CPSC 203 PROLOG LAB 1

  This lab introduces you to the programming language PROLOG (short 
for "Programming in Logic").  You will practice defining basic clauses
and queries.  You need to finish AT LEAST part 1 in lab.  Parts 2 and 3
may be completed outside of class, and are due Wednesday 11/4.


1. Start Prolog.  At the "?-" prompt, type in the following, observe and
   become intrigued at what happens.  Whenever Prolog returns with something
   like "X = 3" instead of just "yes" or "no", type a ";" and see what 
   happens. RECORD THE RESULTS on paper (or in another file) - you'll be 
   required to hand this in.  For each result, write down a short 
   explanation as to why PROLOG responded the way it did.  I've written
   the explanations for the first couple of cases:
   
 a. "true."      	"yes" means true, or proved.
 b. "false."		"false" always fails, and "no" means failure.
 c. "true, false."
 d. "true; false."
 e. "X = 3, X >= 2."  ("=<" is less than or equal to)
 f. "X = 3, X = 4."
 g. "X = 3; X = 4."
 h. "X = (3 + 4)."
 i. "X is (3 + 4)."     is EVALUATES the expression before unification.
 j. "(X + 0) + Y = (Y + X) + 0."  did prolog produce ALL possible solutions?
 k. "member(3,[4,3,6,2])."
 l. "member(Y,[4,3,X])."
 m. "not(member(3,[4,2,6]))."
   

2. Using your favorite editor, create a text file with the following clauses:
   
  flight(lax,bos).
  flight(lga,lax).
  flight(dul,bdl).
  flight(bos,dul).
  flight(phl,sfo).
  flight(sfo,lax).
  flight(phl,bos).

  These clauses reflect all the flights operated by Cheapskate Discount
  Air Travel, Inc.  For example, "flight(lax,bos)" is intended to mean
  "there are flights from lax (LA) to bos (Boston)."  

A.  Load the file into PROLOG with "compile('filename').", and try the
    following queries:
  
  	?- flight(bos,lax).
        ?- flight(X,lax).

B.  You are to axiomatize a predicate "route(A,B)" to indicate that there's
    a way to "Fly Cheap" from city A to city B via the various flights
    offered, with as many connections as necessary.  The first clause 
    should just be:

		route(A,B) :- flight(A,B).

  This means that it's possible to get from A to B if there's a direct
  flight from A to B.

  As a further hint, you should look at how we axiomatized the "above" 
  predicate in the blocks world.  Test your program with interesting
  examples.  Try quries with variables such as "route(X,bos)".  Record
  the results.


3.  Modify the program to include two more parameters to the flight
    predicate indicating the time of the flights.  For example,
    "flight(lax,bos,12,19)" should be intended to mean "there's a flight
    from lax to bos, departing at noon and arriving at 7pm. You then need
    to redefine the "route" predicate to also take four parameters,
    so that "route(A,B,DT,AT)" should hold if and only if there's a way 
    to fly from city A to city B, DEPARTING NO EARLIER than time DT, and 
    ARRIVING NO LATER than time AT, with AT LEAST one hour for all 
    connections.  For example, "route(phl,sfo,9,15)" would mean that there's
    a way to get from Philadelphia to San Francisco, departing no earlier 
    than 9am, and arriving no later than 3pm.  You can use the following 
    test clauses, but you should also make up some of your own:

	  flight(lax,bos,9,14).
	  flight(lga,lax,7,13).
	  flight(dul,bdl,19,22).
	  flight(bos,dul,15,17).
	  flight(phl,sfo,12,18).
	  flight(sfo,lax,5,7).
	  flight(phl,bos,13,16).
	  flight(bos,lax,16,21).
 	  flight(lax,phl,12,18).
  	  flight(phl,bdl,20,23).

    Test your solution with sample queries including, BUT NOT LIMITED TO:
	
	?- route(sfo,bdl,5,23).  
	?- route(sfo,bdl,7,23).
	?- route(sfo,bdl,5,20).
	?- route(phl,lax,12,22).


IMPORTANT HINT: arithmetics is strange in PROLOG.  Do not use clauses such 
  as "p(T+1)" even when you know that T will be instantiated with a number.  
  Instead, use the conjunction "T2 is (T + 1), p(T2)".  In general,
  you'll find that unification (pattern matching) when arithemtics 
  is involved will not work the way you hope it would; i.e., do not expect 
  (X > 3, X < 5) to return X = 4.  Prolog can only perform SYMBOLIC
  reasoning when pattern matching (that's why "is" is different from "=").