/* LPAD and CP-Logic reasoning suite File lpad.pl Goal-oriented interpreter for LPADs based on SLG Copyright (c) 2007, Fabrizio Riguzzi Based on the SLG System, see below */ /***************************************************************************/ /* */ /* The SLG System */ /* Authors: Weidong Chen and David Scott Warren */ /* Copyright (C) 1993 Southern Methodist University */ /* 1993 SUNY at Stony Brook */ /* See file COPYRIGHT_SLG for copying policies and disclaimer. */ /* */ /***************************************************************************/ /*========================================================================== File : slg.pl Last Modification : November 1, 1993 by Weidong Chen =========================================================================== File : lpad.pl Last Modification : November 14, 2007 by Fabrizio Riguzzi ===========================================================================*/ /* ----------- beginning of system dependent features --------------------- To run the SLG system under a version of Prolog other than Quintus, comment out the following Quintus-specific code, and include the code for the Prolog you are running. */ :- module(lpad, [s/2,s/6, sc/3,sc/7, p/1, slg/3,setting/2,set/2 ]). :-source. :- dynamic wfs_trace/0. :-use_module(library(ugraphs)). :-use_module(library(lists)). :- use_module(library(charsio)). :- op(1200,xfx,<--). :- op(900,xfx,<-). /* SLG tracing: xtrace: turns SLG trace on, which prints out tables at various points xnotrace: turns off SLG trace */ xtrace :- ( wfs_trace -> true ; assert(wfs_trace) ). xnotrace :- ( wfs_trace -> retractall(wfs_trace) ; true ). /* isprolog(Call): Call is a Prolog subgoal */ isprolog(Call) :- builtin(Call). /* slg(Call): It returns all true answers of Call under the well-founded semantics one by one. */ slg(Call,C,D):- slg(Call,[],C,[],D). slg(Call,C0,C,D0,D):- ( isprolog(Call) -> call(Call), C=C0, D=D0 ; oldt(Call,Tab,C0,C1,D0,D1), delete(D1,(goal(_),_),D), ground(Call,Ggoal), find(Tab,Ggoal,Ent), ent_to_anss(Ent,Anss), member_anss(d(Call,Delay),Anss), (Delay=[]-> C=C1 ; write('Unsound program'), nl, C=unsound ) ). get_new_atom(Atom):- retract(new_number(N)), N1 is N+1, assert(new_number(N1)), number_atom(N,NA), atom_concat('$call',NA,Atom). s(GoalsList,Prob):- convert_to_goal(GoalsList,Goal), solve(Goal,Prob). s(GoalsList,Prob,CPUTime1,0.0,WallTime1,0.0):- statistics(cputime,[_,_]), statistics(walltime,[_,_]), convert_to_goal(GoalsList,Goal), solve(Goal,Prob), statistics(cputime,[_,CT1]), CPUTime1 is CT1/1000, statistics(walltime,[_,WT1]), WallTime1 is WT1/1000. convert_to_goal([Goal],Goal):-Goal \= (\+ _) ,!. convert_to_goal(GoalsList,Head):- get_new_atom(Atom), extract_vars(GoalsList,[],V), Head=..[Atom|V], assertz(def_rule(goal(Atom),_,Head,GoalsList)). solve(Goal,Prob):- (setof(C,D^slg(Goal,C,D),LDup)-> (member(unsound,LDup)-> format("Unsound program ~n",[]), Prob=unsound ; rem_dup_lists(LDup,[],L), (ground(L)-> build_formula(L,Formula,[],Var), var2numbers(Var,0,NewVar), (setting(save_dot,true)-> format("Variables: ~p~n",[Var]), compute_prob(NewVar,Formula,_Prob,1) ; compute_prob(NewVar,Formula,Prob,0) ) ; format("It requires the choice of a head atom from a non ground head~n~p~n",[L]), Prob=non_ground ) ) ; Prob=0 ). compute_prob(Var,For,Prob,_):- compute_prob_term(Var,For,0,Prob). compute_prob_term(_Var,[],Prob,Prob). compute_prob_term(Var,[H|T],Prob0,Prob):- compute_prob_factor(Var,H,1,PF), Prob1 is Prob0 + PF, compute_prob_term(Var,T,Prob1,Prob). compute_prob_factor(_Var,[],PF,PF). compute_prob_factor(Var,[[N,Value]|T],PF0,PF):- nth0(N,Var,[_N,_NH,ListProb]), nth0(Value,ListProb,P), PF1 is PF0*P, compute_prob_factor(Var,T,PF1,PF). sc(Goals,Evidences,Prob):- convert_to_goal(Goals,Goal), convert_to_goal(Evidences,Evidence), solve_cond(Goal,Evidence,Prob). sc(Goals,Evidences,Prob,CPUTime1,0.0,WallTime1,0.0):- statistics(cputime,[_,_]), statistics(walltime,[_,_]), convert_to_goal(Goals,Goal), convert_to_goal(Evidences,Evidence), solve_cond(Goal,Evidence,Prob), statistics(cputime,[_,CT1]), CPUTime1 is CT1/1000, statistics(walltime,[_,WT1]), WallTime1 is WT1/1000. solve_cond(Goal,Evidence,Prob):- (setof(DerivE,D^slg(Evidence,DerivE,D),LDupE)-> rem_dup_lists(LDupE,[],LE), build_formula(LE,FormulaE,[],VarE), var2numbers(VarE,0,NewVarE), compute_prob(NewVarE,FormulaE,ProbE,0), solve_cond_goals(Goal,LE,ProbGE), Prob is ProbGE/ProbE ; format("P(Evidence)=0~n",[]), Prob=undefined ). solve_cond_goals(Goals,LE,ProbGE):- (setof(DerivGE,find_deriv_GE(LE,Goals,DerivGE),LDupGE)-> rem_dup_lists(LDupGE,[],LGE), build_formula(LGE,FormulaGE,[],VarGE), var2numbers(VarGE,0,NewVarGE), call_compute_prob(NewVarGE,FormulaGE,ProbGE) ; ProbGE=0 ). solve_cond_goals(Goals,LE,0):- \+ find_deriv_GE(LE,Goals,_DerivGE). find_deriv_GE(LD,GoalsList,Deriv):- member(D,LD), slg(GoalsList,D,DerivDup,[],_Def), remove_duplicates(DerivDup,Deriv). call_compute_prob(NewVarGE,FormulaGE,ProbGE):- (setting(save_dot,true)-> format("Variables: ~p~n",[NewVarGE]), compute_prob(NewVarGE,FormulaGE,ProbGE,1) ; compute_prob(NewVarGE,FormulaGE,ProbGE,0) ). /* emptytable(EmptTab): creates an initial empty stable. */ emptytable(0:[]). /* slgall(Call,Anss): slgall(Call,Anss,N0-Tab0,N-Tab): If Call is a prolog call, findall is used, and Tab = Tab0; If Call is an atom of a tabled predicate, SLG evaluation is carried out. */ slgall(Call,Anss) :- slgall(Call,Anss,0:[],_). slgall(Call,Anss,N0:Tab0,N:Tab) :- ( isprolog(Call) -> findall(Call,Call,Anss), N = N0, Tab = Tab0 ; ground(Call,Ggoal), ( find(Tab0,Ggoal,Ent) -> ent_to_anss(Ent,Answers), Tab = Tab0 ; new_init_call(Call,Ggoal,Ent,[],S1,1,Dfn1), add_tab_ent(Ggoal,Ent,Tab0,Tab1), oldt(Call,Ggoal,Tab1,Tab,S1,_S,Dfn1,_Dfn,maxint-maxint,_Dep,N0:[],N:_TP), find(Tab,Ggoal,NewEnt), ent_to_anss(NewEnt,Answers) ), ansstree_to_list(Answers,Anss,[]) ). /* oldt(QueryAtom,Table,C0,C,D0,D): top level call for SLG resolution. It returns a table consisting of answers for each relevant subgoal. For stable predicates, it basically extract the relevant set of ground clauses by solving Prolog predicates and other well-founded predicates. */ oldt(Call,Tab,C0,C,D0,D) :- new_init_call(Call,Ggoal,Ent,[],S1,1,Dfn1), add_tab_ent(Ggoal,Ent,[],Tab1), oldt(Call,Ggoal,Tab1,Tab,S1,_S,Dfn1,_Dfn,maxint-maxint,_Dep,0:[],_TP,C0,C1,D0,D,PC), add_PC_to_C(PC,C1,C), ( wfs_trace -> nl, write('Final '), display_table(Tab), nl ; true ). /* oldt(Call,Ggoal,Tab0,Tab,Stack0,Stack,DFN0,DFN,Dep0,Dep,TP0,TP,C0,C,D0,D,PC) explores the initial set of edges, i.e., all the program clauses for Call. Ggoal is of the form Gcall-Gdfn, where Gcall is numbervar of Call and Gdfn is the depth-first number of Gcall. Tab0/Tab,Stack0/Stack, DFN0/DFN, and Dep0/Dep are accumulators for the table, the stack of subgoals, the DFN counter, and the dependencies. TP0/TP is the accumulator for newly created clauses during the processing of general clauss with universal disjunctions in the body. These clauses are created in order to guarantee polynomial data complexity in processing clauses with universal disjuntions in the body of a clause. The newly created propositions are represented by numbers. C0/C are accumulators for disjunctive clauses used in the derivation of Call: they are list of triples (N,R,S) where N is the number of the head atom used (starting from 0), R is the number of the rule used (starting from 1) and S is the substitution of the variables in the head atom used. S is a list of elements of the form Varname=Term. D0/D are accumulators for definite clauses: they are list of couples (R,S), where R is a rule number and S is a substitution. PC is a list of disjunctive rules selected but not used in the derivation, they are added to the C set afterwards if they are consistent with C (PC stands for Possible C, i.e., possible additions to the C set). */ oldt(Call,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D,PC) :- ( number(Call) -> TP0 = (_ : Tcl), find(Tcl,Call,Clause), edge_oldt(Clause,Ggoal,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1, C0,C,D0,D) ; find_rules(Call,Frames,C0,PC), map_oldt(Frames,Ggoal,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1, C0,C,D0,D) ), comp_tab_ent(Ggoal,Tab1,Tab,S1,S,Dfn1,Dfn,Dep1,Dep,TP1,TP). /* find_rules(Call,Frames,C,PossC) finds rules for Call. Frames is the list of clauses that resolve with Call. It is a list of terms of the form rule(d(Call,[]),Body,R,N,S) C is the current set of disjunctive clauses together with the head selected PossC is the list of possible disjunctive clauses together with the head selected: they are the clauses with an head that does not unify with Call. It is a list of terms of the form rule(d(Call,[]),Body,R,N,S) */ find_rules(Call,Frames,C,PossC):- findall(rule(d(Call,[]),Body,def(N),_,Subs,_),def_rule(N,Subs,Call,Body),Fr1), find_disj_rules(Call,Fr2,C,PossC), append(Fr1,Fr2,Frames). /* find_disj_rules(Call,Fr,C,PossC):- finds disjunctive rules for Call. */ find_disj_rules(Call,Fr,C,[]):- findall(rule(d(Call,[]),Body,R,N,S,LH), find_rule(Call,(R,S,N),Body,LH),Fr). find_disj_rulesold(Call,Fr,C,PossC):- findall(rule(d(Call,[]),Body,R,S,N,LH), find_rule(Call,(R,S,N),Body,LH),LD), (setof((R,LH),(Call,Body,S,N)^member(rule(d(Call,[]),Body,R,S,N,LH),LD),LR)-> choose_rules(LR,LD,[],Fr,C,[],PossC) ; Fr=[], PossC=[] ). /* choose_rules(LR,LD,Fr0,Fr,C,PossC0,PossC) LR is a list of couples (R,LH) where R is a disjunctive rule number and LH is a list of head atoms numbers, from 0 to length(head)-1 LD is the list of disjunctive clauses resolving with Call. Its elements are of the form rule(d(Call,[]),Body,R,N,S) Fr0/Fr are accumulators for the matching disjunctive clauses PossC0/PossC are accumulators for the additional disjunctive clauses */ choose_rules([],Fr,Fr,_C,PC,PC). choose_rules([rule(d(Call,[]),Body,R,S,N1,LH)|LD],Fr0,Fr,C,PC0,PC):- member(N,LH), (N=N1-> % the selected head resolves with Call consistent(N,R,S,C), Fr=[rule(d(Call,[]),Body,R,N,S)|Fr1], PC=PC1 ; % the selected head does not resolve with Call consistent(N,R,S,C), Fr=[rule(d('$null',[]),Body,R,N,S)|Fr1], PC=PC1 ), choose_rules(LD,Fr0,Fr1,C,PC0,PC1). choose_rulesold([],_LD,Fr,Fr,_C,PC,PC). choose_rulesold([(R,LH)|LR],LD,Fr0,Fr,C,PC0,PC):- member(N,LH), (member(rule(d(Call,[]),Body,R,S,N,LH),LD)-> % the selected head resolves with Call consistent(N,R,S,C), Fr=[rule(d(Call,[]),Body,R,N,S)|Fr1], PC=PC1 ; % the selected head does not resolve with Call findall(S,member(rule(d(Call,[]),Body,R,S,_N,LH),LD),LS), % this is done to handle the case in which there are % multiple instances of rule R with different substitutions (merge_subs(LS,S)-> % all the substitutions are consistent, their merge is used consistent(N,R,S,C), Fr=Fr1, PC=[rule(d(_Call,[]),Body,R,N,S)|PC1] ; % the substitutions are inconsistent, the empty substitution is used rule(R,S,_LH,_Head,_Body), consistent(N,R,S,C), Fr=Fr1, PC=[rule(d(_Call,[]),Body,R,N,S)|PC1] ) ), choose_rules(LR,LD,Fr0,Fr1,C,PC0,PC1). merge_subs([],_S). merge_subs([S|ST],S):- merge_subs(ST,S). merge_subs([],_Call,_S). merge_subs([(S,Call)|ST],Call,S):- merge_subs(ST,Call,S). /* consistent(N,R,S,C) head N of rule R with substitution S is consistent with C */ consistent(_N,_R,_S,[]):-!. consistent(N,R,S,[(_N,R1,_S)|T]):- % different rule R\=R1,!, consistent(N,R,S,T). consistent(N,R,S,[(N,R,_S)|T]):- % same rule, same head consistent(N,R,S,T). consistent(N,R,S,[(N1,R,S1)|T]):- % same rule, different head N\=N1, % different substitutions dif(S,S1), consistent(N,R,S,T). map_oldt([],_Ggoal,Tab,Tab,S,S,Dfn,Dfn,Dep,Dep,TP,TP,C,C,D,D). map_oldt([Clause|Frames],Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP, C0,C,D0,D) :- edge_oldt(Clause,Ggoal,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1, C0,C1,D0,D1), find(Tab0,Ggoal,Ent), ent_to_comp(Ent,Comp), (Comp \== true-> map_oldt(Frames,Ggoal,Tab1,Tab,S1,S,Dfn1,Dfn, Dep1,Dep,TP1,TP,C1,C,D1,D) ; Tab=Tab1,S=S1,Dfn=Dfn1,Dep=Dep1,TP=TP1,C=C1,D=D1 ). /* edge_oldt(Clause,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) Clause may be one of the following forms: rule(d(H,Dlist),Blist) rule(d(H,all(Dlist)),all(Blist)) where the second form is for general clauses with a universal disjunction of literals in the body. Dlist is a list of delayed literals, and Blist is the list of literals to be solved. Clause represents a directed edge from Ggoal to the left most subgoal in Blist. */ edge_oldt(Clause,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) :- Clause = rule(Ans,B,Rule,Number,Sub,LH), ( B == [] -> ans_edge(rule(Ans,B,Rule,Number,Sub,LH),Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) ; B = [Lit|_] -> ( Lit = (\+N) -> neg_edge(Clause,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) ; pos_edge(Clause,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) ) ; B = all(Bl) -> ( Bl == [] -> ans_edge(Ans,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) ; Bl = [Lit|_], ( Lit = (\+N) -> aneg_edge(Clause,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) ; apos_edge(Clause,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) ) ) ). /* add_ans_to_C(rule(Head,Body,R,N,S),C0,C,D0,D):- adds rule rule(Head,Body,R,N,S) to the C set if it is disjunctive or to the D set if it is definite. The rule is added only if it is consistent with the current C set */ add_ans_to_C(rule(_,_,def(N),_,S,_),Tab,C,C,D,[(N,S)|D],true):-!. add_ans_to_C(rule(Goal,_B,R,N,S,LH),Tab,C0,C,D,D,HeadSelected):- Goal=d(G,_D), (find(Tab,G,Ent)-> ent_to_anss(Ent,Anss), (member_anss(d(G,[]),Anss)-> C=C0, HeadSelected=false ; add_to_C(R,N,S,LH,C0,C,HeadSelected) ) ; add_to_C(R,N,S,LH,C0,C,HeadSelected) ). add_to_C(R,N,S,LH,C0,C,HeadSelected):- member(N1,LH), (N1=N-> HeadSelected=true ; HeadSelected=false ), \+ already_present_with_a_different_head(N1,R,S,C0), (already_present_with_the_same_head(N1,R,S,C0)-> C=C0 ; C=[(N1,R,S)|C0] ). /* already_present_with_the_same_head(N,R,S,C) succeeds if rule R is present in C with head N and substitution S */ already_present_with_the_same_head(N,R,S,[(N,R,S)|_T]):-!. already_present_with_the_same_head(N,R,S,[(_N,_R,_S)|T]):-!, already_present_with_the_same_head(N,R,S,T). /* already_present_with_a_different_head(N,R,S,C) succeeds if rule R is present in C with susbtitution S and a head different from N */ already_present_with_a_different_head(N,R,S,[(N1,R,S1)|_T]):- different_head(N,N1,S,S1),!. already_present_with_a_different_head(N,R,S,[(_N1,_R1,_S1)|T]):- already_present_with_a_different_head(N,R,S,T). different_head(N,N1,S,S1):- N\=N1,S=S1, !. /* add_PC_to_C(PossC,C0,C) adds the rules in PossC to C if they are consistent with it, otherwise it fails */ add_PC_to_C([],C,C). add_PC_to_C([rule(H,B,R,N,S)|T],C0,C):- add_ans_to_C(rule(H,B,R,N,S),C0,C1,[],[]), add_PC_to_C(T,C1,C). ans_edge(rule(Ans,B,Rule,Number,Sub,LH),Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) :- add_ans_to_C(rule(Ans,B,Rule,Number,Sub,LH),Tab0,C0,C1,D0,D1,HeadSelected), (HeadSelected=false-> Tab = Tab0, S = S0, Dfn = Dfn0, Dep = Dep0, TP = TP0, C=C1, D=D1 ; (add_ans(Tab0,Ggoal,Ans,Nodes,Mode,Tab1) -> (Mode = new_head -> returned_ans(Ans,Ggoal,RAns), map_nodes(Nodes,RAns,Tab1,Tab, S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C1,C,D1,D) ; Mode = no_new_head -> Tab = Tab1, S = S0, Dfn = Dfn0, Dep = Dep0, TP = TP0, C=C1, D=D1 ) ; Tab = Tab0, S = S0, Dfn = Dfn0, Dep = Dep0, TP = TP0, C=C1, D=D1 ) ). neg_edge(Clause,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) :- Clause = rule(_,[\+N|_],_R,_N,_Sub,_LH), ( ground(N) -> true ; write('Flounder: '), write(\+N), nl, fail ), Node = (Ggoal:Clause), Ngoal = N, % N is already ground ( isprolog(N) -> % if N is a Prolog predicate ( call(N) -> % then just call Tab = Tab0, S = S0, Dfn = Dfn0, Dep = Dep0, C=C0, D=D0, TP = TP0 ; apply_subst(Node,d(\+ N,[]),Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C1,D0,D) ) ; ( find(Tab0,Ngoal,Nent) -> Tab2 = Tab0, S2 = S0, Dfn2 = Dfn0, Dep2 = Dep0, TP2 = TP0, C2=C0, D2=D0 ; new_init_call(N,Ngoal,Ent,S0,S1,Dfn0,Dfn1), add_tab_ent(Ngoal,Ent,Tab0,Tab1), oldt(N,Ngoal,Tab1,Tab2,S1,S2,Dfn1,Dfn2,maxint-maxint,Ndep,TP0,TP2,C0,C1,D0,D2,PC), add_PC_to_C(PC,C1,C2), compute_mins(Dep0,Ndep,pos,Dep2), find(Tab2,Ngoal,Nent) ), ent_to_comp(Nent,Ncomp), ent_to_anss(Nent,Nanss), ( succeeded(Nanss) -> Tab = Tab2, S = S2, Dfn = Dfn2, Dep = Dep2, TP = TP2, C =C2, D=D2 ; failed(Nanss), Ncomp == true -> apply_subst(Node,d(\+N,[]),Tab2,Tab,S2,S,Dfn2,Dfn,Dep2,Dep,TP2,TP,C2,C,D2,D) ; apply_subst(Node,d(\+N,[\+N]),Tab2,Tab,S2,S,Dfn2,Dfn,Dep2,Dep,TP2,TP,C2,C,D2,D) ) ). pos_edge(Clause,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) :- Clause = rule(_H,[N|_B],_R,_N,_Sub,_LH), Node = (Ggoal:Clause), ground(N,Ngoal), ( isprolog(N) -> findall(d(N,[]),call(N),Nanss), map_anss_list(Nanss,Node,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) ; ( find(Tab0,Ngoal,Nent) -> ent_to_comp(Nent,Ncomp), ent_to_anss(Nent,Nanss), ( Ncomp \== true -> update_lookup_mins(Ggoal,Node,Ngoal,pos,Tab0,Tab1,Dep0,Dep1), map_anss(Nanss,Node,Ngoal,Tab1,Tab,S0,S,Dfn0,Dfn,Dep1,Dep,TP0,TP,C0,C,D0,D) ; % N is completed. map_anss(Nanss,Node,Ngoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) ) ; % otherwise N is new new_pos_call(Ngoal,Node,Ent,S0,S1,Dfn0,Dfn1), add_tab_ent(Ngoal,Ent,Tab0,Tab1), oldt(N,Ngoal,Tab1,Tab2,S1,S,Dfn1,Dfn,maxint-maxint,Ndep,TP0,TP,C0,C1,D0,D,PC), add_PC_to_C(PC,C1,C), update_solution_mins(Ggoal,Ngoal,pos,Tab2,Tab,Ndep,Dep0,Dep) ) ). aneg_edge(Clause,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) :- Clause = rule(_H,all([\+N|_B])), Node = (Ggoal:Clause), ground(N,Ngoal), ( isprolog(N) -> findall(d(N,[]),call(N),Nanss), return_to_disj_list(Nanss,Node,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) ; ( find(Tab0,Ngoal,Nent) -> ent_to_comp(Nent,Ncomp), ent_to_anss(Nent,Nanss), ( Ncomp \== true -> update_lookup_mins(Ggoal,Node,Ngoal,aneg,Tab0,Tab,Dep0,Dep), S = S0, Dfn = Dfn0, TP = TP0 ; % N is completed. return_to_disj(Nanss,Node,Ngoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) ) ; % otherwise N is new new_aneg_call(Ngoal,Node,Ent,S0,S1,Dfn0,Dfn1), add_tab_ent(Ngoal,Ent,Tab0,Tab1), oldt(N,Ngoal,Tab1,Tab2,S1,S,Dfn1,Dfn,maxint-maxint,Ndep,TP0,TP), update_solution_mins(Ggoal,Ngoal,pos,Tab2,Tab,Ndep,Dep0,Dep) ) ). apos_edge(Clause,Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) :- Clause = rule(d(H,D),all([N|B])), ( ground(N) -> true ; write('Flounder in a universal disjunction: '), write(N), nl, fail ), pos_edge(rule(d(H,[]),[N]),Ggoal,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1), edge_oldt(rule(d(H,D),all(B)),Ggoal,Tab1,Tab,S1,S,Dfn1,Dfn,Dep1,Dep,TP1,TP). apply_subst(Ggoal:Cl,d(An,Vr),Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) :- copy_term(Cl,rule(d(Ac,Vc),Body,R,N,Sub,LH)), ( Body = [Call|NBody] -> Call = An, append(Vr,Vc,Vn) ; Body = all([Call|Calls]), % Call = An, % An is the numbervar-ed version of Call. ( Vc == [] -> Vn = all(Vr) ; Vc = all(Vc0), append(Vr,Vc0,Vn0), Vn = all(Vn0) ), NBody = all(Calls) ), edge_oldt(rule(d(Ac,Vn),NBody,R,N,Sub,LH),Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D). /* map_nodes(Nodes,Ans,....): return Ans to each of the waiting nodes in Nodes, where a node is of the form Ggoal:Clause. */ map_nodes([],_Ans,Tab,Tab,S,S,Dfn,Dfn,Dep,Dep,TP,TP,C,C,D,D). map_nodes([Node|Nodes],Ans,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) :- apply_subst(Node,Ans,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1,C0,C1,D0,D1), map_nodes(Nodes,Ans,Tab1,Tab,S1,S,Dfn1,Dfn,Dep1,Dep,TP1,TP,C1,C,D1,D). map_anss([],_Node,_Ngoal,Tab,Tab,S,S,Dfn,Dfn,Dep,Dep,TP,TP,C,C,D,D). map_anss(l(_GH,Lanss),Node,Ngoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) :- ( Lanss == [] -> Tab = Tab0, S = S0, Dfn = Dfn0, Dep = Dep0, TP = TP0, C=C0, D=D0 ; Lanss = [Ans|_], returned_ans(Ans,Ngoal,RAns), apply_subst(Node,RAns,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) ). map_anss(n2(T1,_,T2),Node,Ngoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) :- map_anss(T1,Node,Ngoal,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1,C0,C1,D0,D1), map_anss(T2,Node,Ngoal,Tab1,Tab,S1,S,Dfn1,Dfn,Dep1,Dep,TP1,TP,C1,C,D1,D). map_anss(n3(T1,_,T2,_,T3),Node,Ngoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) :- map_anss(T1,Node,Ngoal,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1,C0,C1,D0,D1), map_anss(T2,Node,Ngoal,Tab1,Tab2,S1,S2,Dfn1,Dfn2,Dep1,Dep2,TP1,TP2,C1,C2,D1,D2), map_anss(T3,Node,Ngoal,Tab2,Tab,S2,S,Dfn2,Dfn,Dep2,Dep,TP2,TP,C2,C,D2,D). map_anss_list([],_Node,Tab,Tab,S,S,Dfn,Dfn,Dep,Dep,TP,TP,C,C,D,D). map_anss_list([Ans|Lanss],Node,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP,C0,C,D0,D) :- apply_subst(Node,Ans,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1,C0,C1,D0,D1), map_anss_list(Lanss,Node,Tab1,Tab,S1,S,Dfn1,Dfn,Dep1,Dep,TP1,TP,C1,C,D1,D). /* return_to_disj(Nanss,Node,Ngoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) Nanss: an answer table for Ngoal Node: is of the form (Ggoal:Clause), where Clause is of the form rule(d(H,D),all([\+N|B])) It carries out resolution of each answer with Clause, and constructs a new clause rule(Head,NBody), where the body is basically a conjunction of all the resolvents. If a resolvent is a disjunction or a non-ground literal, a new proposition is created (which is actually represented by a number), which has a clause whose body is the resolvent. */ return_to_disj(Nanss,Node,Ngoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) :- Node = (Ggoal : Clause), Clause = rule(Head,all(Body)), TP0 = (N0 : Tcl0), negative_return_all(Nanss,Body,Ngoal,NBody,[],N0,N,Tcl0,Tcl), TP1 = (N : Tcl), edge_oldt(rule(Head,NBody),Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP1,TP). negative_return_all([],_Body,_Ngoal,NBody,NBody,N,N,Tcl,Tcl). negative_return_all(l(_GH,Lanss),Body,Ngoal,NBody0,NBody,N0,N,Tcl0,Tcl) :- ( Lanss == [] -> NBody0 = NBody, N = N0, Tcl = Tcl0 ; Lanss = [Ans|_], negative_return_one(Ans,Body,Ngoal,NBody0,NBody,N0,N,Tcl0,Tcl) ). negative_return_all(n2(T1,_,T2),Body,Ngoal,NBody0,NBody,N0,N,Tcl0,Tcl) :- negative_return_all(T1,Body,Ngoal,NBody0,NBody1,N0,N1,Tcl0,Tcl1), negative_return_all(T2,Body,Ngoal,NBody1,NBody,N1,N,Tcl1,Tcl). negative_return_all(n3(T1,_,T2,_,T3),Body,Ngoal,NBody0,NBody,N0,N,Tcl0,Tcl) :- negative_return_all(T1,Body,Ngoal,NBody0,NBody1,N0,N1,Tcl0,Tcl1), negative_return_all(T2,Body,Ngoal,NBody1,NBody2,N1,N2,Tcl1,Tcl2), negative_return_all(T3,Body,Ngoal,NBody2,NBody,N2,N,Tcl2,Tcl). negative_return_one(d(H,Tv),Body,Ngoal,NBody0,NBody,N0,N,Tcl0,Tcl) :- copy_term(Body,[\+Call|Bs]), H = Call, ( Tv == [] -> % no delay ( (Bs = [Lit], ground(Lit)) -> % resovlent is a ground literal NBody0 = [Lit|NBody], N = N0, Tcl = Tcl0 ; Lit = N0, % otherwise, replace it with a number N is N0+1, NBody0 = [Lit|NBody], Clause = rule(d(Lit,[]),all(Bs)), add_tab_ent(Lit,Clause,Tcl0,Tcl) ) ; ( ground(H) -> % if there is delay, always replace with number NewTv = [\+H] ; ground(H,GH), NewTv = [Ngoal - (\+GH)] ), Lit = N0, N is N0+1, NBody0 = [Lit|NBody], Clause = rule(d(Lit,all(NewTv)),all(Bs)), add_tab_ent(Lit,Clause,Tcl0,Tcl) ). return_to_disj_list(Lanss,Node,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) :- Node = (Ggoal : Clause), Clause = rule(Head,all(Body)), TP0 = (N0 : Tcl0), negative_return_list(Lanss,Body,NBody,[],N0,N,Tcl0,Tcl), TP1 = (N : Tcl), edge_oldt(rule(Head,NBody),Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP1,TP). negative_return_list([],_Body,NBody,NBody,N,N,Tcl,Tcl). negative_return_list([d(H,[])|Lanss],Body,NBody0,NBody,N0,N,Tcl0,Tcl) :- copy_term(Body,[\+Call|Bs]), H = Call, ( Bs = [Lit], ground(Lit) -> NBody0 = [Lit|NBody1], N1 = N0, Tcl1 = Tcl0 ; Lit = N0, N1 is N0+1, NBody0 = [Lit|NBody1], Clause = rule(d(Lit,[]),all(Bs)), add_tab_ent(Lit,Clause,Tcl0,Tcl1) ), negative_return_list(Lanss,Body,NBody1,NBody,N1,N,Tcl1,Tcl). /* comp_tab_ent(Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) check if Ggoal and subgoals on top of it on the stack are completely evaluated. */ comp_tab_ent(Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) :- ( Dep0 == maxint-maxint -> process_pos_scc(Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep,TP0,TP) ; update_mins(Ggoal,Dep0,pos,Tab0,Tab1,Gdfn,Gdep), Gdep = Gpmin-Gnmin, ( Gdfn @=< Gpmin, Gnmin == maxint -> process_pos_scc(Ggoal,Tab1,Tab,S0,S,Dfn0,Dfn,Dep,TP0,TP) ; Gdfn @=< Gpmin, Gdfn @=< Gnmin -> process_neg_scc(Ggoal,Tab1,Tab,S0,S,Dfn0,Dfn,Dep,TP0,TP) ; Tab = Tab1, S0 = S, Dfn = Dfn0, Dep = Gdep, TP = TP0 ) ). process_pos_scc(Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep,TP0,TP) :- ( wfs_trace -> write('Stack: '), nl, display_stack(S0,Tab0), write('Completed call found: '), write(Ggoal), nl, display_table(Tab0), write('Completing calls ......'), nl, nl ; true ), pop_subgoals(Ggoal,S0,S1,[],Scc), complete_comp(Scc,Tab0,Tab1,Alist,[]), return_aneg_nodes(Alist,Tab1,Tab,S1,S,Dfn0,Dfn,maxint-maxint,Dep,TP0,TP). /* pop_subgoals(Ggoal,S0,S,Scc0,Scc) pop off the stack subgoals up to and including Ggoal */ pop_subgoals(Ggoal,S0,S,Scc0,Scc) :- S0 = [Sent|S1], ( Ggoal == Sent -> S = S1, Scc = [Sent|Scc0] ; pop_subgoals(Ggoal,S1,S,[Sent|Scc0],Scc) ). /* complete_comp(Scc,Tab0,Tab,Alist0,Alist): process the list Scc of subgoals that are completely evaluated. */ complete_comp([],Tab,Tab,Alist,Alist). complete_comp([Ggoal|Scc],Tab0,Tab,Alist0,Alist) :- complete_one(Ggoal,Tab0,Tab1,Alist0,Alist1), complete_comp(Scc,Tab1,Tab,Alist1,Alist). /* complete_one(Ggoal,Tab0,Tab,Alist0,Alist) process one subgoal that has been completely evaluated: 1. set its Nodes and Negs to [] and Comp to true; 2. simplify its answers and set up links for further simplification later; 3. use the truth value of Ggoal to simplify answers of other complete subgoals (possibly including itself). 4. set Alist0/Alist: a list of negation nodes with universal disjunctions with associated answers for the selected negative literal. */ complete_one(Ggoal,Tab0,Tab,Alist0,Alist) :- updatevs(Tab0,Ggoal,Ent0,Ent,Tab1), Ent0 = e(_Nodes,ANegs,Anss0,Delay,_Comp,Gdfn,Slist0), Ent = e([],[],Anss,Delay,true,Gdfn,Slist), ( Delay == true -> reduce_ans(Anss0,Anss,Tab0), setup_simp_links(Anss,Ggoal,Slist0,Slist1,Tab1,Tab2) ; % Delay == false Anss = Anss0, Tab2 = Tab1, Slist1 = Slist0 ), extract_known(Ggoal,Anss,Slist1,Slist,Klist), simplify(Klist,Tab2,Tab,[]), ( ANegs == [] -> Alist0 = Alist ; Alist0 = [(Anss,Ggoal)-ANegs|Alist] ). setup_simp_links([],_,Slist,Slist,Tab,Tab). setup_simp_links(l(GH,Lanss),Ggoal,Slist0,Slist,Tab0,Tab) :- setup_simp_links_list(Lanss,Ggoal-GH,Ggoal,Slist0,Slist,Tab0,Tab). setup_simp_links(n2(T1,_,T2),Ggoal,Slist0,Slist,Tab0,Tab) :- setup_simp_links(T1,Ggoal,Slist0,Slist1,Tab0,Tab1), setup_simp_links(T2,Ggoal,Slist1,Slist,Tab1,Tab). setup_simp_links(n3(T1,_,T2,_,T3),Ggoal,Slist0,Slist,Tab0,Tab) :- setup_simp_links(T1,Ggoal,Slist0,Slist1,Tab0,Tab1), setup_simp_links(T2,Ggoal,Slist1,Slist2,Tab1,Tab2), setup_simp_links(T3,Ggoal,Slist2,Slist,Tab2,Tab). /* setup_simp_link_list(Lanss,Ggoal-GH,Ggoal,Slist0,Slist,Tab0,Tab) Ggoal-GH is to tell what portion of answers of Ggoal can be simplified. */ setup_simp_links_list([],_,_,Slist,Slist,Tab,Tab). setup_simp_links_list([d(_,D)|Anss],GHead,Ggoal,Slist0,Slist,Tab0,Tab) :- ( D = all(Ds) -> true ; Ds = D ), links_from_one_delay(Ds,GHead,Ggoal,Slist0,Slist1,Tab0,Tab1), setup_simp_links_list(Anss,GHead,Ggoal,Slist1,Slist,Tab1,Tab). /* A link ((Ggoal-GH):Lit) in an entry for Ngoal means that the literal Lit in an answer with head GH in Ggoal can be potentially simplified if we know answers for Ngoal. */ links_from_one_delay([],_,_,Slist,Slist,Tab,Tab). links_from_one_delay([D|Ds],GHead,Ggoal,Slist0,Slist,Tab0,Tab) :- ( D = (\+ Ngoal) -> ( Ggoal == Ngoal -> Tab1 = Tab0, Slist1 = [GHead:D|Slist0] ; add_link_to_ent(Tab0,Ngoal,GHead:D,Tab1), Slist1 = Slist0 ) ; D = (Ngoal-_) -> ( Ggoal == Ngoal -> Slist1 = [GHead:D|Slist0], Tab1 = Tab0 ; Slist1 = Slist0, add_link_to_ent(Tab0,Ngoal,GHead:D,Tab1) ) ), links_from_one_delay(Ds,GHead,Ggoal,Slist1,Slist,Tab1,Tab). /* extract_known(Ggoal,Anss,Links,Slist,Klist): Given Ggoal and its answers Anss, and its simplification Links, it partitioned Links into Slist and Klist of links, where Klist is a list of links that are known to be either true or false. Klist is either of the form Val-Links, or a list of the form Val-Link. In case of non-ground calls, the corresponding portion of Anss has to be searched. */ extract_known(Ggoal,Anss,Links,Slist,Klist) :- ( failed(Anss) -> Klist = fail-Links, Slist = [] ; Anss = l(GH,Lanss) -> ( Ggoal == GH -> % Ground or most general call ( memberchk(d(_,[]),Lanss) -> Klist = succ-Links, Slist = [] ; Klist = [], Slist = Links ) ; % non-ground call extract_known_anss(Links,Anss,[],Slist,[],Klist) ) ; % non-ground call extract_known_anss(Links,Anss,[],Slist,[],Klist) ). extract_known_anss([],_,Slist,Slist,Klist,Klist). extract_known_anss([Link|Links],Anss,Slist0,Slist,Klist0,Klist) :- Link = (_:Lit), extract_lit_val(Lit,Anss,true,Val), ( Val == undefined -> Slist1 = [Link|Slist0], Klist1 = Klist0 ; Slist1 = Slist0, Klist1 = [Val-Link|Klist0] ), extract_known_anss(Links,Anss,Slist1,Slist,Klist1,Klist). /* extract_lit_val(Lit,Anss,Comp,Val): extract the truth value of Lit according to Anss and Comp. In case of a non-ground calls, the corresponding portion of Anss has to be searched. */ extract_lit_val(Lit,Anss,Comp,Val) :- ( Lit = (\+ _) -> ( succeeded(Anss) -> Val = fail ; failed(Anss), Comp == true -> Val = succ ; Val = undefined ) ; Lit = (_ - (\+GH)) -> ( find(Anss,GH,Lanss) -> ( (\+ \+ memberchk(d(GH,[]),Lanss)) -> Val = fail ; Lanss == [], Comp == true -> Val = succ ; Val = undefined ) ; ( Comp == true -> Val = succ ; Val = undefined ) ) ; Lit = (_-GH) -> ( find(Anss,GH,Lanss) -> ( (\+ \+ memberchk(d(GH,[]),Lanss)) -> Val = succ ; Lanss == [], Comp == true -> Val = fail ; Val = undefined ) ; ( Comp == true -> Val = fail ; Val = undefined ) ) ). /* simplify(KnownLinks,Tab0,Tab,Abd): Given a list of KnownLinks, Tab0 and Abd, it tries to simplify answers according to KnownLinks. When a subgoal is found to be true or false according to answers, consistency with assumed truth values in Abd is checked. */ simplify([],Tab,Tab,_Abd). simplify([Val-Link|Klist],Tab0,Tab,Abd) :- simplify_one(Val,Link,Tab0,Tab1,Abd), simplify(Klist,Tab1,Tab,Abd). simplify(Val-Links,Tab0,Tab,Abd) :- simplify_list(Links,Val,Tab0,Tab,Abd). simplify_list([],_,Tab,Tab,_Abd). simplify_list([Link|Links],Val,Tab0,Tab,Abd) :- Link = (_ : Lit), ( ( Lit = (\+_); Lit = (_ - (\+_)) ) -> ( Val = fail -> LVal = succ; LVal = fail ) ; LVal = Val ), simplify_one(LVal,Link,Tab0,Tab1,Abd), simplify_list(Links,Val,Tab1,Tab,Abd). simplify_one(Val,Link,Tab0,Tab,Abd) :- Link = ((Ngoal - GH) : Lit), updatevs(Tab0,Ngoal,Ent0,Ent,Tab1), Ent0 = e(Nodes,ANegs,Anss0,Delay,Comp,Dfn,Slist0), Ent = e(Nodes,ANegs,Anss,Delay,Comp,Dfn,Slist), ( updatevs(Anss0,GH,Lanss0,Lanss,Anss) -> simplify_anss(Lanss0,Val,Lit,[],Lanss,C), ( C == true -> ( find(Abd,GH,Aval) -> ( Aval == true, Lanss == [] -> % deduced result inconsistent with assumption fail ; Aval == false, memberchk( d(_ , []), Lanss) -> fail ; true ) ; true ), extract_known(Ngoal,Anss,Slist0,Slist,Klist), simplify(Klist,Tab1,Tab,Abd) ; Tab = Tab0 ) ; Tab = Tab0 ). /* simplify_anss(List,Val,Lit,Lanss0,Lanss,C): Given a List of answers, Val of Lit, it simplifies the List and construct a new list Lanss0/Lanss of answers. C is unified with true if some simplification is carried out. As soon as a true answer is detected, all other answers with the same head are deleted. */ simplify_anss([],_,_,Anss,Anss,_). simplify_anss([Ans|Rest],Val,Lit,Anss0,Anss,C) :- ( simplified_ans(Ans,Val,Lit,NewAns,C) -> ( NewAns = d(_,[]) -> Anss = [NewAns] ; Anss1 = [NewAns|Anss0], simplify_anss(Rest,Val,Lit,Anss1,Anss,C) ) ; C = true, simplify_anss(Rest,Val,Lit,Anss0,Anss,C) ). simplified_ans(Ans,Val,Lit,NewAns,C) :- Ans = d(H,Ds), ( Ds == [] -> NewAns = Ans ; Ds = all(Dlist) -> ( Val == fail -> delete_lit(Dlist,Lit,NewDlist,[],C), ( NewDlist == [] -> fail ; NewAns = d(H,all(NewDlist)) ) ; % Val == succ -> ( memberchk(Lit,Dlist) -> NewAns = d(H,[]), C = true ; NewAns = Ans ) ) ; % Ds is a conjunction ( Val == fail -> ( memberchk(Lit,Ds) -> fail ; NewAns = Ans ) ; % Val == succ -> delete_lit(Ds,Lit,NewDs,[],C), NewAns = d(H,NewDs) ) ). /* delete_lit(Delays,Lit,Ds0,Ds,C): deletes Lit from Delays. Delays is a list of delayed literals and it is guaranteed to have no duplicates. */ delete_lit([],_,Ds,Ds,_). delete_lit([D|Rest],Lit,Ds0,Ds,C) :- ( D == Lit -> Ds0 = Rest, C = true ; Ds0 = [D|Ds1], delete_lit(Rest,Lit,Ds1,Ds,C) ). % return answers to negative nodes within universal disjunctions return_aneg_nodes([],Tab,Tab,S,S,Dfn,Dfn,Dep,Dep,TP,TP). return_aneg_nodes([(Anss,Ngoal)-ANegs|Alist],Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) :- map_anegs(ANegs,Anss,Ngoal,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1), return_aneg_nodes(Alist,Tab1,Tab,S1,S,Dfn1,Dfn,Dep1,Dep,TP1,TP). map_anegs([],_Anss,_Ngoal,Tab,Tab,S,S,Dfn,Dfn,Dep,Dep,TP,TP). map_anegs([Node|ANegs],Anss,Ngoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) :- return_to_disj(Anss,Node,Ngoal,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1), map_anegs(ANegs,Anss,Ngoal,Tab1,Tab,S1,S,Dfn1,Dfn,Dep1,Dep,TP1,TP). /* process a component of subgoals that may be involved in negative loops. */ process_neg_scc(Ggoal,Tab0,Tab,S0,S,Dfn0,Dfn,Dep,TP0,TP) :- ( wfs_trace -> write('Stack: '), nl, display_stack(S0,Tab0), write('Possible negative loop: '), write(Ggoal), nl, display_table(Tab0) ; true ), extract_subgoals(Ggoal,S0,Scc,[]), reset_nmin(Scc,Tab0,Tab1,Ds,[]), ( wfs_trace -> write('Delaying: '), display_dlist(Ds) ; true ), delay_and_cont(Ds,Tab1,Tab2,S0,S1,Dfn0,Dfn1,maxint-maxint,Dep1,TP0,TP1), recomp_scc(Scc,Tab2,Tab,S1,S,Dfn1,Dfn,Dep1,Dep,TP1,TP). /* extract_subgoals(Ggoal,S0,Scc0,Scc) extract subgoals that may be involved in negative loops, but leave the stack of subgoals intact. */ extract_subgoals(Ggoal,[Sent|S],[Sent|Scc0],Scc) :- ( Ggoal == Sent -> Scc0 = Scc ; extract_subgoals(Ggoal,S,Scc0,Scc) ). /* reset_nmin(Scc,Tab0,Tab,Dnodes0,Dnodes) reset NegLink and collect all waiting nodes that need to be delayed. Dnodes0/Dnodes is a difference list. */ reset_nmin([],Tab,Tab,Ds,Ds). reset_nmin([Ggoal|Scc],Tab0,Tab,Ds0,Ds) :- get_and_reset_negs(Tab0,Ggoal,ANegs,Tab1), ( ANegs == [] -> Ds0 = Ds1 ; Ds0 = [Ggoal-ANegs|Ds1] ), reset_nmin(Scc,Tab1,Tab,Ds1,Ds). delay_and_cont([],Tab,Tab,S,S,Dfn,Dfn,Dep,Dep,TP,TP). delay_and_cont([Ggoal-Negs|Dnodes],Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) :- map_nodes(Negs,d(\+Ggoal,[\+Ggoal]),Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1), delay_and_cont(Dnodes,Tab1,Tab,S1,S,Dfn1,Dfn,Dep1,Dep,TP1,TP). recomp_scc([],Tab,Tab,S,S,Dfn,Dfn,Dep,Dep,TP,TP). recomp_scc([Ggoal|Scc],Tab0,Tab,S0,S,Dfn0,Dfn,Dep0,Dep,TP0,TP) :- comp_tab_ent(Ggoal,Tab0,Tab1,S0,S1,Dfn0,Dfn1,Dep0,Dep1,TP0,TP1), recomp_scc(Scc,Tab1,Tab,S1,S,Dfn1,Dfn,Dep1,Dep,TP1,TP). /* routines for incremental update of dependency information */ /* update_mins(Ggoal,Dep,Sign,Tab0,Tab,Gdfn,Gdep) update the PosLink and NegLink of Ggoal according to Dep and Sign */ update_mins(Ggoal,Dep,Sign,Tab0,Tab,Gdfn,Gdep) :- Ent0 = e(Nodes,ANegs,Anss,Delay,Comp,Gdfn:Gdep0,Slist), Ent = e(Nodes,ANegs,Anss,Delay,Comp,Gdfn:Gdep,Slist), updatevs(Tab0,Ggoal,Ent0,Ent,Tab), compute_mins(Gdep0,Dep,Sign,Gdep). /* update_lookup_mins(Ggoal,Node,Ngoal,Sign,Tab0,Tab,Dep0,Dep) There is a lookup edge (Node) from Ggoal to Ngoal with Sign. It adds Node to the corresponding waiting list in Ngoal and then update the dependencies of Ggoal. */ update_lookup_mins(Ggoal,Node,Ngoal,Sign,Tab0,Tab,Dep0,Dep) :- updatevs(Tab0,Ngoal,Ent0,Ent,Tab1), ( Sign == pos -> pos_to_newent(Ent0,Ent,Node) ; Sign == aneg -> aneg_to_newent(Ent0,Ent,Node) ), Ent0 = e(_,_,_,_,_,_Ndfn:Ndep,_), compute_mins(Dep0,Ndep,Sign,Dep), update_mins(Ggoal,Ndep,Sign,Tab1,Tab,_,_). /* update_solution_mins(Ggoal,Ngoal,Sign,Tab0,Tab,Ndep,Dep0,Dep) There is an edge with Sign from Ggoal to Ngoal, where Ngoal is a new subgoal. Ndep is the final dependency information of Ngoal. Dep0/Dep is for the most recent enclosing new call. This predicate is called after Ngoal is solved. */ update_solution_mins(Ggoal,Ngoal,Sign,Tab0,Tab,Ndep,Dep0,Dep) :- find(Tab0,Ngoal,Nent), ent_to_comp(Nent,Ncomp), ( Ncomp == true -> ( Ndep == maxint-maxint -> Tab = Tab0, Dep = Dep0 ; update_mins(Ggoal,Ndep,pos,Tab0,Tab,_,_), compute_mins(Dep0,Ndep,pos,Dep) ) ; update_mins(Ggoal,Ndep,Sign,Tab0,Tab,_,_), compute_mins(Dep0,Ndep,Sign,Dep) ). compute_mins(Gpmin-Gnmin,Npmin-Nnmin,Sign,Newpmin-Newnmin) :- ( Sign == pos -> min(Gpmin,Npmin,Newpmin), min(Gnmin,Nnmin,Newnmin) ; % (Sign == neg; Sign == aneg) -> Newpmin=Gpmin, min(Gnmin,Npmin,Imin), min(Imin,Nnmin,Newnmin) ). min(X,Y,M) :- ( X @< Y -> M=X; M=Y ). %%%%%%%%%%%%%%% Local table manipulation predicates %%%%%%%%%% /* Table Entry Structure: For each Call, its table entry is identified with its number-vared version -- Ggoal. Its value is a term of the form e(Nodes,ANegs,Anss,Delay,Comp,Dfn:Dep,Slist) where Nodes: positive suspension list ANegs: negative suspension list (for universal disjunction clauss) Anss: another table. Delay: whether Anss contains any answer with delay Comp: whether Call is completely evaluated or not Dfn: depth-first number of Gcall Dep: (PosLink-NegLink) --- dependency information Slist: a list of nodes whose answers may be simplified if the truth value of Ggoal is known. Each element of Slist is of the form (Ngoal-GH):Literal. Stack Entry Structure: Ggoal */ /* routines for accessing individual fields of an entry */ ent_to_nodes(e(Nodes,_,_,_,_,_,_),Nodes). ent_to_anegs(e(_,ANegs,_,_,_,_,_),ANegs). ent_to_anss(e(_,_,Anss,_,_,_,_),Anss). ent_to_delay(e(_,_,_,Delay,_,_,_),Delay). ent_to_comp(e(_,_,_,_,Comp,_,_),Comp). ent_to_dfn(e(_,_,_,_,_,Dfn,_),Dfn). ent_to_slist(e(_,_,_,_,_,_,Slist),Slist). get_and_reset_negs(Tab0,Ggoal,ANegs,Tab) :- Ent0 = e(Nodes,ANegs,Anss,Delay,Comp,Gdfn: (Gpmin - _),Slist), Ent = e(Nodes,[],Anss,Delay,Comp,Gdfn:Gpmin-maxint,Slist), updatevs(Tab0,Ggoal,Ent0,Ent,Tab). /* adding a new table entry */ add_tab_ent(Ggoal,Ent,Tab0,Tab) :- addkey(Tab0,Ggoal,Ent,Tab). /* The following three routines are for creating new calls */ /* a new call with empty suspensions */ new_init_call(Call,Ggoal,Ent,S0,S,Dfn0,Dfn) :- ground(Call,Ggoal), S = [Ggoal|S0], Dfn is Dfn0+1, Ent = e([],[],[],false,false,Dfn0:Dfn0-maxint,[]). /* a new call with an initial negative suspension from inside a universal disjunction */ new_aneg_call(Ngoal,Neg,Ent,S0,S,Dfn0,Dfn) :- S = [Ngoal|S0], Dfn is Dfn0+1, Ent = e([],[Neg],[],false,false,Dfn0:Dfn0-maxint,[]). /* a new call with an initial positive suspension */ new_pos_call(Ngoal,Node,Ent,S0,S,Dfn0,Dfn) :- S = [Ngoal|S0], Dfn is Dfn0+1, Ent = e([Node],[],[],false,false,Dfn0:Dfn0-maxint,[]). /* routines for adding more information to a table entry. */ aneg_to_newent(Ent0,Ent,ANeg) :- Ent0 = e(Nodes,ANegs,Anss,Delay,Comp,Dfn,Slist), Ent = e(Nodes,[ANeg|ANegs],Anss,Delay,Comp,Dfn,Slist). pos_to_newent(Ent0,Ent,Node) :- Ent0 = e(Nodes,ANegs,Anss,Delay,Comp,Dfn,Slist), Ent = e([Node|Nodes],ANegs,Anss,Delay,Comp,Dfn,Slist). add_link_to_ent(Tab0,Ggoal,Link,Tab) :- updatevs(Tab0,Ggoal,Ent0,Ent,Tab), link_to_newent(Ent0,Ent,Link). link_to_newent(Ent0,Ent,Link) :- Ent0 = e(Nodes,ANegs,Anss,Delay,Comp,Dfn,Slist), Ent = e(Nodes,ANegs,Anss,Delay,Comp,Dfn,[Link|Slist]). /* routines for manipulating answers */ ansstree_to_list([],L,L). ansstree_to_list(l(_GH,Lanss),L0,L) :- attach(Lanss,L0,L). ansstree_to_list(n2(T1,_M,T2),L0,L) :- ansstree_to_list(T1,L0,L1), ansstree_to_list(T2,L1,L). ansstree_to_list(n3(T1,_M2,T2,_M3,T3),L0,L) :- ansstree_to_list(T1,L0,L1), ansstree_to_list(T2,L1,L2), ansstree_to_list(T3,L2,L). attach([],L,L). attach([d(H,B)|R],[X|L0],L) :- ( B == [] -> X = H ; X = (H <- B) ), attach(R,L0,L). member_anss(Ans,Anss) :- member_anss_1(Anss,Ans). member_anss_1(l(_,Lanss),Ans) :- member(Ans,Lanss). member_anss_1(n2(T1,_,T2),Ans) :- ( member_anss_1(T1,Ans) ; member_anss_1(T2,Ans) ). member_anss_1(n3(T1,_,T2,_,T3),Ans) :- ( member_anss_1(T1,Ans) ; member_anss_1(T2,Ans) ; member_anss_1(T3,Ans) ). /* failed(Anss): Anss is empty */ failed([]). failed(l(_,[])). /* succeeded(Anss): Anss contains a single definite answer */ succeeded(l(_,Lanss)) :- memberchk(d(_,[]),Lanss). /* add_ans(Tab0,Goal,Ans,Nodes,Mode,Tab): If Ans is not subsumed by any existing answer then Ans is added to Anss(Goal); If some existing answer also has head H then Mode = no_new_head else Mode = new_head else fail. */ add_ans(Tab0,Ggoal,Ans,Nodes,Mode,Tab) :- Ans = d(H,[]), ground(H), H=Ggoal,!, updatevs(Tab0,Ggoal,Ent0,Ent,Tab), new_ans_ent1(Ent0,Ent,Ans,Nodes,Mode). add_ans(Tab0,Ggoal,Ans,Nodes,Mode,Tab) :- updatevs(Tab0,Ggoal,Ent0,Ent,Tab), Ans = d(H,Ds), ( Ds == [] -> new_ans_ent(Ent0,Ent,Ans,Nodes,Mode) ; setof(X,member(X,Ds),NewDs), new_ans_ent(Ent0,Ent,d(H,NewDs),Nodes,Mode) ). new_ans_ent1(Ent0,Ent,Ans,Nodes,Mode) :- Ent0 = e(Nodes,ANegs,Anss0,Delay0,Comp,Dfn,Slist), Ent = e(Nodes,ANegs,Anss,Delay,true,Dfn,Slist), Ans = d(H,[]), ( updatevs(Anss0,H,Lanss0,Lanss,Anss) -> Lanss = [Ans], Mode = no_new_head ; addkey(Anss0,H,[Ans],Anss), Mode = new_head ), Delay = Delay0 . new_ans_ent(Ent0,Ent,Ans,Nodes,Mode) :- Ent0 = e(Nodes,ANegs,Anss0,Delay0,Comp,Dfn,Slist), Ent = e(Nodes,ANegs,Anss,Delay,Comp,Dfn,Slist), Ans = d(H,D), ground(H,GH), ( updatevs(Anss0,GH,Lanss0,Lanss,Anss) -> ( D == [] -> \+(memberchk(d(_,[]),Lanss0)), Lanss = [Ans] ; not_subsumed_ans(Ans,Lanss0), Lanss = [Ans|Lanss0] ), Mode = no_new_head ; addkey(Anss0,GH,[Ans],Anss), Mode = new_head ), ( D == [] -> Delay = Delay0 ; Delay = true ). /* returned_ans(Ans,Ggoal,RAns): determines whether SLG resolution or SLG factoring should be applied. */ returned_ans(d(H,Tv),Ggoal,d(H,NewTv)) :- ( Tv = [] -> NewTv = [] ; ground(H,GH), NewTv = [Ggoal-GH] ). % reduce a list of answers, by reducing delay list, and by subsumption reduce_ans(Anss0,Anss,Tab) :- reduce_completed_ans(Anss0,Anss,Tab). % simplify all the delay lists in a list of answers. reduce_completed_ans([],[],_Tab). reduce_completed_ans(l(GH,Lanss0),l(GH,Lanss),Tab) :- reduce_completed_anslist(Lanss0,[],Lanss,Tab). reduce_completed_ans(n2(T1,M,T2),n2(NT1,M,NT2),Tab) :- reduce_completed_ans(T1,NT1,Tab), reduce_completed_ans(T2,NT2,Tab). reduce_completed_ans(n3(T1,M2,T2,M3,T3),n3(NT1,M2,NT2,M3,NT3),Tab) :- reduce_completed_ans(T1,NT1,Tab), reduce_completed_ans(T2,NT2,Tab), reduce_completed_ans(T3,NT3,Tab). reduce_completed_anslist([],Lanss,Lanss,_Tab). reduce_completed_anslist([d(G,D0)|List],Lanss0,Lanss,Tab) :- ( D0 = all(Dlist1) -> ( filter_delays(Dlist1,[],Dlist,disj,V,Tab) -> ( V == true -> % true answer Lanss = [d(G,[])] ; Dlist == [] -> % false answer, ignore reduce_completed_anslist(List,Lanss0,Lanss,Tab) ; reduce_completed_anslist(List,[d(G,all(Dlist))|Lanss0],Lanss,Tab) ) ; reduce_completed_anslist(List,Lanss0,Lanss,Tab) ) ; ( filter_delays(D0,[],D,conj,_V,Tab) -> ( D == [] -> Lanss = [d(G,[])] ; reduce_completed_anslist(List,[d(G,D)|Lanss0],Lanss,Tab) ) ; reduce_completed_anslist(List,Lanss0,Lanss,Tab) ) ). % simplify a delay list by the completed table: delete true negations, % fail if a false one. filter_delays([],Fds,Fds,_DC,_V,_Tab). filter_delays([Lit|Ds],Fds0,Fds,DC,V,Tab) :- lit_to_call(Lit,Gcall), find(Tab,Gcall,Gent), ent_to_comp(Gent,Gcomp), ent_to_anss(Gent,Ganss), extract_lit_val(Lit,Ganss,Gcomp,Val), ( Val == succ -> ( DC == conj -> filter_delays(Ds,Fds0,Fds,DC,V,Tab) ; DC == disj -> V = true ) ; Val == fail -> ( DC == conj -> fail ; DC == disj -> filter_delays(Ds,Fds0,Fds,DC,V,Tab) ) ; % Val == undefined filter_delays(Ds,[Lit|Fds0],Fds,DC,V,Tab) ). lit_to_call(\+G,G). lit_to_call(Gcall-_,Gcall). not_subsumed_ans(Ans,Lanss0) :- \+ ( numbervars(Ans,0,_), subsumed_ans1(Ans,Lanss0) ). % succeed if answer is subsumed by any in list1 or 2. subsumed_ans(Tv,List1,List2) :- \+ (numbervars(Tv,0,_), \+ subsumed_ans1(Tv,List1), \+ subsumed_ans1(Tv,List2) ). % check if a delay is subsumed one of the element in the list subsumed_ans1(d(T,V),List) :- member(d(T,V1),List), ( V1 == [] ; V = all(LV), V1 = all(LV1) -> subset(LV,LV1) ; subset(V1,V) ). /****************** auxiliary routines *******************/ % variantchk/2 finds a variant in a list of atoms. variantchk(G,[G1|_]) :- variant(G,G1), !. variantchk(G,[_|L]) :- variantchk(G,L). variant(A, B) :- A == B -> true ; subsumes_chk(A, B), subsumes_chk(B, A), A = B. /* subsumes_chk(General, Specific) :- \+ ( numbervars(Specific, 0, _), \+ General = Specific ). */ ground(O,C) :- ground(O) -> C = O ; copy_term(O,C), numbervars(C,0,_). subset([],_). subset([E|L1],L2) :- memberchk(E,L2), subset(L1,L2). reverse([],R,R). reverse([Goal|Scc],R0,R) :- reverse(Scc,[Goal|R0],R). /***************** routines for debugging *******************/ % Debugging help: pretty-prints strongly connected components and local table. display_stack(Stack,Tab) :- reverse(Stack,[],Rstack), display_st(Rstack,Tab). display_st([],_Tab). display_st([Ggoal|Scc],Tab) :- find(Tab,Ggoal,Ent), ent_to_dfn(Ent,Dfn:Pmin-Nmin), tab(2), write(Ggoal-Dfn), write(': '), write('Pmin='), write(Pmin), write('; '), write('Nmin='), write(Nmin), write('; '), nl, display_st(Scc,Tab). display_dlist([]) :- nl,nl. display_dlist([Ngoal-_|Dlist]) :- write(\+ Ngoal), write('; '), display_dlist(Dlist). display_table(Tab) :- write('Table: '), nl, write_tab(Tab). display_final(Tab) :- write(' Final Set of Answers: '), nl, display_final1(Tab). display_final1([]). display_final1(l(_,e(_,_,Anss,_,_,_,_))) :- write_anss(Anss). display_final1(n2(X,_,Y)) :- display_final1(X), display_final1(Y). display_final1(n3(X,_,Y,_,Z)) :- display_final1(X), display_final1(Y), display_final1(Z). write_tab([]). write_tab(l(G,e(Nodes,ANegs,Anss,_,Comp,Dfn:_,_))) :- write(' Entry: '), write(G-Dfn), write(': '), ( Comp == true -> write('Complete!') ; write('Incomplete!') ), nl, ( Anss == [] -> true ; write(' Anss: '), nl, write_anss(Anss) ), ( ( Comp == true; Nodes == []) -> true ; write(' Nodes: '), write(Nodes), nl ), ( ( Comp == true; ANegs == []) -> true ; write(' ANegs: '), write(ANegs), nl ). write_tab(n2(X,_,Y)) :- write_tab(X), write_tab(Y). write_tab(n3(X,_,Y,_,Z)) :- write_tab(X), write_tab(Y), write_tab(Z). write_anss([]). write_anss(l(_,Lanss)) :- write_anss_list(Lanss). write_anss(n2(T1,_,T2)) :- write_anss(T1), write_anss(T2). write_anss(n3(T1,_,T2,_,T3)) :- write_anss(T1), write_anss(T2), write_anss(T3). write_anss_list([]). write_anss_list([Ans|Anss]) :- write_ans(Ans), write_anss_list(Anss). write_ans(d(H,Ds)) :- write(' '), write(H), ( Ds == [] -> true ; write(' :- '), ( Ds = all([D|Ds1]) -> ( D = (_-GH) -> write(GH) ; write(D) ), write_delay(Ds1,'; ') ; Ds = [D|Ds1], ( D = (_-GH) -> write(GH) ; write(D) ), write_delay(Ds1,', ') ) ), write('.'), nl. write_delay([],_). write_delay([D|Ds1],Sep) :- write(Sep), ( D = (_Gcall-GH) -> write(GH) ; write(D) ), write_delay(Ds1,Sep). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% /* This is a set of routines that supports indexed tables. Tables are sets of key-value_list pairs. With each key is associated a list of values. It uses 2-3 trees for the index (modified by D.S. Warren from Ivan Bratko: ``Prolog Programming for Artificial Intelligence'', Addison Wesley, 1986). Operations are: Keys must be ground! (so numbervar them) addkey(Tree,Key,V,Tree1) adds a new Key with value V, returning new Tree1. Fails if the key is already there. find(Tree,Key,V) finds the entry with Key and returns associated values in V. updatevs(Tree,Key,OldV,NewV,Tree1) replaces value of entry with key Key and value OldV with NewV. */ addkey([],X,V,l(X,V)):-!. addkey(Tree,X,V,Tree1) :- ins2(Tree,X,V,Trees), cmb0(Trees,Tree1). find(l(X,V),Xs,V) :- X == Xs. find(n2(T1,M,T2),X,V) :- M @=< X -> find(T2,X,V) ; find(T1,X,V). find(n3(T1,M2,T2,M3,T3),X,V) :- M2 @=< X -> (M3 @=< X -> find(T3,X,V) ; find(T2,X,V) ) ; find(T1,X,V). % updatevs(Tab0,X,Ov,Nv,Tab) updates Tab0 to Tab, by replacing % Ov of entry with key X by Nv. /* updatevs(Tab0,X,Ov,Nv,Tab) :- updatevs(Tab0,X,Ov,Nv), Tab = Tab0. updatevs(Tab,X,Ov,Nv) :- ( Tab = l(Xs,Ov), Xs == X -> setarg(2,Tab,Nv) ; Tab = n2(T1,M,T2) -> ( M @=< X -> updatevs(T2,X,Ov,Nv) ; updatevs(T1,X,Ov,Nv) ) ; Tab = n3(T1,M2,T2,M3,T3) -> ( M2 @=< X -> ( M3 @=< X -> updatevs(T3,X,Ov,Nv) ; updatevs(T2,X,Ov,Nv) ) ; updatevs(T1,X,Ov,Nv) ) ). */ updatevs(l(X,Ov),Xs,Ov,Nv,l(X,Nv)) :- X == Xs. updatevs(n2(T1,M,T2),X,Ov,Nv,n2(NT1,M,NT2)) :- M @=< X -> NT1=T1, updatevs(T2,X,Ov,Nv,NT2) ; NT2=T2, updatevs(T1,X,Ov,Nv,NT1). updatevs(n3(T1,M2,T2,M3,T3),X,Ov,Nv,n3(NT1,M2,NT2,M3,NT3)) :- M2 @=< X -> (M3 @=< X -> NT2=T2, NT1=T1, updatevs(T3,X,Ov,Nv,NT3) ; NT1=T1, NT3=T3, updatevs(T2,X,Ov,Nv,NT2) ) ; NT2=T2, NT3=T3, updatevs(T1,X,Ov,Nv,NT1). ins2(n2(T1,M,T2),X,V,Tree) :- M @=< X -> ins2(T2,X,V,Tree1), cmb2(Tree1,T1,M,Tree) ; ins2(T1,X,V,Tree1), cmb1(Tree1,M,T2,Tree). ins2(n3(T1,M2,T2,M3,T3),X,V,Tree) :- M2 @=< X -> (M3 @=< X -> ins2(T3,X,V,Tree1), cmb4(Tree1,T1,M2,T2,M3,Tree) ; ins2(T2,X,V,Tree1), cmb5(Tree1,T1,M2,M3,T3,Tree) ) ; ins2(T1,X,V,Tree1), cmb3(Tree1,M2,T2,M3,T3,Tree). ins2(l(A,V),X,Vn,Tree) :- A @=< X -> (X @=< A -> fail ; Tree = t(l(A,V),X,l(X,Vn)) ) ; Tree = t(l(X,Vn),A,l(A,V)). cmb0(t(Tree),Tree). cmb0(t(T1,M,T2),n2(T1,M,T2)). cmb1(t(NT1),M,T2,t(n2(NT1,M,T2))). cmb1(t(NT1a,Mb,NT1b),M,T2,t(n3(NT1a,Mb,NT1b,M,T2))). cmb2(t(NT2),T1,M,t(n2(T1,M,NT2))). cmb2(t(NT2a,Mb,NT2b),T1,M,t(n3(T1,M,NT2a,Mb,NT2b))). cmb3(t(NT1),M2,T2,M3,T3,t(n3(NT1,M2,T2,M3,T3))). cmb3(t(NT1a,Mb,NT1b),M2,T2,M3,T3,t(n2(NT1a,Mb,NT1b),M2,n2(T2,M3,T3))). cmb4(t(NT3),T1,M2,T2,M3,t(n3(T1,M2,T2,M3,NT3))). cmb4(t(NT3a,Mb,NT3b),T1,M2,T2,M3,t(n2(T1,M2,T2),M3,n2(NT3a,Mb,NT3b))). cmb5(t(NT2),T1,M2,M3,T3,t(n3(T1,M2,NT2,M3,T3))). cmb5(t(NT2a,Mb,NT2b),T1,M2,M3,T3,t(n2(T1,M2,NT2a),Mb,n2(NT2b,M3,T3))). :-dynamic rule/5,def_rule/4,setting/2. /* start of list of parameters that can be set by the user with set(Parameter,Value) */ setting(epsilon_parsing,0.00001). setting(save_dot,false). setting(ground_body,true). /* find_rule(G,(R,S,N),Body,C) takes a goal G and the current C set and returns the index R of a disjunctive rule resolving with G together with the index N of the resolving head, the substitution S and the Body of the rule */ find_rule(H,(R,S,N),Body,LH):- rule(R,S,_,Head,Body), member_head(H,Head,0,N), length(Head,NH), listN(0,NH,LH). find_rule(H,(R,S,Number),Body,C):- rule(R,S,_,uniform(H:1/_Num,_P,Number),Body), not_already_present_with_a_different_head(Number,R,S,C). not_already_present_with_a_different_head(_N,_R,_S,[]). not_already_present_with_a_different_head(N,R,S,[(N1,R,S1)|T]):- not_different(N,N1,S,S1),!, not_already_present_with_a_different_head(N,R,S,T). not_already_present_with_a_different_head(N,R,S,[(_N1,R1,_S1)|T]):- R\==R1, not_already_present_with_a_different_head(N,R,S,T). not_different(N,N,S,S). not_different(_N,_N1,S,S1):- S\=S1,!. not_different(N,N1,S,S1):- N\=N1,!, dif(S,S1). not_different(N,N,S,S). member_head(H,[(H:_P)|_T],N,N). member_head(H,[(_H:_P)|T],NIn,NOut):- N1 is NIn+1, member_head(H,T,N1,NOut). /* rem_dup_lists removes the C sets that are a superset of another C sets further on in the list of C sets */ rem_dup_lists([],L,L). rem_dup_lists([H|T],L0,L):- (member_subset(H,T);member_subset(H,L0)),!, rem_dup_lists(T,L0,L). rem_dup_lists([H|T],L0,L):- rem_dup_lists(T,[H|L0],L). member_subset(E,[H|_T]):- subset_my(H,E),!. member_subset(E,[_H|T]):- member_subset(E,T). rem_dup_lists_tab([],L,L). rem_dup_lists_tab([(H,_Tab)|T],L0,L):- (member_subset_tab(H,T);member_subset_tab(H,L0)),!, rem_dup_lists_tab(T,L0,L). rem_dup_lists_tab([(H,Tab)|T],L0,L):- rem_dup_lists_tab(T,[(H,Tab)|L0],L). member_subset_tab(E,[(H,_Tab)|_T]):- subset_my(H,E),!. member_subset_tab(E,[_H|T]):- member_subset_tab(E,T). /* predicates for building the formula to be converted into a BDD */ /* build_formula(LC,Formula,VarIn,VarOut) takes as input a set of C sets LC and a list of Variables VarIn and returns the formula and a new list of variables VarOut Formula is of the form [Term1,...,Termn] Termi is of the form [Factor1,...,Factorm] Factorj is of the form (Var,Value) where Var is the index of the multivalued variable Var and Value is the index of the value */ build_formula([],[],Var,Var). build_formula([D|TD],[F|TF],VarIn,VarOut):- build_term(D,F,VarIn,Var1), build_formula(TD,TF,Var1,VarOut). build_term([],[],Var,Var). build_term([(N,R,S)|TC],[[NVar,N]|TF],VarIn,VarOut):- (nth0_eq(0,NVar,VarIn,(R,S))-> Var1=VarIn ; append(VarIn,[(R,S)],Var1), length(VarIn,NVar) ), build_term(TC,TF,Var1,VarOut). /* nth0_eq(PosIn,PosOut,List,El) takes as input a List, an element El and an initial position PosIn and returns in PosOut the position in the List that contains an element exactly equal to El */ nth0_eq(N,N,[H|_T],El):- H==El,!. nth0_eq(NIn,NOut,[_H|T],El):- N1 is NIn+1, nth0_eq(N1,NOut,T,El). /* var2numbers converts a list of couples (Rule,Substitution) into a list of triples (N,NumberOfHeadsAtoms,ListOfProbabilities), where N is an integer starting from 0 */ var2numbers([],_N,[]). var2numbers([(R,S)|T],N,[[N,ValNumber,Probs]|TNV]):- find_probs(R,S,Probs), length(Probs,ValNumber), N1 is N+1, var2numbers(T,N1,TNV). find_probs(R,S,Probs):- rule(R,S,_N,Head,_Body), get_probs(Head,Probs). get_probs(uniform(_A:1/Num,_P,_Number),ListP):- Prob is 1/Num, list_el(Num,Prob,ListP). get_probs([],[]). get_probs([_H:P|T],[P1|T1]):- P1 is P, get_probs(T,T1). list_el(0,_P,[]):-!. list_el(N,P,[P|T]):- N1 is N-1, list_el(N1,P,T). /* end of predicates for building the formula to be converted into a BDD */list_el(0,_P,[]):-!. /* p(File) parses the file File.cpl. It can be called more than once without exiting yap */ p(File):- parse(File). parse(File):- atom_concat(File,'.cpl',FilePl), open(FilePl,read,S), read_clauses(S,C), close(S), retractall(rule(_,_,_,_,_)), retractall(def_rule(_,_,_,_)), retractall(new_number(_)), assert(new_number(0)), process_clauses(C,1),!. process_clauses([(end_of_file,[])],_N). process_clauses([((H:-B),V)|T],N):- H=uniform(A,P,L),!, list2and(BL,B), process_body(BL,V,V1), remove_vars([P],V1,V2), append(BL,[length(L,Tot),nth0(Number,L,P)],BL1), append(V2,['Tot'=Tot],V3), assertz(rule(N,V3,_NH,uniform(A:1/Tot,L,Number),BL1)), N1 is N+1, process_clauses(T,N1). process_clauses([((H:-B),V)|T],N):- H=(_;_),!, list2or(HL1,H), process_head(HL1,HL), list2and(BL,B), process_body(BL,V,V1), length(HL,LH), listN(0,LH,NH), assertz(rule(N,V1,NH,HL,BL)), N1 is N+1, process_clauses(T,N1). process_clauses([((H:-B),V)|T],N):- H=(_:_),!, list2or(HL1,H), process_head(HL1,HL), list2and(BL,B), process_body(BL,V,V1), length(HL,LH), listN(0,LH,NH), assertz(rule(N,V1,NH,HL,BL)), N1 is N+1, process_clauses(T,N1). process_clauses([((H:-B),V)|T],N):-!, list2and(BL,B), assert(def_rule(N,V,H,BL)), N1 is N+1, process_clauses(T,N1). process_clauses([(H,V)|T],N):- H=(_;_),!, list2or(HL1,H), process_head(HL1,HL), length(HL,LH), listN(0,LH,NH), assertz(rule(N,V,NH,HL,[])), N1 is N+1, process_clauses(T,N1). process_clauses([(H,V)|T],N):- H=(_:_),!, list2or(HL1,H), process_head(HL1,HL), length(HL,LH), listN(0,LH,NH), assertz(rule(N,V,NH,HL,[])), N1 is N+1, process_clauses(T,N1). process_clauses([(H,V)|T],N):- assert(def_rule(N,V,H,[])), N1 is N+1, process_clauses(T,N1). /* if the annotation in the head are not ground, the null atom is not added and the eventual formulas are not evaluated */ process_head(HL,NHL):- (ground_prob(HL)-> process_head_ground(HL,0,NHL) ; NHL=HL ). ground_prob([]). ground_prob([_H:PH|T]):- ground(PH), ground_prob(T). process_head_ground([H:PH],P,[H:PH1|Null]):- PH1 is PH, PNull is 1-P-PH1, setting(epsilon_parsing,Eps), EpsNeg is - Eps, PNull > EpsNeg, (PNull>Eps-> Null=['':PNull] ; Null=[] ). process_head_ground([H:PH|T],P,[H:PH1|NT]):- PH1 is PH, P1 is P+PH1, process_head_ground(T,P1,NT). /* setof must have a goal of the form B^G where B is a term containing the existential variables */ process_body([],V,V). process_body([setof(A,B^_G,_L)|T],VIn,VOut):-!, get_var(A,VA), get_var(B,VB), remove_vars(VA,VIn,V1), remove_vars(VB,V1,V2), process_body(T,V2,VOut). process_body([setof(A,_G,_L)|T],VIn,VOut):-!, get_var(A,VA), remove_vars(VA,VIn,V1), process_body(T,V1,VOut). process_body([bagof(A,B^_G,_L)|T],VIn,VOut):-!, get_var(A,VA), get_var(B,VB), remove_vars(VA,VIn,V1), remove_vars(VB,V1,V2), process_body(T,V2,VOut). process_body([bagof(A,_G,_L)|T],VIn,VOut):-!, get_var(A,VA), remove_vars(VA,VIn,V1), process_body(T,V1,VOut). process_body([_H|T],VIn,VOut):-!, process_body(T,VIn,VOut). get_var_list([],[]). get_var_list([H|T],[H|T1]):- var(H),!, get_var_list(T,T1). get_var_list([H|T],VarOut):-!, get_var(H,Var), append(Var,T1,VarOut), get_var_list(T,T1). get_var(A,[A]):- var(A),!. get_var(A,V):- A=..[_F|Args], get_var_list(Args,V). remove_vars([],V,V). remove_vars([H|T],VIn,VOut):- delete_var(H,VIn,V1), remove_vars(T,V1,VOut). delete_var(_H,[],[]). delete_var(V,[VN=Var|T],[VN=Var|T1]):- V\==Var,!, delete_var(V,T,T1). delete_var(_V,[_H|T],T). read_clauses(S,Clauses):- (setting(ground_body,true)-> read_clauses_ground_body(S,Clauses) ; read_clauses_exist_body(S,Clauses) ). read_clauses_ground_body(S,[(Cl,V)|Out]):- read_term(S,Cl,[variable_names(V)]), (Cl=end_of_file-> Out=[] ; read_clauses_ground_body(S,Out) ). read_clauses_exist_body(S,[(Cl,V)|Out]):- read_term(S,Cl,[variable_names(VN)]), extract_vars_cl(Cl,VN,V), (Cl=end_of_file-> Out=[] ; read_clauses_exist_body(S,Out) ). extract_vars_cl(end_of_file,[]). extract_vars_cl(Cl,VN,Couples):- (Cl=(H:-_B)-> true ; H=Cl ), extract_vars(H,[],V), pair(VN,V,Couples). pair(_VN,[],[]). pair([VN= _V|TVN],[V|TV],[VN=V|T]):- pair(TVN,TV,T). extract_vars(Var,V0,V):- var(Var),!, (member_eq(Var,V0)-> V=V0 ; append(V0,[Var],V) ). extract_vars(Term,V0,V):- Term=..[_F|Args], extract_vars_list(Args,V0,V). extract_vars_list([],V,V). extract_vars_list([Term|T],V0,V):- extract_vars(Term,V0,V1), extract_vars_list(T,V1,V). listN(N,N,[]):-!. listN(NIn,N,[NIn|T]):- N1 is NIn+1, listN(N1,N,T). /* end of predicates for parsing an input file containing a program */ /* start of utility predicates */ list2or([X],X):- X\=;(_,_),!. list2or([H|T],(H ; Ta)):-!, list2or(T,Ta). list2and([X],X):- X\=(_,_),!. list2and([H|T],(H,Ta)):-!, list2and(T,Ta). member_eq(A,[H|_T]):- A==H. member_eq(A,[_H|T]):- member_eq(A,T). subset_my([],_). subset_my([H|T],L):- member_eq(H,L), subset_my(T,L). remove_duplicates_eq([],[]). remove_duplicates_eq([H|T],T1):- member_eq(H,T),!, remove_duplicates_eq(T,T1). remove_duplicates_eq([H|T],[H|T1]):- remove_duplicates_eq(T,T1). builtin(_A is _B). builtin(_A > _B). builtin(_A < _B). builtin(_A >= _B). builtin(_A =< _B). builtin(_A =:= _B). builtin(_A =\= _B). builtin(true). builtin(false). builtin(_A = _B). builtin(_A==_B). builtin(_A\=_B). builtin(_A\==_B). builtin(length(_L,_N)). builtin(member(_El,_L)). builtin(average(_L,_Av)). builtin(max_list(_L,_Max)). builtin(min_list(_L,_Max)). builtin(nth0(_,_,_)). builtin(nth(_,_,_)). average(L,Av):- sum_list(L,Sum), length(L,N), Av is Sum/N. clique([],[]):-!. clique(Graph,Clique):- vertices(Graph,Candidates), extend_cycle(Graph,Candidates,[],[],Clique). extend_cycle(G,[H|T],Not,CS,CSOut):- neighbours(H, G, Neigh), intersection(Neigh,T,NewCand), intersection(Neigh,Not,NewNot), extend(G,NewCand,NewNot,[H|CS],CSOut). extend_cycle(G,[H|T],Not,CS,CSOut):- extend_cycle(G,T,[H|Not],CS,CSOut). extend(_G,[],[],CompSub,CompSub):-!. extend(G,Cand,Not,CS,CSOut):- extend_cycle(G,Cand,Not,CS,CSOut). intersection([],_Y,[]). intersection([H|T],Y,[H|Z]):- member(H,Y),!, intersection(T,Y,Z). intersection([_H|T],Y,Z):- intersection(T,Y,Z). /* set(Par,Value) can be used to set the value of a parameter */ set(Parameter,Value):- retract(setting(Parameter,_)), assert(setting(Parameter,Value)). /* end of utility predicates */