/* 

  Inductive Logic Programming in Picat v3.

  This is a port of the program hyper.pl in
  I. Bratko, "Prolog Programming for Artificial Intelligence", 4th edn.,
  Pearson Education / Addison-Wesley 2012
  Page 507ff (Figure 21.7 and 21.3)
       
  The module hyper_v3 is here
  http://hakank.org/picat/hyper_v3.pi

  Result (0.06s):
  Hypotheses generated: 378
  Hypotheses refined:   10
  To be refined:        261

  arch(A,B,C):-
    support(B,C),
    not touch(A,B),
    support(A,C),
    isa(C,stable_poly).
  """

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

*/

import hyper_v3.

main => go.


go ?=>
  induce(H),
  show_hyp(H),
  nl.

go => true.


% Moved from from hyper_v3.pi
max_proof_length( 16).   % Max. proof length, counting calls to preds. in hypothesis
max_clauses( 14).        % Max. number of clauses in hypothesis
max_clause_length( 17).  % Max. number of literals in a clause

% Original:
% max_proof_length( 6).   % Max. proof length, counting calls to preds. in hypothesis
% max_clauses( 4).        % Max. number of clauses in hypothesis
% max_clause_length( 5).  % Max. number of literals in a clause


% Figure 21.12  Learning the concept of arch.


% Learning about arch

backliteral( isa(X,Y), [type(X,object)], [])  :-
  member( Y, [polygon,convex_poly,stable_poly,unstable_poly,triangle,
              rectangle, trapezium, unstable_triangle, hexagon]).      % Y is any figure

backliteral( support(X,Y), [type(X,object), type(Y,object)], []).
backliteral( touch(X,Y), [type(X,object), type(Y,object)], []).
backliteral( \+(G), [type(X,object),type(Y,object)], [])  :-
  G = $touch(X,Y); G = $support(X,Y).

% hakank: added this since it was missing...
term( list, [X|L], [ type(X,item), type(L,list)]).
term( list, [], []).


prolog_predicate( isa(X,Y)).
prolog_predicate( support(X,Y)).
prolog_predicate( touch(X,Y)).
prolog_predicate( \+(G)).

ako( polygon, convex_poly).         % Convex polygon is a kind of polygon
ako( convex_poly, stable_poly).     % Stable polygon is a kind of convex polygon
ako( convex_poly, unstable_poly).   % Unstable polygon is a kind of convex poly.
ako( stable_poly, triangle).        % Triangle is a kind of stable polygon
ako( stable_poly, rectangle).       % Rectangle is a kind of stable polygon
ako( stable_poly, trapezium).       % Trapezium is a kind of stable polygon
ako( unstable_poly, unstable_triangle).  % Unstable triangle is a.k.o. unstable poly.
ako( unstable_poly, hexagon).            % Hexagon is a kind of unstable polygon

ako( rectangle, X)  :-
  member( X, [a1,a2,a3,a4,a5,b1,b2,b3,b4,b5,c1,c2,c3]).    % All rectangles

ako( triangle, c4).                % Stable triangle
ako( unstable_triangle, c5).       % Triangle upside down

isa( Figure1, Figure2)  :-         % Figure1 is a Figure2
  ako( Figure2, Figure1).

isa( Fig0, Fig) :-
  ako( Fig1, Fig0),
  isa( Fig1, Fig).

support(a1,c1).    support(b1,c1).
support(a3,c3).    support(b3,c3).   
support(a4,c4).    support(b4,c4).
support(a5,c5).    support(b5,c5).
touch(a3,b3).

start_clause( [ arch(X,Y,Z)] / [type(X,object),type(Y,object),type(Z,object)]).

ex( arch(a1,b1,c1)).
ex( arch(a4,b4,c4)).

nex( arch(a2,b2,c2)).
nex( arch(a3,b3,c3)).
nex( arch(a5,b5,c5)).
nex( arch(a1,b2,c1)). 
nex( arch(a2,b1,c1)).