%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% GASP 03/07/2009 - for Fundamenta %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% WRT LaSh08 version %%% 1. Added rule indexing for speeding up fixpoints %%% (roughly 35% faster) %%% 2. Added constraint with negated rule for avoiding the permutation problem %%% (inspired from asperix) %%% 3. Added CSP based propagation of false head to positive body, both for constraints and/or rules with false head in the model %%% 4. Constraints handled separately (they are not seen as applicable rules anymore) and %%% processed only by propagators and tp/wf at each iteration of search %%% 5. Added CSP based propagation of unsupported heads (from undefined to false) if every rule with a specific ground head %%% cannot produce the atom. We assume that undefined atoms in body+ are true and undefined atoms in body- are false, to preserve correctness %%% 6. At each application of a rule, added a fixpoint between the two propagation steps and the tp operator. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Libraries, operators, and general parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% :- use_module(library(clpfd)). :- use_module(library(lists)). :- use_module(library(terms)). :- use_module(library(file_systems)). :- op(200,fx,not). :- op(150,fx,'1'). :- op(100,xf,'1'). :- op(300,xfy,neq). :- op(300,xfy,eq). %%%%%%%%%%%%%%%%%%%%%%%%%%% %%% OPTIONAL: setting the working directory my_cd('C:/agostino/lavori/incorso/gasp'). :-my_cd(WD),file_systems:current_directory(_,WD). :-prolog_flag(unknown,_,fail). %%% NOTE: maxint=268435455 for clpfd. %%% ARITY 4 bigM(127). %%% ARITY 3 bigM(645). %%% ARITY 2 bigM(16383). %%% BUILT-INS builtin('<'). builtin('>'). builtin('='). builtin('=='). builtin('eq'). builtin('neq'). %%% go/1 and /2 compute all stable models, go/3 one per time %%% They take the Program as input and computes stable model(s) %%% Launch as :- go('filename.lp'). [default: all solutions and printed] %%% or :- go('filename.lp',write). [The same] %%% or :- go('filename.lp',nowrite). [solutions are hidden] %%% or :- go('filename.lp',Model, write/nowrite) [One solution per time] %%% or :- go('filename.lp',Model, write/nowrite),gasp_statistics. [for statistics] %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% go(Program) :- go(Program,write). go(Program,WriteFlag) :- go(Program,_,WriteFlag), fail. go(_,_) :- gasp_statistics. go(Program,Model,WriteFlag) :- reset, read_program(Program,ProgList), empty_domains(ProgList,IniDoms), split_facts(ProgList,Facts,Rules,Flag), %%% separates facts and rules and dep_graph(IniDoms,Rules), %%% generate the predicate dependency graph writetime('### Loading time: '), %%% tests if it is definite (Flag) facts(Facts,IniDoms,FactDoms), %%% FactDoms: facts are true ( Flag=0, % definite tp(Rules,FactDoms,Model), writeln('### P is a definite program. Its minimum model is:'), update(model) ,write_model(WriteFlag,Model) ; (Flag=1;Flag=2), %%% =1 without constraints =2 with constraints wf(Rules, FactDoms, WFModel), %%write('DEBUG: wellfounded model'),write(Flag), %%write_model(write,WFModel), ( wf_stable(WFModel,Flag),!, % writeln('### There is a wellfounded model'), update(model), write_model(WriteFlag,WFModel),!, Model=WFModel ; writeln('### There are no wellfounded models. ###'), dom_update([false],WFModel,WFModel1), %% for fixpoint(Rules,WFModel1,Model), update(model), %%% it updates sol(N) writetime('### Next stable model computed in time: '),%%% write_model(WriteFlag,Model) ) ; Flag=3, %%% =3 with function(s): particular cases wf(Rules, FactDoms, WFModel), fun_fixpoint(Rules,WFModel,Model,Program), update(model), writetime('### Next Stable model computed in: ')%%% ,write_model(WriteFlag,Model) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% MODELS: %%% Each predicate p of arity N is assigned to a term %%% - atom(p,N,POSDOM,NEGDOM) %%% where POSDOM,NEGDOM are fdsets. %%% - POSDOM is the set of true values for p %%% - NEGDOM is the set of false values for p %%% If the program is definite, then NEGDOM=[] %%% otherwise NEGDOM contains elements to satisfy negative %%% literals when looking for stable models %%% A model is a list of those atoms (actually, the list of POSDOM) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% For arity 0 predicates, DOM =[] means false, DOM = [0] true %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% empty_domains sets to [] all domains for non-builtin predicates %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% empty_domains([],[]). empty_domains([rule(A,B,C)|R], DOMS) :- append([A,B,C], ATOMS), atom_dom(ATOMS, DOMS1), empty_domains(R, DOMS2), disj_union(DOMS1,DOMS2,DOMS). atom_dom([],[atom(false,0,[],[])]). %%% atom_dom([A|R],S) :- A =.. [P|_], builtin(P),!, atom_dom(R,S). atom_dom([A|R],[atom(P,N,[],[])|S]) :- A =.. [P|Args], length(Args,N), atom_dom(R,S). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Standard T_P of logic programming (see below notes for negative %%% literals) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% tp(ProgList,I,M) :- tp_step(ProgList,I,I1,[],F),!, %% tp_step is deterministic. (F=[],!, M = I1; %% we added a ! to avoid to enter F=[0],! , fail; %% there is no rule 0: fails %tp(Prog,I1,M)). %%% Naive version choose_rules(F,RULES,1), tp(RULES,I1,M)). %% FASTER, with indexing tp_step([],I,I,F,F). tp_step(_,_I,_I1,[0],[0]):-!. %% as soon as get an inconsistency -> break tp_step([Rule|ProgList],I,I1,F0,F2) :- apply_def_rule(Rule,I,Inew,F0,F1), tp_step(ProgList,Inew,I1,F1,F2). choose_rules(F,RULES_real,Flag) :- %%% Flag=2 means that: sort(F,Fsort), %%% only the positive part of the ( Flag=1, findall(RULES, %%% program is used (member(A,Fsort),dependency(A,_,RULES)), RULES_F); Flag=2, findall(RULES, (member(A,Fsort),posdependency(A,_,RULES)), RULES_F)), append(RULES_F,RULES_Flat), %%% append unario. Lento? sort(RULES_Flat,RULES_Flat2), map_rules(RULES_Flat2,RULES_real). map_rules([],[]). map_rules([Num|NR],[Rule|RR]) :- rule_no(Num,Rule), map_rules(NR,RR). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% update_dom computes the effect of T_P on a single rule %%%%% T_P considers also negation for its use in S.M. search %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% apply_def_rule(rule([H],PBody,NBody),I,[atom(F,ARITY,NEWPDOM,NEG)|PARTI],F0,F1) :- copy_term([H,PBody,NBody],[H1,PBody1,NBody1]), %%% variable renaming term_variables([H1,PBody1],VARS), %%% collect fresh vars bigM(M),M1 is M-1,domain(VARS,0,M1), %%% fix (wide) domains for the fresh vars H1 =..[F|ARGS], tuple_num(ARGS,VAR,ARITY), select(atom(F,ARITY,OLD,NEG),I,PARTI), %%% ( build_constraint(PBody1,I,1,pos), %%% C3 = 1 iff the positive body is satisfied by I build_constraint(NBody1,I,1,negknown), %%% C4 = 1 iff the negative body is satisfied by I nin_set(ARITY,VAR,OLD), %%% do not apply if head is already true % nin_set(ARITY,VAR,NEG), %%% Rimosso consistency check, devo applicare e poi fallire, non skip dell'applicazione della regola! findall(X,(X #= VAR,labeling([ff],VARS)),[L|IST]), ( check_consistent([L|IST],ARITY,NEG), list_to_fdset([L|IST],SET), fdset_union(OLD,SET,NEWPDOM), %%% UPDATE F1=[F|F0],! ; %%% check_consistent fails on the domain updating: F1=[0]), ! ; %%% Nothing to update NEWPDOM=OLD, F1 = F0 ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% Computing Standard (definite) T_P %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% build_constraint returns a constraint that must hold for %%%% the rule is applied %%%% Negative literals treatment: if Sign=negknown, %%%% it is implemented as: %%%%% - A in T_P(I,J) iff (A :- B, not C) in P and %%%%% B in I and C in J %%%%% (I true facts, J false facts) %%%% Otherwise it is left as a constraint (neg) as called by %%%% the wellfounded part. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% build_constraint is used for computing wellfouned sets %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% build_constraint([R|Rs],I,C,Sign):- %%% Built-in ATOMS R =.. [F|ARGS], builtin(F),!, expression(F,ARGS,C2), C #<=> C2 #/\ C1, build_constraint(Rs,I,C1,Sign). build_constraint([R|Rs],I,C,Sign):- %%% Other ATOMS R =.. [F|ARGS],!, tuple_num(ARGS,VAR,ARITY), member(atom(F,ARITY,DOMF,NDOMF),I), ( Sign=notneg,!, %%% Negative unknown nin_set(ARITY,VAR,NDOMF,C2); Sign=neg,!, %%% Negative unknown nin_set(ARITY,VAR,DOMF,C2); Sign=pos,!, %%% Positive C2 #<=> VAR in_set DOMF; Sign=negknown, %%% Negative known C2 #<=> VAR in_set NDOMF; Sign=nowhere,!, %%% not in positive and not in negative nin_set(ARITY,VAR,DOMF,C3), nin_set(ARITY,VAR,NDOMF,C4), C2 #<=> C3 #/\ C4 ), build_constraint(Rs,I,C1,Sign), C #<=> C1 #/\ C2. build_constraint([],_,1,_). %%% special constraint: computes the number of atoms in the list R|Rs are in I+ %%% and set it to HowMany (exclude the expressions, for which only constraints are set). %%% Moreover every el in list R|Rs is not in I- %%% Pos is unified with the position in the List of the atom that is not in I+ %%% TotalRules is a ground value that account for the number of non expression atoms (useful to know how many non-expression atoms are satisfiable at most) build_constraint_one_nonground([R|Rs],I,HowMany, TotalRules, Pos, Ct):- R =.. [F|ARGS], builtin(F),!, expression(F,ARGS,1), Pos #\= Ct, Ct1 is Ct+1, build_constraint_one_nonground(Rs,I,HowMany,TotalRules, Pos, Ct1). build_constraint_one_nonground([R|Rs],I,HowMany, TotalRules1, Pos, Ct):- R =.. [F|ARGS], tuple_num(ARGS,VAR,ARITY), member(atom(F,ARITY,DOMF,NDOMF),I), nin_set(ARITY,VAR,NDOMF,1), %% never negative % in_set(ARITY,VAR,DOMF,C3), C3 #<=> VAR in_set DOMF, HowMany #= C3 + HowMany1, C3 #= 0 #<=> Pos #=Ct, Ct1 is Ct+1, TotalRules1 #= TotalRules+1, build_constraint_one_nonground(Rs,I,HowMany1,TotalRules, Pos, Ct1). build_constraint_one_nonground([],_I,0, 0, _Pos, _Ct). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% facts adds the domain values imposed by (ground) facts %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% facts([],DOMS,DOMS). facts([rule([A],[],[])|R],OLDDOMS,NEWDOMS) :- A =..[P|ARGS], tuple_num(ARGS,D,ARITY), select(atom(P,ARITY,PDOM,NEG),OLDDOMS,PARTDOMS), fdset_add_element(PDOM,D,NEWPDOM), facts(R,[atom(P,ARITY,NEWPDOM,NEG)|PARTDOMS],NEWDOMS). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% well founded models computed as described in: %%% Improving the Alternating Fixpoint: The Transformation Approach %%% by Zukowski, Brass, and Freitag %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% wf(ProgList,Empty, M) :- def_rules(ProgList,DefProg), alternating(2,DefProg, Empty,Empty,K0), %% K0 = lfp(T_P) alternating(1,ProgList, K0, Empty,U0), %% U0 = lpf(T_{P,K0}) wf(ProgList,Empty, K0, U0, M). wf(ProgList,Empty,Ki,Ui,M) :- alternating(1,ProgList, Ui, Empty,Ki1), % Ki1 = lfp(T_{P,U_{i}}) ( Ki1==Ki, !, wellfoundedmodel(Ki,Ui,M); alternating(1,ProgList, Ki1,Empty,Ui1), % Ui1 = lfp(T_{P,K_i1}) wf(ProgList,Empty,Ki1,Ui1,M) ). %%% W*_P = K union {not(A) : A in U} wellfoundedmodel([],_,[]). wellfoundedmodel([atom(P,AR,PDOM,_)|K],U,[atom(P,AR,PDOM,NDOM)|M]) :- select(atom(P,AR,UDOM,_),U,RU), complement_set(AR,UDOM,NDOM), wellfoundedmodel(K,RU,M). %%% The first call is with the definite program (Flag=2): %%% particular case. The other with Flag=1 alternating(Flag,ProgList,J,I,M) :- wf_step(ProgList,J,I,I1,[],F),!, (F = [], !, M = I; %%%% Naive VERSION alternating(Flag, ProgList,J,I1,M)). % choose_rules(F,RULES,Flag), %%% Faster, with indexing alternating(Flag,RULES,J,I1,M)). wf_step([],_J,I,I,F0,F0). wf_step([Rule|ProgList],J,I,I1,F0,F2) :- alternating_apply_rule(Rule,J,I,Inew,F0,F1), wf_step(ProgList,J,Inew,I1,F1,F2). %%% T_{P,J}(I) = { A : (A :- PBody, neg NBody) in P , %%% PBody \subseteq I and %%% NBody \cap J = \emptyset } alternating_apply_rule(rule([H],PBody,NBody),J,I,[atom(F,ARITY,NEWPDOM,NEG)|PARTI],F0,F1) :- copy_term([H,PBody,NBody],[H1,PBody1,NBody1]), %%% variable renaming term_variables([H1,PBody1],VARS), %%% collect fresh vars bigM(M),M1 is M-1,domain(VARS,0,M1), %%% fix (wide) domains for the fresh vars H1 =..[F|ARGS], tuple_num(ARGS,VAR,ARITY), select(atom(F,ARITY,OLD,NEG),I,PARTI), ( build_constraint(PBody1,I,1,pos), %%% C = 1 iff the body is satisfied by I build_constraint(NBody1,J,1,neg), nin_set(ARITY,VAR,OLD,1), %%% do not apply if head is already true %%% nin_set(ARITY,VAR,NEG,C4), %%% consistency check findall(X,(X #= VAR,labeling([ff],VARS)),[L|IST]), list_to_fdset([L|IST],SET), fdset_union(OLD,SET,NEWPDOM), F1=[F|F0], !; NEWPDOM=OLD, F1 = F0 ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Non determinsitic fixpoint procedure. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% fixpoint(Rules,I1,I2) :- % propagate(Rules,I1,I11,_), fixpoint_tp_propagate(Rules,I1,I11), %write_fdmodel_complete(I11), lev_fixpoint(Rules,I11,I2,[],0). lev_fixpoint(Rules,I1,I2, PrevRules,Level) :- statistics(runtime,_), %%% TIMINGS collect_applicable_rules(Rules,I1,ApplRules), %%% slow point update(time_applicable), %%% TIMINGS (ApplRules=[], %%% writeln('No appl rules'), !, I2=I1; %%%IT1=I2; %% no rules -> stable model %%% remove the rules that would be failing (head is false in I1). if the remainder is empty this is not a stable model! remove_head_conflict_rules(ApplRules,ApplRulesOK), %%% remove from applicable rules the ones that are already applied (they would be failing here) %%% compute the sublist (left) to be appened as next PrevRules (collect the left part for each parent) diff_list(ApplRulesOK,PrevRules,ActualApplRules), %%% diff_list -> n log n %write_fdmodel_complete(I1), %writeln([applrules,lev,Level]), %write_applrules(ApplRulesOK), sublist(ActualApplRules,[GRULE],LeftRulesIdx,1,_), prefix_length(ActualApplRules,LeftRules,LeftRulesIdx), %% get the left set of rules append(PrevRules,LeftRules,NewPrevRules), get_bodyMinus(LeftRules,NewLeftProgram), append(Rules,NewLeftProgram,NewRules), apply_rule_1(GRULE, I1, IN, _), update(nodes), %%% TIMINGS %writeln([Level,GRULE]), %% collect list of already used rules statistics(runtime,_), %%% TIMINGS %write_fdmodel_complete(IN), fixpoint_tp_propagate(NewRules,IN,IN3), %writeln([ok]), update(time_prop), %%% TIMINGS Level1 is Level+1, lev_fixpoint(NewRules,IN3,I2,NewPrevRules,Level1) ). remove_head_conflict_rules([[_,0]|R],R1):- remove_head_conflict_rules(R,R1). remove_head_conflict_rules([[Rule,1]|R],[Rule|R1]):- remove_head_conflict_rules(R,R1). remove_head_conflict_rules([],[]). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% "MODEL" Checking procedures %%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% wf_stable/2 %%% Tests if a well-founded model is complete, hence stable wf_stable([],_). wf_stable([atom(false,_,_,_)|M],1) :- %% particular case !, wf_stable(M,1). %% for constraints-free programs wf_stable([atom(_,AR,PDOM,NDOM)|M],Flag) :- complement_set(AR,PDOM,NDOM), wf_stable(M,Flag). %%%%%%%% check_consistent/3 %%% fails if one element in the list is in the negative domain check_consistent([],_ARITY,_NEG). check_consistent([L|Rest],ARITY,NEG):- nin_set(ARITY,L,NEG), check_consistent(Rest,ARITY,NEG). %%%%%%%%% constraints_check/1 %%% Tests if the constraints are verified. %%% Observe that for each constraint :- Goal %%% we add a rule %%% false :- Goal. %%% When false is present in a model -> %%% a constraint has been falsified (Goal is true in the Model) %%% Using apply_rule1 should be useless constraints_check(Model) :- member(atom(false,0,[],_),Model). %%%% get_bodyMinus % retieves the negative part of the bodies get_bodyMinus([],[]). get_bodyMinus([rule(_H,_BP,[false|BM])|LeftRules],[rule([false],[],[false|BM])|NewLeftConstraints]):-!, get_bodyMinus(LeftRules,NewLeftConstraints). get_bodyMinus([rule(_H,_BP,BM)|LeftRules],[rule([false],[],[false|BM])|NewLeftConstraints]):- get_bodyMinus(LeftRules,NewLeftConstraints). %%%%% collect_applicable_rules/3 %% collects all the applicable rules given the interpretation I. %% Notice the (non standard) the use of findall/4 to avoid an append %% HeadNoConflict states whether the application of the rule produces a head that is already in the model as positive/undefined or in the negative form collect_applicable_rules([Rule|Rules],I,List):- collect_applicable_rules(Rules,I,B), findall(Output,(apply_rule(Rule,I, _M, GroundRule,HeadNoConflict), Output=[GroundRule,HeadNoConflict] % ,constraints_check(M) ),List,B). collect_applicable_rules([],_I,[]). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% non deterministic rule application: apply_rule (_1) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% used for building the set of applicable rules (constraints included) %% cannot include apply_rule_1, otherwise if a constraint cannot be satisfied, %% it results that the rule is not applicable apply_rule(rule([H],Bpos,Bneg),I1,I2,rule([H1],Bpos1,Bneg1),HeadNoConflict) :- statistics(runtime,_), %%% TIMINGS Bneg \= [], %%% Must have negative literals copy_term([H,Bpos,Bneg],[H1,Bpos1,Bneg1]), H1 =.. [F|ARGS], term_variables([H1,Bpos1],VARS), %%% All vars are in the positive part bigM(M), M1 is M-1, domain(VARS,0,M1), build_constraint(Bpos1,I1,1,pos), %%% 1 means positive part is satisfied build_constraint(Bneg1,I1,1,neg), tuple_num(ARGS,Arg,ARITY), member(atom(F,ARITY,PDOM,NDOM),I1), nin_set(ARITY,Arg,PDOM), nin_set(ARITY,Arg,NDOM,HeadNoConflict), %% flag to export that states wheter the application of the rule contradicts the model (helps in deciding when the stable model / failure is reached) update(time_csp), %%% TIMINGS statistics(runtime,_), %%% TIMINGS labeling([ff],VARS), %%% Positive part satisfied update(time_labeling), %%% TIMINGS dom_update(Bneg1,I1,I2). %%% Update negative part %%% apply_rule_1 unfolds apply_rule optimizing the constraint case apply_rule_1(rule([false],Bpos,Bneg),I1,I2,rule([false],Bpos1,Bneg1)) :- !, Bneg \= [], %%% Must have negative literals copy_term([Bpos,Bneg],[Bpos1,Bneg1]), sub_list(Bneg1, BnegNOC, BnegC), BnegC=[_|_], %% at least one element in BnegC term_variables(Bpos1,VARS), %%% All vars are in the positive part bigM(M), M1 is M-1, domain(VARS,0,M1), build_constraint(Bpos1,I1,1,pos), %%% 1 means positive part is satisfied build_constraint(BnegNOC,I1,1,neg), %%% a part of the negative part is satisfied build_constraint(BnegC,I1,1,pos), %%% the rest is falsified labeling([ff],VARS), %%% Positive part satisfied dom_update(Bneg1,I1,I2). %%% Update negative part apply_rule_1(rule([H],Bpos,Bneg),I1,I2,rule([H1],Bpos1,Bneg1)) :- H\=false,!, Bneg \= [], %%% Must have negative literals copy_term([H,Bpos,Bneg],[H1,Bpos1,Bneg1]), H1 =.. [F|ARGS], term_variables([H1,Bpos1],VARS), %%% All vars are in the positive part bigM(M), M1 is M-1, domain(VARS,0,M1), build_constraint(Bpos1,I1,1,pos), %%% 1 means positive part is satisfied build_constraint(Bneg1,I1,1,neg), %%% 1 means negative part is satisfied tuple_num(ARGS,Arg,ARITY), member(atom(F,ARITY,PDOM,_),I1), nin_set(ARITY,Arg,PDOM), %%% This avoids to use the same rule twice labeling([ff],VARS), %%% Positive part satisfied dom_update(Bneg1,I1,I2). %%% Update negative part %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% PROPAGATION %%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% fixpoint_tp_propagate(NewRules,I,IOut):- tp(NewRules,I,IN2), %writeln(tpOk), constraints_check(IN2), %writeln(checkOk), update(time_tp), %%% TIMINGS statistics(runtime,_), %%% TIMINGS (inutile?) %%% uncomment one of the two following lines (activate propagator) propagate(NewRules,IN2,IN3,Changed), (Changed=0,!, IOut=IN3; fixpoint_tp_propagate(NewRules,IN3,IOut) ). %%% for each rule, build a CSP that produces the ground literals that are set to false %%% if there is a body+ completely ground, but one literal %%% AND the head is false %%% Changed >0 if a changed happened propagate(Rules,I1,I4,Changed):- propagate1(Rules,I1,I2,Changed1), %%% head false -> try to imply a false predicate in the body propagate2(Rules,I2,I2,I3,Changed2), %%% undef head (ground) -> try to set it = false (no support) (Changed1+Changed2#>0,!,propagate(Rules,I3,I4,Changed3),Changed#=Changed1+Changed2+Changed3; I3=I4,Changed#=Changed1+Changed2). propagate2(_,[],M,M,0). propagate2(Rules,[Atom|R],In,Out,Changed):- actual_propagation2(Atom,Rules,In,In1,Changed1), Changed#=Changed1+Changed2, propagate2(Rules,R,In1,Out,Changed2). %%% for each undef domain value for the predicate P %%% check if this is supported by at least one rule %%% assuming that undef val are set to true in positive body and to false in negative body %%% if no support for any rule -> the atom is set to false actual_propagation2(atom(P,Arity,Dom,NDom),Rules,In,In1,Changed):- %writeln(atom(P,Arity,Dom,NDom)), %% slow point get_rules_with_head(Rules,P,Arity,List), %writeln([rules,List]), compute_support(P,Arity,In,List,ListPotentiallySupported), %writeln([supported,ListPotentiallySupported]), complement_set(Arity,Dom,CDom), fdset_subtract(CDom,NDom,UDom), %indefinito %writeln([undef,UDom]), (ListPotentiallySupported=[],!,NewNegatives=UDom; %% Udom - ListPotentiallySupported => become negative -> dom_update In-->In1 list_to_fdset(ListPotentiallySupported,SET), fdset_subtract(UDom,SET,NewNegatives) ), %writeln([becomeNeg,NewNegatives]), (NewNegatives=[],!,In1=In,Changed=0; select(atom(P,Arity,PDOM,NEGDOM),In,Irest), fdset_union(NEGDOM,NewNegatives,NEWDOM), %% if D is already in NEGDOM In1=[atom(P,Arity,PDOM,NEWDOM)|Irest], Changed=1 ) . %%% given a rule and model I1 compute the tuples supported by the rule compute_support(_P,_Arity,_I1,[],[]). compute_support(P,Arity,I1,[rule([H],Bpos,Bneg)|R],R2):- copy_term([H,Bpos,Bneg],[H1,Bpos1,Bneg1]), H1 =.. [F|ARGS], term_variables(Bpos1,VARS), %%% All vars are in the positive part bigM(M), M1 is M-1, domain(VARS,0,M1), build_constraint(Bpos1,I1,1,notneg), %%% positive body can be true/undefined but no in negative (otherwise no applicability) build_constraint(Bneg1,I1,1,neg), %%% negative body can be false/undefined but no in positive (otherwise no applicability) %% the head is currently unknown tuple_num(ARGS,Arg,ARITY), member(atom(F,ARITY,PDOM,NDOM),I1), nin_set(ARITY,Arg,PDOM), nin_set(ARITY,Arg,NDOM), findall(Head,(labeling([ff],VARS),Head=Arg),Supported), append(Supported,R1,R2), compute_support(P,Arity,I1,R,R1). compute_support(P,Arity,I1,[_|R],R1):-!, compute_support(P,Arity,I1,R,R1). %%% get_rules_with_head/3: %%% given a predicate and arity, collects all the rules with matching head get_rules_with_head([],_P,_Arity,[]). get_rules_with_head([rule([H],PBody,NBody)|Rules],P,Arity,[rule([H],PBody,NBody)|R1]):- H =.. [F|ARGS], tuple_num(ARGS,_,ARITY), F=P, ARITY=Arity,!, get_rules_with_head(Rules,P,Arity,R1). get_rules_with_head([_|Rules],P,Arity,R1):- get_rules_with_head(Rules,P,Arity,R1). propagate1([],I,I,0). propagate1([R|Rules],I,I1,Changed1):-!, actual_propagation(R,I,I2,Changed), propagate1(Rules,I2,I1,Changed2), Changed1#=Changed+Changed2. %%% propagation rule: CSP with %%% if Bp and Bn are in the model I, then enforce Pp and/or Pn in the new model actual_propagation(rule([false],Bpos,Bneg),I1,I2,Changed) :- %writeln([prop,rule([false],Bpos,Bneg)]), copy_term([Bpos,Bneg],[Bpos1,Bneg1]), % delete(Bneg1,false,Bneg2), term_variables([Bpos1],VARS), %%% All vars are in the positive part bigM(M), M1 is M-1, domain(VARS,0,M1), length(Bpos1,Len), domain([Pos],1,Len), build_constraint_one_nonground(Bpos1,I1,NTrue,MaxTrue,Pos,1), %%% count how many are in I+, and we set it to Len-1. all of them are NOT in I-. Pos is the position of the only undefined literal NTrue #= MaxTrue -1, build_constraint(Bneg1,I1,1,neg), %%% 1 means negative part is satisfied findall(Ground,(labeling([ff],[Pos|VARS]),nth1(Pos,Bpos1,Ground) %,writeln([Ground,':-',Bpos1,Bneg1]) ),[L|IST]), dom_update([L|IST],I1,I2), %%% Update negative part Changed=1, !. actual_propagation(rule([H],Bpos,Bneg),I1,I2,Changed) :- H\=false, %writeln([prop,rule([H],Bpos,Bneg)]), %trace, copy_term([H,Bpos,Bneg],[H1,Bpos1,Bneg1]), % delete(Bneg1,false,Bneg2), H1 =.. [F|ARGS], term_variables(Bpos1,VARS), %%% All vars are in the positive part tuple_num(ARGS,Arg,ARITY), member(atom(F,ARITY,_PDOM,NDOM),I1), Arg in_set NDOM, length(Bpos1,Len), domain([Pos],1,Len), build_constraint_one_nonground(Bpos1,I1,NTrue,MaxTrue,Pos,1), %%% count how many are in I+, and we set it to Len-1. all of them are NOT in I-. Pos is the position of the only undefined literal NTrue #= MaxTrue -1, build_constraint(Bneg1,I1,1,neg), %%% 1 means negative part is satisfied findall(Ground,(labeling([ff],[Pos|VARS]),nth1(Pos,Bpos1,Ground) %,writeln([Ground,[H1],':-',Bpos1,Bneg1]) ),[L|IST]), dom_update([L|IST],I1,I2) %%% Update negative part ,Changed=1 ,! . actual_propagation(_P,I,I,0). %% if fails -> no propagation for rule %%%actual_propagation([Bp,Bn,Pp,Pn],I,I2):- %%% copy_term([Bp,Bn,Pp,Pn],[Bp1,Bn1,Pp1,Pn1]), %%% term_variables([Bp1,Pp1],VARS), %%% %%% bigM(M), M1 is M-1, domain(VARS,0,M1), %%% build_constraint(Bp1,I,1,pos), %%% 1 means positive part is satisfied %%% build_constraint(Bn1,I,1,negknown), %%% 1 means negative part is satisfied %%% (Pn1==[],!, %% Pp1 not in pos AND not in neg %%% build_constraint(Pp1,I,1,nowhere) %%% nowhere -> the atom is not yet decided %%% ; %%% Pp1==[], %%% build_constraint(Pn1,I,1,nowhere) %%% nowhere %%% ), % %%%% %%% %%% (Pn1==[],!, %% Pp1 not in pos AND not in neg %%% findall(X,(labeling([ff],VARS),[X]=Pp1),[L|IST]), %%% dom_pos_update([L|IST],I,I2) %%% ; %%% Pp1==[], %%% findall(X,(labeling([ff],VARS),[X]=Pn1),[L|IST]), %%%writeln([prop ,[L|IST]]), %%% dom_update([L|IST],I,I2) %%% ),!. %%% %%%%%% if no propagation is possible (fail while building constraints) -> no model change %actual_propagation(_P,I,I). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% domain updating %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dom_update([],I,I). dom_update([A|R],I1,I2) :- A =.. [F|ARGS], tuple_num(ARGS,D,ARITY), select(atom(F,ARITY,PDOM,NEGDOM),I1,Irest), fdset_add_element(NEGDOM,D,NEWDOM), %% if D is already in NEGDOM dom_update(R,[atom(F,ARITY,PDOM,NEWDOM)|Irest],I2).%% then NEWDOM=NEGDOM dom_pos_update([],I,I). dom_pos_update([A|R],I1,I2) :- A =.. [F|ARGS], tuple_num(ARGS,D,ARITY), select(atom(F,ARITY,PDOM,NEGDOM),I1,Irest), fdset_add_element(PDOM,D,NEWPDOM), dom_neg_update(R,[atom(F,ARITY,NEWPDOM,NEGDOM)|Irest],I2).%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% expression parses algebraic expressions into FD expressions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% expression(F,[TX,TY],C2) :- term_conv(TX,TERMX), term_conv(TY,TERMY), (F = '=', !, C2 #<=> TERMX #= TERMY; F = 'eq', !, C2 #<=> TERMX #= TERMY; F = '==',!, C2 #<=> TERMX #= TERMY; F = '<', !, C2 #<=> TERMX #< TERMY; F = '>', !, C2 #<=> TERMX #> TERMY; F = 'neq', !, C2 #<=> TERMX #\= TERMY). term_conv(V,V) :- var(V),!. term_conv(N,N) :- number(N),!. %% binary functions term_conv(TI,TO) :- TI =.. [OP,A,B],!, term_conv(A,A1), term_conv(B,B1), (OP = '+', !, TO #= A1 + B1; OP = '-', !, TO #= A1 - B1; OP = '/', !, TO #= A1 / B1; OP = 'mod',!, TO #= A1 mod B1; OP = '*', TO #= A1 * B1). %% unary functions term_conv(TI,TO) :- TI =.. [OP,A], term_conv(A,A1), (OP = 'abs', !, TO #= abs(A1); OP = '-', !, TO #= -(A1)). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%% PARSING PHASE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %(ok)%%%%%%%%%%%%% read_program/2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% Given a prolog file name ProgFile %%%%% output a list of clauses in the form %%%%% rule([H],Body+,Body-) %%%%% where H is rule head atom %%%%% Body+ is the list of positive atoms in body %%%%% Body- is the list of atoms occuring negated in body %%%%% example ProgList=[rule([p],[q,r(X)],[s(X,a)]), %%% p :- q,r(X),not s(X,a). %%%%% rule([p],[],[q]), %%% p :- not q. %%%%% rule([],[a],[b]), ] %%% :- a, not b. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% read_program(ProgFile,ProgList) :- see(ProgFile), read_all(ProgList), writeln('### Program read without errors ###'), writeln(ProgFile), seen. read_all([Rule|ProgList]) :- read(Clause), Clause \== end_of_file, !, ( Clause = ('1'({ A : B })'1' :- C),!, %%% Aggregate clause split_pos_neg(C,P,N), %%% restricted syntax Rule = rule([A],[B|P],N) %%% Use with parsimony ; Clause = (A :- B),!, %% Rules with Body split_pos_neg(B,P,N), Rule = rule([A],P,N) ; Clause = (:- B),!, %%% Constraints split_pos_neg(B,P,N), %%% Introduced faked rules Rule = rule([false],P,[false|N]) ; Rule = rule([Clause],[],[])), %% Facts read_all(ProgList). read_all([]). %(ok)%%%%%%% input rules split_pos_neg/3 and split_facts/3 split_pos_neg((not C1,D),R1,[C1|R2]):- !, split_pos_neg(D,R1,R2). split_pos_neg((C,D),[C|R1],R2):- !, split_pos_neg(D,R1,R2). split_pos_neg(not A,[],[A]):- !. split_pos_neg(P,[P],[]). %%%% The 4th parameter of split_facts is %%%% 0 for definite program, %%%% 1 for general programs without constraints and %%%% 2 for programs with constraints but without functions %%%% 3 for programs with functions split_facts([],[],[],0). split_facts([rule([INTERVAL],[],[])|ProgList], %%% This is the case of "domain" [rule([H1],[],[])|Facts], %%% predicates, such as p(1..3). [rule([H2],[H3, X = Y + 1, X < B + 1],[])|Rules],ND):- INTERVAL =.. [P,A..B], !, H1 =..[P,A], H2 =..[P,X], H3 =..[P,Y], split_facts(ProgList,Facts,Rules,ND). split_facts([rule([FUNCTION],_,_)|ProgList], Facts,Rules,3):- %%% case of functions FUNCTION =.. [assignment|_],!, split_facts(ProgList,Facts,Rules,_). split_facts([rule(A,[],[])|ProgList],[rule(A,[],[])|Facts],Rules,ND):- !, split_facts(ProgList,Facts,Rules,ND). split_facts([rule(A,B,[])|ProgList], Facts,[rule(A,B,[])|Rules],ND):- !, split_facts(ProgList,Facts,Rules,ND). split_facts([rule([false],B,C)|ProgList],Facts,[rule([false],B,C)|Rules],Flag):- !, split_facts(ProgList,Facts,Rules,ND), Flag is max(ND,2). split_facts([NRULE|ProgList], Facts,[NRULE|Rules],Flag):- split_facts(ProgList,Facts,Rules,ND), Flag is max(ND,1). def_rules([],[]). def_rules([rule(_,_,[_|_])|ProgList], Defrules) :- !, def_rules(ProgList,Defrules). def_rules([RULE|ProgList],[RULE|Defrules]) :- def_rules(ProgList,Defrules). %%%% dep_graph/2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% It generates a dependency graph. %%%% Each rule is assigned to an integer %%%% and asserted as rule_no(NUMBER,RULE) %%%% Each predicate p of arity AR is assigned %%%% to the list of rules where it appears "positively" %%%% in the body. Facts of the form %%%% dependency(p,AR,[(rule)N1,...,(rule)Np). %%%% Moreover, a fact of the form %%%% posdependency(p,AR,[(rule)N1,...,(rule)Np). %%%% is also asserted to link the definite clauses %%%% where p occur in the body. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% dep_graph(IniDoms,Rules):- retractall(dependency(_,_,_)), retractall(posdependency(_,_,_)), retractall(rule_no(_,_)), list_rules(Rules,1), dep_graph_aux(IniDoms,Rules). list_rules([],_). %%% Currently, constraints are used as %%% other rules %%% list_rules([rule([false],_,_)|R],N) :- !, list_rules(R,N). list_rules([RULE|R],N) :- assert(rule_no(N,RULE)), M is N + 1, list_rules(R,M). dep_graph_aux([],_). dep_graph_aux([atom(false,_,_,_)|R],ProgList) :- !, dep_graph_aux(R,ProgList). dep_graph_aux([atom(P,N,_,_)|R],ProgList) :- functor(Atom,P,N), findall(K, ( member(rule(A,B,C),ProgList), memberchk(Atom,B), %%%append(B,C,D),memberchk(Atom,D), rule_no(K,RULE1), copy_term(rule(A,B,C),RULE1) ), RULES), assert(dependency(P,N,RULES)), %% avoid multiple occs findall(H, ( member(rule(A1,B1,[]),ProgList), memberchk(Atom,B1), rule_no(H,RULE2), copy_term(rule(A1,B1,[]),RULE2) ), POSRULES), assert(posdependency(P,N,POSRULES)), %% avoid multiple occs %%% write(dependency(P,N,RULES)),nl, dep_graph_aux(R,ProgList). %remove_false([],[]). %remove_false([false|R],T):-!, % remove_false(R,T). %remove_false([A|R],[A|T]):- % %%%A\=false,!, % remove_false(R,T). %% for each element, produce a constraint %% if a predicate is the only one not in the model -> force the false version of it loop_for_each_el(_,[],_,_,L,L). loop_for_each_el(Ra,[R|Rs],[],BN,L,L1):- R =.. [F|_ARGS], %% builtin -> no propagation builtin(F),!, loop_for_each_el([R|Ra],Rs,[],BN,L,L1). loop_for_each_el(Ra,[R|Rs],[],BN,L,L1):- append(Ra,Rs,RR), loop_for_each_el([R|Ra],Rs,[],BN,[[RR,BN,[],[R]]|L],L1). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%% AUXILIARY PREDICATES %%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% tuple_num returns the code VAL associated to a tuple %%%% and the arity AR of a tuple %%%% it works for N <= 3. It is easy to be extended %%%% It is called by most of the predicates tuple_num(ARGS,VAL,ARITY) :- (ARGS = [],!, VAL=0, ARITY=0; ARGS = [VAL],!, ARITY=1; ARGS = [Arg1,Arg2],!, bigM(M), ARITY=2, VAL #= M*Arg1+Arg2; ARGS = [Arg1,Arg2,Arg3], bigM(M), ARITY=3, VAL #= M*M*Arg1+M*Arg2+Arg3). %%% num_tuple it the reverse function (from VAL to ARGS) num_tuple(ARGS,VAL,ARITY) :- (ARITY=0,!, ARGS = [], VAL=0 ; ARITY=1,!, ARGS = [VAL] ; ARITY=2,!, bigM(M), Arg1 is VAL//M, Arg2 is VAL mod M, ARGS = [Arg1,Arg2]; ARITY=3,!, bigM(M), Arg1 is VAL//(M*M), Arg2 is (VAL-Arg1*M*M)//M, Arg3 is VAL mod M, ARGS = [Arg1,Arg2,Arg3]). %%% pair_proj is bi-directional and works for pairs pair_proj(PAIR,X,Y) :- bigM(M), PAIR #= M*X + Y, X #= PAIR/M, Y #= PAIR mod M. triple_proj(TRIPLE,X,Y,Z) :- bigM(M), TRIPLE #= M*M*X + M*Y + Z, X #= TRIPLE/M/M, Y #= (TRIPLE/M) mod M, Z #= TRIPLE mod M. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% nin_set/4 sets the constraint C to 1 iff %% X is not in SET. %% nin_set/3 adds the constraint X is not in SET. nin_set(ARITY,X,SET,C) :- complement_set(ARITY,SET,COMPL), C #<=> X in_set COMPL. nin_set(ARITY,X,SET) :- complement_set(ARITY,SET,COMPL), X in_set COMPL. %% complement set computes the complement wrt a universe set %% of the fd_set UDOM. The universe set changes according to the %% arity complement_set(AR,UDOM,NDOM) :- bigM(M), (AR=0,!,VAL=0; AR=1,!,VAL is M -1; AR=2,!,VAL is M*M -1; AR=3,VAL is M*M*M -1), fdset_interval(Universe,0,VAL), %write(acca(Universe,0,VAL,UDOM)), fdset_subtract(Universe,UDOM,NDOM). %%% diff_list(X,Y,Z) returns in Z the list of elements in X and not in Y %%% diff_list(X,Y,Z,K) returns in Z the list of elements in X and not in Y, K is sort(X), %%% nlogn version (if sort is n log n) diff_list(ApplRules,PrevRules,NewRules) :- sort(PrevRules,SortedPrevRules), %% SORT is not important here. sort(ApplRules,SortedApplRules), %% Only to fast the rest extract_new_rules(SortedPrevRules,SortedApplRules,NewRules). diff_list(ApplRules,PrevRules,NewRules,SortedApplRules) :- sort(PrevRules,SortedPrevRules), %% SORT is not important here. sort(ApplRules,SortedApplRules), %% Only to fast the rest extract_new_rules(SortedPrevRules,SortedApplRules,NewRules). extract_new_rules([A|R1],[A|R2],R3):- !, extract_new_rules(R1,R2,R3). extract_new_rules([A|R1],[B|R2],R3):- compare(<,A,B),!, extract_new_rules(R1,[B|R2],R3). extract_new_rules([A|R1],[B|R2],[B|R3]):- % compare(>,A,B),!, extract_new_rules([A|R1],R2,R3). extract_new_rules([],A,A):-!. extract_new_rules(_,[],[]). %%% disj_union appends two lists and sort them without repetitions disj_union(A,B,C) :- append(A,B,D), sort(D,C). %%% remove_dups(D,C). %%% computes non-deterministically P(List) i.e. lists with elements from input list %%% third arg -> complement sub_list([],[],[]). sub_list([A|R],[A|R1],R2):- sub_list(R,R1,R2). sub_list([A|R],R1,[A|R2]):- sub_list(R,R1,R2). %%% increasing(List) :- lex_chain([List],[increasing]), labeling([],List). %%% Reset of global parameters (timings, number of solutions) reset :- statistics(runtime,[It,_]), %% RETRACT ALL OLD VALUES retractall(sol(_)), retractall(it(_)), retractall(time_applicable(_)), retractall(time_implicit(_)), retractall(time_tp(_)), retractall(time_csp(_)), retractall(time_prop(_)), retractall(time_labeling(_)), retractall(nodes(_)), retractall(last_time(_)), %% ASSERT INITIAL VALUES assert(sol(0)), assert(it(It)), assert(time_applicable(0)), assert(time_implicit(0)), assert(time_tp(0)), assert(time_csp(0)), assert(time_prop(0)), assert(time_labeling(0)), assert(nodes(0)), assert(last_time(It)). %%% To skip timings, uncomment the following line: %%% update(_) :-!. update(model) :- !, retract(sol(N)), N1 is N+1, assert(sol(N1)). update(nodes) :- !, retract(nodes(N)), N1 is N+1, assert(nodes(N1)). update(F) :- %%% for various time_... statistics(runtime,[_,A]), Tin =.. [F,B], retract(Tin), C is A+B, Tout =.. [F,C], assert(Tout). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%% PRINTING PREDICATES %%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% writeln(A) :- write(A),nl. writetime(String) :- statistics(runtime,[T,_]), last_time(T1), T2 is T-T1, retract(last_time(T1)), assert(last_time(T)), write(String),write(T2),writeln(' ms ###'). %%%% write_model/2: if the flag is "write" prints a stable model write_model(write,MOD) :- !, writeln('###############################################'), writeln('############# Computed model ##################'), writeln('###############################################'), write_fdmodel(MOD), writeln('###############################################'). write_model(_,_) :- writeln('### Computed model not printed, as requested ###'). write_fdmodel([]). %write_fdmodel([atom(false,0,_,_)|R]):- !, % write_fdmodel(R). write_fdmodel([atom(P,0,Dom,_)|R]):- format("### ~a/0: ",[P]), (Dom=[],!, writeln(false); writeln(true)), write_fdmodel(R). write_fdmodel([atom(P,1,Dom,_)|R]):- format("### ~a/1: ",[P]), fdset_to_list(Dom,LDom), writelist(LDom),nl, write_fdmodel(R). write_fdmodel([atom(P,2,Dom,_)|R]):- format("### ~a/2: ",[P]), fdset_to_list(Dom,LDom),write_proj(2,LDom),nl, write_fdmodel(R). write_fdmodel([atom(P,3,Dom,_)|R]):- format("### ~a/3: ",[P]), fdset_to_list(Dom,LDom), write_proj(3,LDom),nl, write_fdmodel(R). write_fdmodel_complete([]). %write_fdmodel_complete([atom(false,0,_,_)|R]):- !, % write_fdmodel_complete(R). write_fdmodel_complete([atom(P,0,Dom,NDom)|R]):- format("### ~a/0: ",[P]), (Dom=[],!, write('?'); write(true)), (NDom=[],!, write('?'); write(false)), nl, write_fdmodel_complete(R). write_fdmodel_complete([atom(P,1,Dom,NDom)|R]):- format("### ~a/1: ",[P]), fdset_to_list(Dom,LDom), complement_set(1,Dom,CDom), % write(cacca(Dom,CDom)),nl, fdset_subtract(CDom,NDom,UDom), %indefinito fdset_to_list(UDom,LUDom), writelist(LDom), write(' undef'), writelist(LUDom), nl, write_fdmodel_complete(R). write_fdmodel_complete([atom(P,2,Dom,NDom)|R]):- format("### ~a/2: ",[P]), fdset_to_list(Dom,LDom), complement_set(2,Dom,CDom), % write(cacca(Dom,CDom)),nl, fdset_subtract(CDom,NDom,UDom), %indefinito fdset_to_list(UDom,LUDom), write_proj(2,LDom), write(' undef'), write_proj(2,LUDom), nl, write_fdmodel_complete(R). write_fdmodel_complete([atom(P,3,Dom,NDom)|R]):- format("### ~a/3: ",[P]), fdset_to_list(Dom,LDom), write_proj(3,LDom), complement_set(3,Dom,CDom), % write(cacca(Dom,CDom)),nl, fdset_subtract(CDom,NDom,UDom), %indefinito write(' undef'), fdset_to_list(UDom,LUDom), write_proj(3,LUDom), nl, write_fdmodel_complete(R). write_proj(_,[]):-!. write_proj(2,[D|R]) :-!, bigM(M), X is D//M, Y is D mod M, format("(~d,~d) ",[X,Y]), write_proj(2,R). write_proj(3,[D|R]) :-!, bigM(M), X is D//(M*M), Y is (D-X*M*M)//M, Z is D mod M, format("(~d,~d,~d) ",[X,Y,Z]), write_proj(3,R). writelist([]). writelist([D|R]) :- write(D),write(' '), writelist(R). gasp_statistics :- sol(N), statistics(runtime,[T,_]), it(IT), TotT is (T - IT)/1000, time_applicable(TimeA),TotTimeA is TimeA/1000, time_implicit(TimeI),TotTimeI is TimeI/1000, time_tp(TimeT),TotTimeT is TimeT/1000, time_csp(TimeC),TotTimeC is TimeC/1000, time_prop(TimeP),TotTimeP is TimeP/1000, time_labeling(TimeL),TotTimeL is TimeL/1000, nodes(Nodes), format("### Computed ~d stable model(s) in ~2F s ###\n",[N,TotT]), format("### Time for implicit rule ~2F s ###\n",[TotTimeI]), format("### Time for applicable rule ~2F s ###\n",[TotTimeA]), format("### Time for csp ~2F s ###\n",[TotTimeC]), format("### Time for labeling ~2F s ###\n",[TotTimeL]), format("### Time for propagation ~2F s ###\n",[TotTimeP]), format("### Time for tp + check ~2F s ###\n",[TotTimeT]), format("### Nodes ~d ###\n",[Nodes]), write('############################################ END'). write_applrules([]). write_applrules([R|Ules]):- writeln(R), write_applrules(Ules). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% EXTRA CODE 1. SIMPLE ASP COMPUTATION (without any ordering control) %%% It can replace fixpoint predicate %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% slow_fixpoint(Rules,I0,M) :- (nd_choice(Rules,I0,I1), tp(Rules,I1,I2), constraints_check(I2), slow_fixpoint(Rules,I2,M); stable(Rules,I0),!, M=I0). nd_choice([Rule|_], I1,I2 ) :- apply_rule(Rule, I1, I2,_,_). nd_choice([_|Rules], I1, I2 ) :- nd_choice(Rules, I1, I2). stable(Rules,I0) :- constraints_check(I0), \+ nd_choice(Rules,I0,_). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% BETA PART: Functions-driven fixpoint, fun_fixpoint(Rules,I1,I2,Program) :- writeln('### Started function part '), functions(I1,Inew,Program), %%% Constraint-based function tp(Rules,Inew,Ineww), constraints_check(Ineww), fixpoint(Rules,Ineww,I2). functions(WFModel, [atom(assignment,2,ASS,NDOM)|RModel],Program) :- member(atom(domain,1,NUM,_),WFModel), %%% general: function domain member(atom(range,1,RAN,_),WFModel), %%% general: function range select(atom(assignment,2,_,NDOM),WFModel,RModel), %%% general: function fdset_size(NUM,L), length(Xs,L), length(Ys,L), funbuild(Xs,Ys,NUM,RAN,FUN), %%% general: map of (X,Y) increasing(Xs), %% general: removes symmetries and grounds the domain %% all_different(Ys), %%% use for one-to-one functions constraint_adhoc(Program,FUN,RModel), labeling([],FUN), list_to_fdset(FUN,ASS). functions(WFModel, [atom(assignment,3,ASS,NDOM)|RModel],Program) :- member(atom(domain,1,NUM,_),WFModel), %%% general: function domain member(atom(range1,1,RAN1,_),WFModel), %%% general: function range member(atom(range2,1,RAN2,_),WFModel), %%% general: function range select(atom(assignment,3,_,NDOM),WFModel,RModel), %%% general: function fdset_size(NUM,L), length(Xs,L), length(Ys,L), length(Zs,L), funbuild(Xs,Ys,Zs,NUM,RAN1,RAN2,FUN), %%% general: map of (X,Y,Z) increasing(Xs), %% general: removes symmetries and grounds the domain %% all_different(Ys), %%% use for one-to-one functions constraint_adhoc(Program,FUN,RModel), labeling([],FUN), writeln(FUN), list_to_fdset(FUN,ASS). funbuild([],[],_,_,[]). funbuild([X|Xs],[Y|Ys],DOM,RAN,[D|Fun]) :- X in_set DOM, Y in_set RAN, tuple_num([X,Y],D,2), funbuild(Xs,Ys,DOM,RAN,Fun). funbuild([],[],[],_,_,_,[]). funbuild([X|Xs],[Y|Ys],[Z|Zs],DOM,RAN1,RAN2,[D|Fun]) :- X in_set DOM, Y in_set RAN1,Z in_set RAN2, tuple_num([X,Y,Z],D,3), funbuild(Xs,Ys,Zs,DOM,RAN1,RAN2,Fun). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% AD-HOC PART %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% constraint_adhoc(Program,FUN,Model) :- ( Program='test5.lp' -> write(constraintSchur), constraint_schur(FUN),!; % Program='test3.lp' -> constraint_marriage(Model,FUN),!; Program='test6.lp' -> constraint_marriage(Model,FUN),!; Program='test9.lp' -> constraint_square(Model,FUN),!; Program='test4.lp' -> constraint_queens(FUN),!; true ). %%% :- domain(X),range(Y), assignment(X,Y), X < Y. %%%%% Do not consider "domain" and "range" %%%%% One occurrence of "assignment" => one level of recursion %%%%% only one built-in atom "X= Y, %%% The complement of the atom constraint_test3(FUN). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% From "queens" %%% TWO ASP CONSTRAINTS constraint_queens(FUN) :- constraint_queens_horizontal(FUN), constraint_queens_diagonal(FUN). %%% Horizontal %%% :- assignment(X1,Y1), assignment(X2,Y2), %%% Y1==Y2,neq(X1,X2). %%% Two "assignment": double recursion %%% two built-in atoms constraint_queens_horizontal([]). constraint_queens_horizontal([PAIR|FUN]) :- constraint_queens_horizontal_2(PAIR,FUN), constraint_queens_horizontal(FUN). constraint_queens_horizontal_2(_,[]). constraint_queens_horizontal_2(PAIR1,[PAIR2|FUN]) :- pair_proj(PAIR1,X1,Y1), pair_proj(PAIR2,X2,Y2), (X1 \= X2,!,Y1 #\= Y2; true), %%% Actually, since we know that X1 < X2 %%% thus one could write simply Y1 #\= Y2 constraint_queens_horizontal_2(PAIR1,FUN). %%% Diagonal %%%:- assignment(X1,Y1), assignment(X2,Y2), %%% neq(X1,X2), abs(X1-X2) == abs(Y1-Y2). %%% Two "assignments": double recursion %%% Two built-in atoms constraint_queens_diagonal([]). constraint_queens_diagonal([PAIR|FUN]) :- constraint_queens_diagonal_2(PAIR,FUN), constraint_queens_diagonal(FUN). constraint_queens_diagonal_2(_,[]). constraint_queens_diagonal_2(PAIR1,[PAIR2|FUN]) :- pair_proj(PAIR1,X1,Y1), pair_proj(PAIR2,X2,Y2), %%% (X1 \= X2,!, abs(X1-X2) #\= abs(Y1-Y2); true), %%% The complement of the atom %%% Actually, we know that X1 < X2 %%% thus one could write simply abs(X1-X2) #\= abs(Y1-Y2) constraint_queens_diagonal_2(PAIR1,FUN). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% From Schur %%% :- assignment(X1,Y), assignment(X2,Y), assignment(X3,Y), %%% X3 = X1+X2. %%% Three assignments: triple recursion. %%% TAKE CARE THAT HERE RECURSION USES <= !!! constraint_schur([]). constraint_schur([PAIR|FUN]) :- constraint_schur2(PAIR,[PAIR|FUN]), constraint_schur(FUN). constraint_schur2(_,[]). constraint_schur2(PAIR1,[PAIR2|FUN]) :- constraint_schur3(PAIR1,PAIR2,[PAIR2|FUN]), constraint_schur2(PAIR1,FUN). constraint_schur3(_,_,[]). constraint_schur3(PAIR1,PAIR2,[PAIR3|FUN]) :- pair_proj(PAIR1,X1,Y1), pair_proj(PAIR2,X2,Y2), pair_proj(PAIR3,X3,Y3), %%% we know that Xi's are ground %%%(Y1 #= Y2 #/\ Y1 #= Y3) #=> (X3 #\= X1 + X2), (X3 =:= X1+X2,!,(Y1 #= Y2 #=> Y1 #\= Y3); true), constraint_schur3(PAIR1,PAIR2,FUN). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% :- hate(X,Y),assignment(X,Y). %%% 1 occ of assignment: one recursion %%% predicate non built.in hate: the model is needed %%% as parameter %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% constraint_marriage(Model,FUN) :- member(atom(hate,2,EDGES,_),Model), constraint_marriage_rec(FUN,EDGES). constraint_marriage_rec([],_). constraint_marriage_rec([PAIR|FUN],EDGES) :- nin_set(2,PAIR,EDGES), constraint_marriage_rec(FUN,EDGES). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% square: for each pair of squares, no overlap %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% constraint_square(Model,FUN) :- constraint_square(Model,0,FUN), %%% no overlap constraint_square1(Model,0,FUN). %% inside master square constraint_square1(_,_,[]). constraint_square1(Model,N,[TRIPLE|FUN]) :- triple_proj(TRIPLE,N,X1,Y1), %%% retrieve master size member(atom(master_size,1,MSIZE,_),Model), member(atom(size,2,SIZE,_),Model), %% retrieve size of current square pair_proj(PAIR,N,Size), PAIR in_set SIZE, MS in_set MSIZE, X1+Size#==X1+Size1 #\/ Y2+Size2#==Y1+Size1, S21 is S2+1, constraint_square_2(Model,S1,TRIPLE1,S21,FUN). %%%%%%%%% END %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%