%%% ============================
%%%  CMPU-181, Spring 2013
%%%  April 3, 2013
%%% ============================

%%%  swipl  <--- starts the Prolog interpreter

%%%  halt.  <--- terminates swipl

%%%  The proposition A is true:

a.

%%%  If A is true, then so is B:

b :- a.

%% =======================
%%  A theory of ancestry
%% =======================
%%  anc(X,Y) -- X is an ancestor of Y
%%  par(X,Y) -- X is a parent of Y
%% -----------------------

%%  Rules in prolog employ UNIVERSALLY QUANTIFIED variables:
%%  for all X and Y:  if X is a parent of Y, then X is an ancestor of Y
%%    par(X,Y) => anc(X,Y)

anc(X,Y) :- par(X,Y).

%%  for all X, Y and Z:  if X is an ancestor of Y, and Y is a parent of Z,
%%                       then X is an ancestor of Z.
%%    anc(X,Y) AND par(Y,Z) => anc(X,Z)

anc(X,Z) :- anc(X,Y), par(Y,Z).

%%  some facts about particular people

par(amb,bert).  %% Amberley is a parent of Bertrand

par(bert,kate). %% Bertrand is a parent of Kate

%%  NOTE:  X, Y and Z are upper-case VARIABLES
%%         amb, bert, kate are lower-case CONSTANTS

%%  anc(amb,kate) ???
%%  anc(amb,bert) ???

%%  anc(X,kate)  <--- i.e., is there a value for X that makes anc(X,kate) true?
%%                    Variables in a *query* are EXISTENTIALLY QUANTIFIED...
%%                    "Does there EXIST a value for X such that ...?"
%%  anc(amb,Y)

%%  LIST CONCATENATION
%% ---------------------------------------
%%  conc(Xs,Ys,Zs) holds if Zs is the concatenation of Xs and Ys.

%%  Base Case:  The first list is empty
%%    For all Ys, if you concatenate [] onto Ys, you end up with Ys.

conc([], Ys, Ys).

%%  Recursive Case:  The first list is non-empty

conc([X|Xs], Ys, [X|Zs]) :- conc(Xs,Ys,Zs).