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CSE505 Assignment 4

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CSE505
Assignment 4 Problem 1
(may be done by a team of two students)
Problem 1 is given below. A problem on lambda calculus to be posted later.
Problem 1: Constraints (due: May 3, 11:59 pm)
Consider the following two relations:
db_student(S, L, M, F) – a student S has a list of assignment scores L, a midterm score M,
and final exam score F. As the final exam has not yet taken place, the value for F is left unbound.
map(Lo, Hi, G) – meaning, the letter grade is G if the weighted average score W ≥ Lo and
W < Hi, where the weighted average score W is obtained assuming that the assignments are
collectively weighted 40% and the mid-term and final are weighted 30% each.

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CSE505
Assignment 4 Problem 1
(may be done by a team of two students)
Problem 1 is given below. A problem on lambda calculus to be posted later.
Problem 1: Constraints (due: May 3, 11:59 pm)
Consider the following two relations:
db_student(S, L, M, F) – a student S has a list of assignment scores L, a midterm score M,
and final exam score F. As the final exam has not yet taken place, the value for F is left unbound.
map(Lo, Hi, G) – meaning, the letter grade is G if the weighted average score W ≥ Lo and
W < Hi, where the weighted average score W is obtained assuming that the assignments are
collectively weighted 40% and the mid-term and final are weighted 30% each.
Sample facts for the two relations are shown below; they also in file grade.pl posted on Piazza.
db_student(tom, [85,95,80,75],75, _).
db_student(ding, [80,90,70,80],85, _).
db_student(hari, [90,70,60,55],65,_).
db_student(ann, [95,80,70,85],55,_).
db_student(aisha, [100,90,95,100],95,_).
db_student(aidong, [70,65,70,55],65,_).
db_student(zhazha, [5,5,5,5],10,_).
map(90, 100.01, ‘A’).
map(80, 90, ‘A-‘).
map(70, 80, ‘B+’).
map(60, 70, ‘B’).
map(50, 60, ‘B-‘).
map(40, 50, ‘C+’).
map(30, 40 ,’C’).
map(20, 30, ‘C-‘).
map(10, 20, ‘D’).
map(0, 10, ‘F’).
Using the above relations, define a Prolog predicate grade(S,F,G), where S is a student, F is
his/her final exam score, and G is his/her overall letter grade. The predicate should work for any
combination of given input parameters and should produce the correct output for the remaining
parameters. Examples:
?- grade(tom, 90, ‘A’). % Can tom get an ‘A’ grade with 90 on the final?
false
?- grade(tom, 90, Answer). % What grade can tom get with 90 on final?
Answer = ‘A-’
A key aspect in this problem is the reporting of constraints as answers.
?- grade(Student, Final, ‘A’). % Who can earn an ‘A’ on the course?
Student = aisha,
{Final>=76.66666666666667, Final=<100.0, _13366=67.0+0.3*F} ;
false.
For the above query, the only student who can earn an A grade is aisha provided her
Final >= 76.666… and Final <= 100.0.
?- grade(Student, F,’A-‘). % Who can earn an ‘A-’ on the course?
% Report answers one at a time
Student = tom,
{F>=80.0, F=<100.0, _18190=56.0+0.3*F} ;
Student = ding,
{F>=75.0, F=<100.0, _22368=57.5+0.3*F} ;
Student = aisha,
{F>=43.333333333333336, F<76.66666666666667, _26510=67.0+0.3*F} ;
false.
?- grade(zhazha, F, G). % What grade(s) can zhazha earn on the course?
% Report answers one at a time.
G = ‘C’,
{F>=83.33333333333334, F=<100.0, _492=5.0+0.3*F} ;
G = ‘C-‘,
{F>=50.0, F<83.33333333333334, _4460=5.0+0.3*F} ;
G = ‘D’,
{F>=16.666666666666668, F<50.0, _8542=5.0+0.3*F} ;
G = ‘F’,
{F>= -0.0, F<16.666666666666668, _12632=5.0+0.3*F}.
IMPORTANT:
The power of constraint programming is that you do not need to write any code to print out
answer constraints. Answer constraints are automatically generated by Prolog provided the
program has laid out the constraints correctly. You can define the grade(S, F, G) predicate with
just one clause containing about 10 lines of code – assuming each goal and each constraint is
written on a separate line.
Note: Prolog has two relevant builtin predicates: sum_list(L, S), which returns in S the sum of the
numbers in list L; and length(L, N), which returns in N the number of elements in list L.
WHAT TO SUBMIT:
Prepare a top-level directory named A4_Problem1_UBITId1_UBITId2 if the assignment is done by
two students; otherwise, name it as A4_Problem1_UBITId if the assignment is done solo.
(Order the UBITId’s in alphabetic order, in the former case.) In this directory, place the file
grade.pl containing the definitions of the predicates db_student, map, and grade.
Compress the directory and submit the compressed file using the online submission
procedure – instructions posted at Resources → Assignments → Online_Submission.pdf.
Only one submission per team is required.
End of Assignment 4 Problem 1