Assignment: Unification & Prolog

CS314 Assignment: Unification & Prolog
Reminder: Lowercase letters and words beginning with a lowercase letter are values/constants. Uppercase letters and words beginning with an uppercase letter are variable names.
Problem 1 - Unification
(a) pointer(a) and pointer(pointer(b)) can be unified. The unifier is: {a → pointer(b)}. (For this
problem, a could’ve been pre-defined to be pointer(b). If you said no to this question, I gave
you full points.)
(b) boo and Baz can be unified. The unifier is: {Baz → boo}.
(c) [H, T] and [a, b, c] can NOT be unified.
(d) foo(a) and foo(X, Y) can NOT be unified.
Problem 2 - Facts & Queries in Prolog
Translate the following into a set of Prolog facts and rules. From (a) through (d), it should be possible
for Prolog to infer (e). Define what your function means. For instance, if you use Department(X, Y)
to be mean ”X is in department Y”, please say so.
(a) j is in the cs department
(b) If someone is in a department, they report to the head of that department.
(c) h is the head of the cs department.
(d) Everyone’s salary is less that the salary of the person they report to.
(e) j’s salary is less than h’s salary.
Here is one possible solution:
department (X , Z ) means " X is in department Z "
report (X , Y ) means " X reports to Y "
head (X , Z ) means " X is the head of department Z "
lsalary (X , Y ) means " X has less salary than Y "
j is in the cs department :
department (j , cs ).
If someone is in a department they report to the head of that department .
report (X , Y ) : - department (X , V ) , head (Y , V ).
h is the head of the cs department .
head (h , cs ).
Everyones salary is less that the salary of the person they report to .
lsalary (X , Y ) : - department (X , _ ) , report (X , Y ).
j ’ s salary is less than h ’ s salary .
Query j ’ s salary is less than h ’ s salary by querying lsalary (j , h ).
lsalary ( joe , sam ).
1
Problem 3 - Cut
Let’s suppose we have the following facts:
likes (a , dogs ).
likes (a , cats ).
likes (b , cats ).
dislikes (c , dogs ).
dislikes (d , dogs ).
dislikes (d , cats ).
What would the following queries print? (Suppose we keep pressing ”;” until false is the output.)
(a) ?- likes(a, Animaltype), dislikes(Person, Animaltype).
Person = c
Animaltype = dogs ;
Person = d
Animaltype = dogs ;
Person = d
Animaltype = cats ;
false .
(b) ?- likes(a, Animaltype), !, dislikes(Person, Animaltype).
Person = c
Animaltype = dogs ;
Person = d
Animaltype = dogs ;
false .
(c) ?- likes(a, Animaltype), dislikes(Person, Animaltype), !.
Person = c
Animaltype = dogs ;
false .
2