2, or others. You must keep
a record of your submission conrmation. This is your proof of submission, which you may
need should a submission problem arises.
6 Grading Scheme
Q1-Q2 2 marks
Q3-Q5 5 marks
Q6 5 marks
Q7 5 marks
Q8 5 marks
Q9 10 marks
Q10 3 marks
Q11 5 marks
Total: 40 marks.
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References
1. swi-prolog: https://swish.swi-prolog.org
2. Lucas sequence: https://brilliant.org/wiki/lucas-numbers/
3. Half-Adder: http://www.circuitstoday.com/half-adder-and-full-adder
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