CSE505 Assignment 1-  Constraints  Solved

Problem 1:  Constraints  

 

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.