/* 

  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


  Final result (30ms):
  """
  Hypotheses generated: 105
  Hypotheses refined:   26
  To be refined:        15

  member(A,[A|B]).
  member(C,[A|B]):-
    member(C,B).
  """

  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 21.5  Problem definition for learning list membership.

% Problem definition for learning about member(X,L)

backliteral( member(X,L), [type(L,list)], [type(X,item)] ).  % Background literal

% Refinement of terms

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

prolog_predicate( fail).          		% No background predicate in Prolog

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

% Positive and negative examples

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

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