Page 73 - Discrete Mathematics and Its Applications

52 1 / The Foundations: Logic and Proofs

enrolled(s, c) to represent that professor p is the instructor of course c and that student s
is enrolled in course c, respectively. For example, the Prolog facts in such a program might
include:

instructor(chan,math273)
instructor(patel,ee222)
instructor(grossman,cs301)
enrolled(kevin,math273)
enrolled(juana,ee222)
enrolled(juana,cs301)
enrolled(kiko,math273)
enrolled(kiko,cs301)
(Lowercase letters have been used for entries because Prolog considers names beginning with
an uppercase letter to be variables.)
A new predicate teaches(p, s), representing that professor p teaches student s, can be
defined using the Prolog rule

teaches(P,S) :- instructor(P,C), enrolled(S,C)

which means that teaches(p, s) is true if there exists a class c such that professor p is the
instructor of class c and student s is enrolled in class c. (Note that a comma is used to represent
a conjunction of predicates in Prolog. Similarly, a semicolon is used to represent a disjunction
of predicates.)
Prolog answers queries using the facts and rules it is given. For example, using the facts
and rules listed, the query

?enrolled(kevin,math273)

produces the response

yes

because the fact enrolled(kevin, math273) was provided as input. The query

?enrolled(X,math273)

produces the response

kevin
kiko
To produce this response, Prolog determines all possible values of X for which
enrolled(X, math273) has been included as a Prolog fact. Similarly, to find all the professors
who are instructors in classes being taken by Juana, we use the query

?teaches(X,juana)

This query returns

patel ▲
grossman