/* 

  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 (0.04s):
  """
  Hypotheses generated: 401
  Hypotheses refined:   35
  To be refined:        109

  path(A,A,A).
  path(A,C,[A,B|E]):-
    link(A,B),
    path(B,C,[D|E]).
  """

  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( 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


% Example

% Figure 21.9  Learning about a path in a graph.


% Learning about path: path(StartNode,GoalNode,Path)

% A directed graph

link(a,b).
link(a,c).
link(b,c).
link(b,d).
link(d,e).

backliteral( link(X,Y), [ type(X,item)], [ type(Y,item)]). 
backliteral( path(X,Y,L), [ type(X,item)], [ type(Y,item), type(L,list)]).

term( list, [X|L], [ type(X,item), type(L,list)]).
term( list, [], []).

prolog_predicate( link(X,Y)).

start_clause( [ path(X,Y,L)] / [type(X,item),type(Y,item),type(L,list)] ).

% Examples

ex( path( a, a, [a])).
ex( path( b, b, [b])).
ex( path( e, e, [e])).
ex( path( f, f, [f])).
ex( path( a, c, [a,c])).
ex( path( b, e, [b,d,e])).
ex( path( a, e, [a,b,d,e])).

nex( path( a, a, [])).
nex( path( a, a, [b])).
nex( path( a, a, [b,b])).
nex( path( e, d, [e,d])).
nex( path( a, d, [a,b,c])).
nex( path( a, c, [a])).
nex( path( a, c, [a,c,a,c])).
nex( path( a, d, [a,d])).