/* 

  Inductive Logic Programming in Picat v3.

  This is a port of the program minihyper.pl + examples in
  I. Bratko, "Prolog Programming for Artificial Intelligence", 4th edn.,
  Pearson Education / Addison-Wesley 2012
  Page 495ff (Figure 21.4)
       
  The module minihyper_v3 is defined in
  See http://hakank.org/picat/minihyper_v3.pi 


  All comments below are from Bratko's code (except this notated with "hakank").

  Using atom/1 in the backliteral/2 (as suggest at page 501) (3.9s)
"""
MaxD = 0
MaxD = 1
MaxD = 2
MaxD = 3
MaxD = 4
MaxD = 5
MaxD = 6
MaxD = 7
MaxD = 8
[[predecessor(_ca8,_cb8),[atom(_ca8),parent(_ca8,_d70)],[atom(_d70),predecessor(_d70,_cb8)]] / [_ca8,_d70,_cb8],[predecessor(_c48,_c58),[atom(_c48),parent(_c48,_c58)]] / [_c48,_c58]]

picat3 minihyper_ex2_v3.pi  3,90s user 0,01s system 99% cpu 3,913 total
"""
 
  Which nicer variable names:
  [[predecessor(A,B),[atom(A),parent(A,C)],[atom(C),predecessor(C,B)]] / [A,C,B],[predecessor(D,E),[atom(D),parent(D,E)]] / [D,E]]

   And as clauses:

   predecessor(A,B) :- atom(A),parent(A,C)],atom(C),predecessor(C,B)
   predecessor(D,E) :- atom(D),parent(D,E)

   And we can skip the atom/1:
   predecessor(A,B) :- parent(A,C)],predecessor(C,B)
   predecessor(D,E) :- parent(D,E)


  Without the atom/1 fix we get the following after 35min 54.12s:
   MaxD = 0
   MaxD = 1
   MaxD = 2
   MaxD = 3
   MaxD = 4
   MaxD = 5
   MaxD = 6
   MaxD = 7
   MaxD = 8
  [[predecessor(_ca8,_ca8),parent(_ca8,_db0)] / [_ca8,_db0],[predecessor(_c48,_c58),parent(_ee0,_c58),predecessor(_c48,_ee0)] / [_c58,_c48,_ee0]]



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

*/

import minihyper_v3.

main => go.


go ?=>
  induce(H),
  println(H),
  % fail,    
  nl.

go => true.



max_proof_length( 6).   % Max. proof length, counting calls to 'non-prolog' pred.
max_clause_length( 3).  % Max. number of literals in a clause



% hakank: This is the input data for the problem

% hakank: Another a little more complex example from page 500 with
% recursive definitione

% Original: 
backliteral( parent(X,Y),  [X,Y]).  % A background literal with vars. [X,Y]
backliteral( predecessor(X,Y), [X,Y]).

% Suggestion at page 501
% backliteral([atom(X), parent(X,Y)],  [X,Y]).  % A background literal with vars. [X,Y]
% backliteral([atom(X), predecessor(X,Y)], [X,Y]).


prolog_predicate( parent(X,Y)).     % Goal parent(_,_) executed directly by Prolog
prolog_predicate( atom(X)).

parent( pam, bob).
parent( tom, bob).
parent( tom, liz).
parent( bob, ann).
parent( bob, pat).
parent( pat, jim).
parent( pat, eve).

ex(predecessor(pam, bob)).
ex(predecessor(pam, jim)).
ex(predecessor(tom, ann)).
ex(predecessor(tom, jim)).
ex(predecessor(tom, liz)).

nex(predecessor(liz,bob)).
nex(predecessor(pat,bob)).
nex(predecessor(pam,liz)).
nex(predecessor(liz,jim)).
nex(predecessor(liz,liz)).

start_hyp([[predecessor(X1,Y1)] / [X1,Y1],
           [predecessor(X2,Y2)] / [X2,Y2]]).