% A sample database.  

% Percent-sign ('%') marks comments to end-of-line.

% FACTS
male(abe).
male(homer).
male(bart).

parent(jackie,marge).

parent(abe,homer).
parent(mona,homer).

parent(homer,bart).
parent(marge,bart).

parent(homer,lisa).
parent(marge,lisa).

parent(homer,maggie).
parent(marge,maggie).

parent(bart,bartJr).
parent(bart,cowabunga).
parent(bartJr,bartJrII).

parent(lisa,lisaJr).
parent(lisaJr,lisaJrII).


% Task: give me a rule for `father/2`.
father(F,C) :- male(F), parent(F,C).

% Task: `isADad/1`
isADad(P) :- father(P,X).
      

%%%% Define grandparent/2:
%%%% (What is the def'n in English, for "Old is a grandparent of Yng"?)
grandparent(Old,Yng) :- parent(Old,Middle), parent(Middle,Yng).


%%%% Task: define *ancestor*:
%anc(Old,Yng) :- parent(Old,Yng).
%anc(Old,Yng) :- parent(Old, Middle), parent(Middle, Yng).
%anc(Old,Yng) :- parent(Old, P1), parent(P1,P2), parent(P2, Yng).
%anc(Old,Yng) :- parent(Old, P1), parent(P1,P2), parent(P2,P3), parent(P3, Yng).

%%%...uh-oh, this is going to take a while.
%%% Try a recursive formulation:

anc(P,P).
anc(Old,Yng) :- parent(Old,P), anc(P,Yng).

% ask: Old=bart,Yng=bartJr ?      Yes, by first rule, since parent(bart,bartJr).
% ask: Old=homer,Yng=bartJr ?     parent(homer,P), anc(P,bartJr) -- P=bart works (by prev case)
% ask: Old=abe,Yng=bartJr ?  parent(abe,P), anc(P,bartJr).  Yes, P=homer works (by prev case).




% define firstCousin/2
firstCousin(P1,P2) :- parent(ParentOfP1, P1), parent(ParentOfP2, P2), sibling( ParentOfP1, ParentOfP2 ).
sibling(A,B) :- parent(P, A), parent(P, B).

firstCousin(P1,P2) :- grandparent(X,P1), grandparent(X,P2).     % (well not quite)
                      % parent(X,Middle1), parent(Middle1,P1),
                      % parent(X,Middle2), parent(Middle2,P2),
                      % Middle1 \= Middle2.

% are P1 and P2 nth-cousins (for any n=-1,0,1,2,3,...?)

nthCousin(P,P).
nthCousin(P1,P2) :- parent(X,P1), parent(Y,P2), nthCousin(X,Y).







% (two possible ways -- one in terms of siblings?)


%%% A and B are 1st-cousins, or 2nd-cousins, or 3rd-cousins, etc.
%%%   N.B. 0th cousins are siblings?
%%%   N.B. -1st cousin is yourself!?!?  ("Nota Bene" -- latin for "notice" or "take note")

%%% Task: write a generalized 'nthCousin':

%nthCousin(A,B) :- A=B.

%%nthCousin(A,B) :- A's parent("AP") and B's parent("BP") are nth cousins.
%% We yearn to say        nthCousin( parent(A), parent(B) )
%% but can't, since Prolog only has T/F predicates (not functions that return people).
%% Instead, we use the predicates+solving to give names to the parents:

% As before, we can re-write `nthCousin(A,B) :- A=B.` as:













%%%%