/* 

  Analogy in Picat.

  Evans' Analogy program.

  This Picat version is based on the Prolog code from
  Leon S. Sterling: "The Art of Prolog", page 270ff

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


% import util.
% import cp.


main => go.

go ?=>
  test_analogy(Name,X),
  writeln([Name,X]),
  nl, 
  fail.
  
go => true.

analogy(AB,CX,Answers) =>
    AB = $is_to(A, B),
    CX = $is_to(C,X), 
    match(A,B,Match),
    match(C,X,Match),
    member(X,Answers).

test_analogy(Name,X) =>
    figures(Name,A,B,C),
    answers(Name,Answers),
    analogy($is_to(A, B),$is_to(C, X),Answers).

% The problem:
%   A is to B as C is to ?
figures(Name,A,B,C) => 
   Name = test1,
   A = $inside(square,triangle),
   B = $inside(triangle,square), 
   C = $inside(circle,square).

%
% The three possible answers
% See Figure 14.5, page 271 in "The Art of Prolog"
%
answers(Name,Answers) => 
   Name = test1,
   Answers = [$inside(circle,triangle), % Answer 1
              $inside(square,circle),   % Answer 2
              $inside(triangle,square)  % Answer 3
              ].

match(A,B,Match) ?=> 
   A = $inside(Figure1,Figure2),
   B = $inside(Figure2,Figure1),
   Match = invert.
match(A,B,Match) => 
   A = $above(Figure1,Figure2),
   B = $above(Figure2,Figure1),
   Match = invert.