CSI 2120

Lab 5: Prolog

Exercise 1. Flight Schedule

Given the following facts:


flight(montreal, chicoutimi, 15:30, 16:15).
flight(montreal, sherbrooke, 17:10, 17:50).
flight(montreal, sudbury, 16:40, 18:45).
flight(northbay, kenora, 13:10, 14:40).
flight(ottawa, montreal, 12:20, 13:10).
flight(ottawa, northbay, 11:25, 12:20).
flight(ottawa, thunderbay, 19:00, 20:30).
flight(ottawa, toronto, 10:30, 11:30).
flight(sherbrooke, baiecomeau, 18:40, 20:05).
flight(sudbury, kenora, 20:15, 21:55).
flight(thunderbay, kenora, 20:00, 21:55).
flight(toronto, london, 13:15, 14:05).
flight(toronto, montreal, 12:45, 14:40).
flight(windsor, toronto, 8:50, 10:10).

Which of the following predicates allows one to decide if one's arrival time at the airport is early enough to catch a certain flight. On-time arrival at the airport is at least 60 minutes prior to the corresponding departure time of the flight.

Rule Set 1:


on_time(H1 : _M1, D, A)  :- 
        flight(D, A, H2 : _M2, _H3 : _M3),H2 - H1 > 1.
on_time(H1 : M1, D, A)  :- 
        flight(D, A, H2 : M2, _H3 : _M3), 
        H2 - H1 =:= 1, MM is 60 - M1,  MM + M2 >= 60.

Rule Set 2:


on_time(H1 : _M1, D, A)  :- 
        flight(D, A, H2 : _M2, _H3 : _M3),H2 - H1 > 2.
on_time(H1 : M1, D, A)  :- 
        flight(D, A, H2 : M2, _H3 : _M3), 
        H2 - H1 =:= 1, MM is 60 - M1,  MM + M2 >= 60.

Rule set 3:


on_time(H1 : _M1, D, A)  :- 
        flight(D, A, H2 : _M2, _H3 : _M3),H2 - H1 > 2.
on_time(H1 : M1, D, A)  :- 
        flight(D, A, H2 : M2, _H3 : _M3), 
        H2 - H1 =\= 1, MM is 60 - M1,  MM + M2 >= 60.

Rule Set 4:


on_time(H1 : _M1, D, A)  :- 
        flight(D, A, H2 : _M2, _H3 : _M3),H2 - H1 > 1.
on_time(H1 : M1, D, A)  :- 
        flight(D, A, H2 : M2, _H3 : _M3), 
        H2 - H1 =:= 1, MM is 60 - M1,  MM - M2 < 60.

Exercise 2. Arrival Predicate

Write an arrival predicate which enables the following type of query with the database of Exercise 1:


?- arrival( flight(montreal,sherbrooke), X).
X=17:10

Exercise 3. Sum of Integers

Write a predicate that finds the sum of the first N numbers, i.e., it should enable queries of the form sum_int(N,X).

Exercise 4 and Quiz: Series

Please hand-in the answer to this question on Virtual Campus during your lab session but at the latest by Friday 6:00pm! Remember, your submission will only count if you have signed the lab attendance sheet.

We would like to define a predicate that calculates the series $ a_n = \frac{1}{2} ( a_{n-1} + \frac{9}{a_{n-1}})$ for $n>1$ with $a_0 = M$.
Use the following head for the rule of the predicate where N is the count for the series and M is the value for $a_0$, while Y is the result.


    seriesNM(0,______,______).
    seriesNM(N,M,Y) :- N > 0,
			_____________,
			_____________,
			_____________.

Example Output:


    ?- seriesNM(20,15,Y).
    Y = 3.0;
    false.


    ?- seriesNM( 2, 50, Y).
    Y = 12.724354324432044 ;
    false.