Prolog day2 4-14-00

Programs are comprised of 
	1. facts : specification of a relation

		Relation is a name predicate, variable or constant
			Predicate naming relationship
				-Constants start with lower case
					eg. inOrder([]).	***NOTE***
			   		 odd(1).		ends with .
		
				-Variables start with Upper Case
					eg. InOrder([x]).

		(example1) 
		   define append relationship
			append ([], L, L).   (appending [] with L gives L)

	2. rules (of inference) 
		form if a is true then b is true

Using Prolog
	- Two phases
		1. program entry
		2. program testing and execution

	- can type interactively. 
		to do, enter '[user].' This begins the user mode and begins 
			program entry.
	
	1. Enter Facts and Rules 
	2. Enter ^D to end entry mode.
		['filename']
	3. Query Mode begins. (Marked by ? prompt.)
		Query mode responds with either yes, true or no, not true, not
			as far as you've told me.
				eg. ?- odd(2).
					no
				    ?- odd(1).
					yes. (checks relevant predicates 1=1.)
				    ?- odd(x).
					x=1 (x must equal 1 for odd(x) to be true.)

Prolog has a different approach to programming.
	-order is not important
	-add new rules

Unification: all occurances of same varible get same value. 
	can use , to use this. (, means and)		
		eg. fatherOf(tom, x) , fatherOf(x, harry).
				  |_____________|
					 |
					\|/
					 V
				   x must be father of Tom
					and
				   x must be son of harry.

	***Note: variables are local to rule.	

Rules of inference
		(the symbol :- means if)
	Form: predicate :- cond1, cond2, cond3...
		head		body
		of rule		of rule

	This is backward to how we ususally think.
	Instead of if true then do this
	it is do this if these conditions hold.
	
	grandMotherOf (x, GM) :- motherOf (x, M), motherOf(M, GM).
	grandMotherOf (x, GM) :- fatherOf (x, F), motherOf(F, GM).

	(You can put multiple rules on a line, but for readability sake,
	 it is not advised.)

	(From now on motherOf will be abbreivated as mO, fatherOf as fO,
	 and grandMotherOf as gMO)

	fO(tom, dick).			mO(tom, judy).
	fO(dick, harry). 		mO(dick, mary).
	fO(jane, harry).		mO(jane, mary).

	example: ?- mO(tom, x).
		   x = judy
		 ?- ;		(; means get another repsonse)
		   no.

		 ?- mO(tome, x), mO(Y,Z).
		   x = judy
		   Y = 	\  Can be any combination of above.
		   Z =  /	Y = tom, Z = judy
				Y = dick, Z = mary
				Y = dick, Z = mary
			    and so, any response is valid. To exhaust
			    all possible responses, keep typing ;s until
			    a no response is received.

	sibs(x,y) :- mO(x,m), fO(x, f), mO(y,m), fO(y,f), not (x = y).
	
	?- gMO(tom, Q).
		tries:  x = tom, GM = Q, m = judy.

			gives:	mO(tom, m), mO(m, Q).
			   	    yes        no
			 	     	FAILS.
		backtracks, and tries:
			x = tom, GM = Q, f = dick
			
			gives: fO(tom, f), mO(f, Q).
				   yes	     yes
				     SOLUTION.