669 lines
		
	
	
		
			25 KiB
		
	
	
	
		
			Prolog
		
	
	
	
	
	
			
		
		
	
	
			669 lines
		
	
	
		
			25 KiB
		
	
	
	
		
			Prolog
		
	
	
	
	
	
| %%% -*- Mode: Prolog; -*-
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| 
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| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| %
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| %  $Date: 2011-11-28 14:41:26 +0100 (Mon, 28 Nov 2011) $
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| %  $Revision: 6764 $
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| %
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| %  This file is part of ProbLog
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| %  http://dtai.cs.kuleuven.be/problog
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| %
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| %  ProbLog was developed at Katholieke Universiteit Leuven
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| %                                                            
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| %  Copyright 2008, 2009, 2010
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| %  Katholieke Universiteit Leuven
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| %                                                              
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| %  Main authors of this file:
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| %  Theofrastos Mantadelis, Dimitar Sht. Shterionov
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| %
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| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| %
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| % Artistic License 2.0
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| %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 
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| :- module(mc_DNF_sampling, [problog_dnf_sampling/3]).
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| 
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| :- use_module(library(lists), [memberchk/2]).
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| 
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| :- use_module(variables).
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| :- use_module(sampling, _, [problog_random/1,
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|                             problog_convergence_check/6]).
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| 
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| :- use_module(flags, _, [problog_define_flag/5,
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|                          problog_flag/2]).
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| 
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| :- use_module(os, _, [convert_filename_to_working_path/2]).
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| 
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| :- use_module(hash_table).
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| 
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| :- initialization((
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|   problog_define_flag(search_method, problog_flag_validate_in_list([linear, binary]), 'search method for picking proof', binary, monte_carlo_sampling_dnf),
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|   problog_define_flag(represent_world, problog_flag_validate_in_list([list, record, array, hash_table]), 'structure that represents sampled world', array, monte_carlo_sampling_dnf),
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| 
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|   problog_var_define(dnf_sampling_time, times, time, messages('DNF Sampling', ':', ' ms')),
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|   problog_var_define(probability_lower, result, untyped, messages('Lower probability bound', ' = ', '')),
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|   problog_var_define(probability_upper, result, untyped, messages('Upper probability bound', ' = ', ''))
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| )).
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| 
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| % problog_independed(T, P):-
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| %   tries:trie_traverse_first(T, FirstRef), !,
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| %   problog_independed(FirstRef, P, 0.0, _, 0).
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| % problog_independed(_T, 0.0).
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| 
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| problog_independed(T, P, ProofCNT):-
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|   tries:trie_traverse_first(T, FirstRef), !,
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|   problog_independed(FirstRef, P, 0.0, ProofCNT, 0).
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| problog_independed(_T, 0.0, 0).
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| 
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| %%% this should be generalized to handle nested tries
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| problog_independed([], P, P, ProofCNT, ProofCNT).
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| problog_independed(ProofRef, P, A, ProofCNT, Index):-
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|   tries:trie_get_entry(ProofRef, Proof),
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|   calculate_prob_proof(Proof, Pproof),
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|   calculate_prob_proof(Proof, Pproof),
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|   NA is A + Pproof,
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|   NIndex is Index + 1,
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|   recordz(problog_mc_dnf, proof(Index, ProofRef, Pproof, NA), _),
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|   (tries:trie_traverse_next(ProofRef, NxtProofRef) ->
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|     NextProofRef = NxtProofRef
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|   ;
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|     NextProofRef = []
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|   ),
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|   problog_independed(NextProofRef, P, NA, ProofCNT, NIndex).
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| 
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| 
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| %%% this should be generalized to handle nested tries
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| calculate_prob_proof([true], 1.0):-!.
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| calculate_prob_proof(Proof, P):-
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|   calculate_curr_prob(Proof, 0.0, L),
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|   P is exp(L).
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| 
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| 
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| calculate_curr_prob([], Acc, Acc).
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| calculate_curr_prob([ID|Rest], AccCurrProb, CurrProb):-
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|   get_log_prob_not_check(ID, IDProb),
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|   AccCurrProb1 is AccCurrProb + IDProb,
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|   calculate_curr_prob(Rest, AccCurrProb1, CurrProb).
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| 
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| %%%% this should be generalized and go to problog_fact module
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| get_log_prob_not_check(not(ID), IDProb):-
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|   !, problog:get_fact_probability(ID, Prob1),
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|   Prob2 is 1 - Prob1, IDProb is log(Prob2).
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| get_log_prob_not_check(ID, IDProb):-
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|   problog:get_fact_log_probability(ID, IDProb).
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| 
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| 
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| problog_mc_DNF(Trie, Delta, P):-
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|   problog_flag(mc_batchsize, Samples),
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|   problog_independed(Trie, Pind, ProofCNT),
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|   (ProofCNT > 1 ->
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|     problog_mc_DNF(Trie, Pind, ProofCNT, Delta, Samples, 0, SamplesSoFar, Naccepted, 0, _Epsilon),
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|     P is Naccepted / SamplesSoFar * Pind
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|   ;
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|     P is Pind,
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|     problog_var_set(probability, P)
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|   ),
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|   eraseall(problog_mc_dnf).
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| 
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| problog_mc_DNF(_Trie, Pind, _ProofCNT, Delta, Samples, SamplesSoFar, SamplesSoFar, Naccepted, Naccepted, Epsilon):-
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|   SamplesSoFar > 0,
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|   SamplesSoFar mod Samples =:= 0,
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|   P is Naccepted / SamplesSoFar * Pind,
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|   problog_timer_pause(dnf_sampling_time, T),
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|   problog_timer_resume(dnf_sampling_time),
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|   problog_convergence_check(T, P, SamplesSoFar, Delta, Epsilon, Converge),
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|   (Converge = true; Converge = terminate), !,
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|   problog_var_set(samples, SamplesSoFar),
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|   problog_var_set(probability, P),
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|   Pl is P - Epsilon,
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|   Ph is P + Epsilon,
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|   problog_var_set(probability_lower, Pl),
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|   problog_var_set(probability_upper, Ph).
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| /*
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| problog_mc_DNF(_Trie, _Pind, _ProofCNT, _Delta, Samples, SamplesSoFar, _SamplesSoFar, _Naccepted, _Naccepted, _Epsilon):-
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|   SamplesSoFar mod Samples =:= 0,
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|   fail.*/
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| 
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| problog_mc_DNF(Trie, Pind, ProofCNT, Delta, Samples, SAcc, SamplesSoFar, Naccepted, NAcc, Epsilon):-
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|   NSAcc is SAcc + 1,
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|   problog_random(RND),
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|   Thr is RND * Pind,
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|   tries:trie_traverse_mode(backward),
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|   (problog_flag(search_method, binary) ->
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|     get_sample_proof_binary(CurRef, Thr, ProofCNT, L_true_pf, L_false_pf)
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|   ;
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|     get_sample_proof_linear(CurRef, Thr, L_true_pf, L_false_pf)
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|   ),
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|   (tries:trie_traverse_next(CurRef, NxtRef) ->
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|     NextRef = NxtRef
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|   ;
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|     NextRef = []
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|   ),
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|   (check_sample_proofs(NextRef, L_true_pf, L_false_pf) ->
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|     NNAcc is NAcc + 1
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|   ;
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|     NNAcc is NAcc
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|   ),
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|   (problog_flag(represent_world, record) ->
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|     eraseall(problog_sample_world)
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|   ;
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|     (problog_flag(represent_world, array) ->
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|       close_static_array(problog_sample_world)
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|     ;
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|       (problog_flag(represent_world, hash_table) ->
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|         hash_table_delete(L_true_pf),
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|         hash_table_delete(L_false_pf)
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|       ;
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|         true
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|       )
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|     )
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|   ),
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|   tries:trie_traverse_mode(forward),
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|   problog_mc_DNF(Trie, Pind, ProofCNT, Delta, Samples, NSAcc, SamplesSoFar, Naccepted, NNAcc, Epsilon).
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| 
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| 
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| get_sample_proof_linear(Ref, Thr, L_true_pf, L_false_pf):-
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|   recorded(problog_mc_dnf, proof(_Index, Ref, _Pproof, Ps), _),
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|   Thr < Ps,
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|   tries:trie_get_entry(Ref, Proof),
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|   (problog_flag(represent_world, hash_table) ->
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|     make_hash_tables(L_true_pf, L_false_pf),
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|     add_proof_to_hash_world(Proof, L_true_pf, L_false_pf)
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|   ;
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|     (problog_flag(represent_world, record) ->
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|       add_proof_to_rec_world(Proof)
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|     ;
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|       (problog_flag(represent_world, array) ->
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|         nb_getval(probclause_counter, ProbFactCNT),
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|         Size is ProbFactCNT + 1,
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|         static_array(problog_sample_world, Size, int),
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|         add_proof_to_array_world(Proof)
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|       ;
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|         add_proof_to_list_world(Proof, L_true_pf, L_false_pf)
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|       )
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|     )
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|   ).
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| 
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| get_sample_proof_binary(Ref, Thr, ProofCNT, L_true_pf, L_false_pf):-
 | |
|   Last is ProofCNT - 1,
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|   binary_search(Thr, 0, Last, Ref), !,
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|   tries:trie_get_entry(Ref, Proof),
 | |
|   (problog_flag(represent_world, hash_table) ->
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|     make_hash_tables(L_true_pf, L_false_pf),
 | |
|     add_proof_to_hash_world(Proof, L_true_pf, L_false_pf)
 | |
|   ;
 | |
|     (problog_flag(represent_world, record) ->
 | |
|       add_proof_to_rec_world(Proof)
 | |
|     ;
 | |
|       (problog_flag(represent_world, array) ->
 | |
|         nb_getval(probclause_counter, ProbFactCNT),
 | |
|         Size is ProbFactCNT + 1,
 | |
|         static_array(problog_sample_world, Size, int),
 | |
|         add_proof_to_array_world(Proof)
 | |
|       ;
 | |
|         add_proof_to_list_world(Proof, L_true_pf, L_false_pf)
 | |
|       )
 | |
|     )
 | |
|   ).
 | |
| 
 | |
| 
 | |
| binary_search(Thr, From, To, Ref):-
 | |
|   1 is To - From, !,
 | |
|   recorded(problog_mc_dnf, proof(From, RefF, _Pproof, PsF), _),
 | |
|   (Thr > PsF ->
 | |
|     recorded(problog_mc_dnf, proof(To, Ref, _PproofTo, _Ps), _)
 | |
|   ;
 | |
|     Ref = RefF
 | |
|   ).
 | |
| 
 | |
| binary_search(_Thr, Index, Index, Ref):-
 | |
|   !, recorded(problog_mc_dnf, proof(Index, Ref, _Pproof, _Ps), _).
 | |
| 
 | |
| binary_search(Thr, From, To, Res):-
 | |
|   Look is From + integer((To - From + 1) / 2),
 | |
|   recorded(problog_mc_dnf, proof(Look, _Ref, _Pproof, Ps), _), !,
 | |
|   (Thr > Ps ->
 | |
|     NewFrom is Look + 1,
 | |
|     NewTo is To
 | |
|   ;
 | |
|     NewFrom is From,
 | |
|     NewTo is Look
 | |
|   ),
 | |
|   binary_search(Thr, NewFrom, NewTo, Res).
 | |
| 
 | |
| 
 | |
| %%%%%%%%% This code can be improved and generalized %%%%%%%%%
 | |
| check_sample_proofs([], _, _).
 | |
| 
 | |
| check_sample_proofs(CurRef, L_true_pf, L_false_pf):-
 | |
|   !, tries:trie_get_entry(CurRef, Proof),
 | |
|   (problog_flag(represent_world, hash_table) ->
 | |
|     check_proof_in_hash_world(Proof, L_true_pf, L_false_pf),
 | |
|     NL_true_pf = L_true_pf,
 | |
|     NL_false_pf = L_false_pf
 | |
|   ;
 | |
|     (problog_flag(represent_world, record) ->
 | |
|       check_proof_in_rec_world(Proof),
 | |
|       NL_true_pf = L_true_pf,
 | |
|       NL_false_pf = L_false_pf
 | |
|     ;
 | |
|       (problog_flag(represent_world, array) ->
 | |
|         check_proof_in_array_world(Proof),
 | |
|         NL_true_pf = L_true_pf,
 | |
|         NL_false_pf = L_false_pf
 | |
|       ;
 | |
|         check_proof_in_list_world(Proof, L_true_pf, NL_true_pf, L_false_pf, NL_false_pf)
 | |
|       )
 | |
|     )
 | |
|   ),
 | |
|   (tries:trie_traverse_next(CurRef, NxtRef) ->
 | |
|     NextRef = NxtRef
 | |
|   ;
 | |
|     NextRef = []
 | |
|   ),
 | |
|   check_sample_proofs(NextRef, NL_true_pf, NL_false_pf).
 | |
| 
 | |
| add_proof_to_array_world([]).
 | |
| add_proof_to_array_world([not(H)|T]):-
 | |
|   !, update_array(problog_sample_world, H, -1), add_proof_to_array_world(T).
 | |
| add_proof_to_array_world([H|T]):-
 | |
|   update_array(problog_sample_world, H, 1), add_proof_to_array_world(T).
 | |
| 
 | |
| 
 | |
| check_proof_in_array_world([not(F)|_Rest]):-
 | |
|   array_element(problog_sample_world, F, 1), !.
 | |
| 
 | |
| check_proof_in_array_world([not(F)|Rest]):-
 | |
|   array_element(problog_sample_world, F, -1), !,
 | |
|   check_proof_in_array_world(Rest).
 | |
| 
 | |
| check_proof_in_array_world([not(F)|Rest]):-
 | |
|   !, problog_random(RND), Dice is RND,
 | |
|   problog:get_fact_probability(F, NumProbF),
 | |
|   (Dice =< NumProbF ->
 | |
|     update_array(problog_sample_world, F, 1)
 | |
|   ;
 | |
|     update_array(problog_sample_world, F, -1),
 | |
|     check_proof_in_array_world(Rest)
 | |
|   ).
 | |
| 
 | |
| check_proof_in_array_world([F|_Rest]):-
 | |
|   array_element(problog_sample_world, F, -1), !.
 | |
| 
 | |
| check_proof_in_array_world([F|Rest]):-
 | |
|   array_element(problog_sample_world, F, 1), !,
 | |
|   check_proof_in_array_world(Rest).
 | |
| 
 | |
| check_proof_in_array_world([F|Rest]):-
 | |
|   !, problog_random(RND), Dice is RND,
 | |
|   problog:get_fact_probability(F, NumProbF),
 | |
|   (Dice > NumProbF ->
 | |
|     update_array(problog_sample_world, F, -1)
 | |
|   ;
 | |
|     update_array(problog_sample_world, F, 1),
 | |
|     check_proof_in_array_world(Rest)
 | |
|   ).
 | |
| 
 | |
| 
 | |
| 
 | |
| 
 | |
| add_proof_to_rec_world([]).
 | |
| add_proof_to_rec_world([not(H)|T]):-
 | |
|   !, recordz(problog_sample_world, false_fact(H), _), add_proof_to_rec_world(T).
 | |
| add_proof_to_rec_world([H|T]):-
 | |
|   recordz(problog_sample_world, true_fact(H), _), add_proof_to_rec_world(T).
 | |
| 
 | |
| check_proof_in_rec_world([not(F)|_Rest]):-
 | |
|   recorded(problog_sample_world, true_fact(F), _), !.
 | |
| 
 | |
| check_proof_in_rec_world([not(F)|Rest]):-
 | |
|   recorded(problog_sample_world, false_fact(F), _), !,
 | |
|   check_proof_in_rec_world(Rest).
 | |
| 
 | |
| check_proof_in_rec_world([not(F)|Rest]):-
 | |
|   !, problog_random(RND), Dice is RND,
 | |
|   problog:get_fact_probability(F, NumProbF),
 | |
|   (Dice =< NumProbF ->
 | |
|     recordz(problog_sample_world, true_fact(F), _)
 | |
|   ;
 | |
|     recordz(problog_sample_world, false_fact(F), _),
 | |
|     check_proof_in_rec_world(Rest)
 | |
|   ).
 | |
| 
 | |
| check_proof_in_rec_world([F|_Rest]):-
 | |
|   recorded(problog_sample_world, false_fact(F), _), !.
 | |
| 
 | |
| check_proof_in_rec_world([F|Rest]):-
 | |
|   recorded(problog_sample_world, true_fact(F), _), !,
 | |
|   check_proof_in_rec_world(Rest).
 | |
| 
 | |
| check_proof_in_rec_world([F|Rest]):-
 | |
|   !, problog_random(RND), Dice is RND,
 | |
|   problog:get_fact_probability(F, NumProbF),
 | |
|   (Dice > NumProbF ->
 | |
|     recordz(problog_sample_world, false_fact(F), _)
 | |
|   ;
 | |
|     recordz(problog_sample_world, true_fact(F), _),
 | |
|     check_proof_in_rec_world(Rest)
 | |
|   ).
 | |
| 
 | |
| 
 | |
| 
 | |
| make_hash_tables(TrueHashTable, FalseHashTable):-
 | |
|   nb_getval(probclause_counter, ProbFactCNT),
 | |
|   hash_table_init(ProbFactCNT, TrueHashTable),
 | |
|   hash_table_init(ProbFactCNT, FalseHashTable).
 | |
| 
 | |
| 
 | |
| add_proof_to_hash_world([], _TrueHashTable, _FalseHashTable).
 | |
| add_proof_to_hash_world([not(H)|T], TrueHashTable, FalseHashTable):-
 | |
|   !, problog_key_to_tuple(H, Tuple),
 | |
|   hash_table_lookup(FalseHashTable, Tuple, _),
 | |
|   add_proof_to_hash_world(T, TrueHashTable, FalseHashTable).
 | |
| add_proof_to_hash_world([H|T], TrueHashTable, FalseHashTable):-
 | |
|   problog_key_to_tuple(H, Tuple),
 | |
|   hash_table_lookup(TrueHashTable, Tuple, _),
 | |
|   add_proof_to_hash_world(T, TrueHashTable, FalseHashTable).
 | |
| 
 | |
| 
 | |
| check_proof_in_hash_world([not(F)|_Rest], TrueHashTable, _FalseHashTable):-
 | |
|   problog_key_to_tuple(F, Tuple),
 | |
|   hash_table_contains(TrueHashTable, Tuple, _), !.
 | |
| 
 | |
| check_proof_in_hash_world([not(F)|Rest], TrueHashTable, FalseHashTable):-
 | |
|   problog_key_to_tuple(F, Tuple),
 | |
|   hash_table_contains(FalseHashTable, Tuple, _), !,
 | |
|   check_proof_in_hash_world(Rest, TrueHashTable, FalseHashTable).
 | |
| 
 | |
| check_proof_in_hash_world([not(F)|Rest], TrueHashTable, FalseHashTable):-
 | |
|   !, problog_random(RND), Dice is RND,
 | |
|   problog:get_fact_probability(F, NumProbF),
 | |
|   problog_key_to_tuple(F, Tuple),
 | |
|   (Dice =< NumProbF ->
 | |
|     hash_table_lookup(TrueHashTable, Tuple, _)
 | |
|   ;
 | |
|     hash_table_lookup(FalseHashTable, Tuple, _),
 | |
|     check_proof_in_hash_world(Rest, TrueHashTable, FalseHashTable)
 | |
|   ).
 | |
| 
 | |
| check_proof_in_hash_world([F|_Rest], _TrueHashTable, FalseHashTable):-
 | |
|   problog_key_to_tuple(F, Tuple),
 | |
|   hash_table_contains(FalseHashTable, Tuple, _), !.
 | |
| 
 | |
| check_proof_in_hash_world([F|Rest], TrueHashTable, FalseHashTable):-
 | |
|   problog_key_to_tuple(F, Tuple),
 | |
|   hash_table_contains(TrueHashTable, Tuple, _), !,
 | |
|   check_proof_in_hash_world(Rest, TrueHashTable, FalseHashTable).
 | |
| 
 | |
| check_proof_in_hash_world([F|Rest], TrueHashTable, FalseHashTable):-
 | |
|   !, problog_random(RND), Dice is RND,
 | |
|   problog:get_fact_probability(F, NumProbF),
 | |
|   problog_key_to_tuple(F, Tuple),
 | |
|   (Dice > NumProbF ->
 | |
|     hash_table_lookup(FalseHashTable, Tuple, _)
 | |
|   ;
 | |
|     hash_table_lookup(TrueHashTable, Tuple, _),
 | |
|     check_proof_in_hash_world(Rest, TrueHashTable, FalseHashTable)
 | |
|   ).
 | |
| 
 | |
| 
 | |
| 
 | |
| add_proof_to_list_world([], [], []).
 | |
| add_proof_to_list_world([not(H)|T], TrueList, [H|FalseList]):-
 | |
|   add_proof_to_list_world(T, TrueList, FalseList).
 | |
| add_proof_to_list_world([H|T], [H|TrueList], FalseList):-
 | |
|   add_proof_to_list_world(T, TrueList, FalseList).
 | |
| 
 | |
| check_proof_in_list_world([not(F)|_Rest], TrueList, TrueList, FalseList, FalseList):-
 | |
|   memberchk(F, TrueList), !.
 | |
| 
 | |
| check_proof_in_list_world([not(F)|Rest], TrueList, NewTrueList, FalseList, NewFalseList):-
 | |
|   memberchk(F, FalseList), !,
 | |
|   check_proof_in_list_world(Rest, TrueList, NewTrueList, FalseList, NewFalseList).
 | |
| 
 | |
| check_proof_in_list_world([not(F)|Rest], TrueList, NewTrueList, FalseList, NewFalseList):-
 | |
|   !, problog_random(RND), Dice is RND,
 | |
|   problog:get_fact_probability(F, NumProbF),
 | |
|   (Dice =< NumProbF ->
 | |
|     NewTrueList = [F|TrueList],
 | |
|     NewFalseList = FalseList
 | |
|   ;
 | |
|     check_proof_in_list_world(Rest, TrueList, NewTrueList, [F|FalseList], NewFalseList)
 | |
|   ).
 | |
| 
 | |
| check_proof_in_list_world([F|_Rest], TrueList, TrueList, FalseList, FalseList):-
 | |
|   memberchk(F, FalseList), !.
 | |
| 
 | |
| check_proof_in_list_world([F|Rest], TrueList, NewTrueList, FalseList, NewFalseList):-
 | |
|   memberchk(F, TrueList), !,
 | |
|   check_proof_in_list_world(Rest, TrueList, NewTrueList, FalseList, NewFalseList).
 | |
| 
 | |
| check_proof_in_list_world([F|Rest], TrueList, NewTrueList, FalseList, NewFalseList):-
 | |
|   !, problog_random(RND), Dice is RND,
 | |
|   problog:get_fact_probability(F, NumProbF),
 | |
|   (Dice > NumProbF ->
 | |
|     NewTrueList = TrueList,
 | |
|     NewFalseList = [F|FalseList]
 | |
|   ;
 | |
|     check_proof_in_list_world(Rest, [F|TrueList], NewTrueList, FalseList, NewFalseList)
 | |
|   ).
 | |
| 
 | |
| 
 | |
| 
 | |
| problog_collect_trie(Goal, Threshold) :-
 | |
|   problog:init_problog_low(Threshold),
 | |
|   problog:problog_control(off, up),
 | |
|   problog:problog_control(on, exact),
 | |
|   problog_var_timer_start(sld_time),
 | |
|   problog:problog_call(Goal),
 | |
|   problog:add_solution,
 | |
|   fail.
 | |
| problog_collect_trie(_, _) :-
 | |
|   problog:problog_control(off, exact),
 | |
|   problog_var_timer_stop(sld_time).
 | |
| 
 | |
| problog_dnf_sampling(Goal, Delta, P):-
 | |
|   % this should be generalized with general log file
 | |
|   problog_flag(mc_logfile, File1),
 | |
|   convert_filename_to_working_path(File1, File),
 | |
|   open(File, write, Log),
 | |
|   format(Log,'# goal: ~q~n#delta: ~w~n',[Goal, Delta]),
 | |
|   format(Log,'# samples  prob   low   high  time~2n',[]),
 | |
|   close(Log),
 | |
| 
 | |
|   problog_collect_trie(Goal, 0.0),
 | |
|   nb_getval(problog_completed_proofs, Trie_Completed_Proofs),
 | |
|   problog_var_timer_start(dnf_sampling_time),
 | |
|   problog_mc_DNF(Trie_Completed_Proofs, Delta, P),
 | |
|   problog_var_timer_stop(dnf_sampling_time),
 | |
|   (problog_flag(verbose, true) ->
 | |
|     print:problog_statistics
 | |
|   ;
 | |
|     true
 | |
|   ),
 | |
|   ptree:delete_ptree(Trie_Completed_Proofs),
 | |
|   problog:clear_tabling.
 |