The Prolog application that you are going to implement will provide access to a database of students and a database of courses.

We encode the database of students using a predicate student (one Prolog fact for each student). The first argument the full name of the student and the second argument a list of courses that the student took. The name of a student is a data structure called name with two arguments: the first name and the last name of the student. A course name is simply a symbol such as csi324.

student(name(john, smith), [mat101, csi108, csi148, csi270]).

student(name(jim, roy), []).

student(name(jane, brown), [mat101, csi108]).

student(name(emily, white), [mat101, csi108, mat246]).

student(name(emma, smith), [mat101, csi108, csi148, mat246]).

We encode the database of courses and their prerequisites as a predicate prereq, with one Prolog fact for each course. The first argument is the name of the course and the second argument is a list of prerequisites required in order to take that course. A prerequisite can be a course name or a list of alternative prerequisites. For example, the fact that csi324 has the prerequisites csi148 and one of csi238 and mat246 is expressed in the last clause below. A list of alternative prerequisites contains two or more alternatives.

prereq(csi108, []).

prereq(csi148, [csi108, mat101]).

prereq(csi238, [csi148]).

prereq(csi260, [csi108]).

prereq(csi270, [csi148]).

prereq(csi310, [[csi260, csi270], [sta107, sta205, sta255]]).

prereq(csi324, [[csi148], [csi238, mat246]])

Implement the following predicates:

1. took has two arguments: a student’s first name and a course name. It verifies if the student already took that course. Assume the two arguments are instantiated. Also assume that the first name uniquely identifies a student (this is not the case, in reality, student numbers would be used as unique identifiers).

2. is_prereq has two-course names as arguments and verifies if the second one is a prerequisite for the first one. Assume that the two arguments are instantiated.

3. can-take with two arguments, a student’s first name and a course, and succeeds if the student has all the prerequisites necessary to take the course. If there are alternative prerequisites, the student is required to have at least one of them. A student cannot take a course if she/he already took it.

4. can-take-list has two arguments, a student’s first name and a list of courses, and succeeds if the student can take all the courses in the list (fails otherwise).