symbolicOutput(0). % set to 1 for DEBUGGING: to see symbolic output only; 0 otherwise. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% We want to schedule a series of events within the next few days. %% Each event should have a moderator assigned to it. There is a limit %% on the number of events per day and also on the amount of days %% where events with the same moderator can take place. Finally, we %% have a list of possible moderators and days for every event. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% begin input example %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% numEvents(15). %% numDays(4). %% numModerators(4). %% maxEventsPerDay(4). %% maxDaysPerModerator(2). %% %event( id, listPossibleModerators, listPossibleDays). %% event(1, [ 2 ,4],[ 2 ]). %% event(2, [1, 3 ],[1,2, 4]). %% event(3, [1,2 ,4],[ 3 ]). %% event(4, [1, 3,4],[1,2, 4]). %% event(5, [ 2,3,4],[1, 3,4]). %% event(6, [ 3,4],[1,2,3 ]). %% event(7, [1,2 ],[1,2, 4]). %% event(8, [1,2 ,4],[ 3,4]). %% event(9, [ 2,3 ],[1,2,3 ]). %% event(10,[ 3,4],[1,2, 4]). %% event(11,[1,2 ,4],[1,2,3 ]). %% event(12,[ 2,3 ],[ 3,4]). %% event(13,[1, 3,4],[1,2 ]). %% event(14,[ 2,3 ],[1, 3,4]). %% event(15,[ 2 ,4],[ 2,3 ]). %%%%%%% end input example %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% Some helpful definitions to make the code cleaner: ==================================== event(E) :- event(E,_,_). eventModerators(E,M) :- event(E,M,_). eventDays(E,D) :- event(E,_,D). day(D) :- numDays(N), between(1,N,D). moderator(M) :- numModerators(N), between(1,N,M). %%%%%%% End helpful definitions =============================================================== %%%%%%% 1. SAT Variables: ==================================================================== satVariable( ed(E,D) ) :- ... %% Complete this! % ... more variables may be needed %%%%%%% 2. Clause generation for the SAT solver: ============================================= writeClauses :- .... %% Complete this! true,!. writeClauses :- told, nl, write('writeClauses failed!'), nl,nl, halt. %%%%%%% 3. DisplaySol: show the solution. Here M contains the literals that are true in the model: % displaySol(M) :- nl, write(M), nl, nl, fail. displaySol(M) :- day(D), nl, write('Day '), write(D), write(': '), findall(E-Mod,(member(ed(E,D),M), member(em(E,Mod),M)), L), member(E-Mod,L), write(' event('), write(E), write(')-mod('), write(Mod), write(') '), fail. displaySol(M) :-nl, moderator(Mod), nl, findall(D,(member(ed(E,D),M), member(em(E,Mod),M)), L), write('Moderator '), write(Mod), write( ' works: '), sort(L,L1), write(L1), fail. displaySol(_). %%%%%%% ======================================================================================= %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Everything below is given as a standard library, reusable for solving %% with SAT many different problems. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%% Cardinality constraints on arbitrary sets of literals Lits: =========================== exactly(K,Lits) :- symbolicOutput(1), write( exactly(K,Lits) ), nl, !. exactly(K,Lits) :- atLeast(K,Lits), atMost(K,Lits),!. atMost(K,Lits) :- symbolicOutput(1), write( atMost(K,Lits) ), nl, !. atMost(K,Lits) :- % l1+...+ln <= k: in all subsets of size k+1, at least one is false: negateAll(Lits,NLits), K1 is K+1, subsetOfSize(K1,NLits,Clause), writeOneClause(Clause),fail. atMost(_,_). atLeast(K,Lits) :- symbolicOutput(1), write( atLeast(K,Lits) ), nl, !. atLeast(K,Lits) :- % l1+...+ln >= k: in all subsets of size n-k+1, at least one is true: length(Lits,N), K1 is N-K+1, subsetOfSize(K1, Lits,Clause), writeOneClause(Clause),fail. atLeast(_,_). negateAll( [], [] ). negateAll( [Lit|Lits], [NLit|NLits] ) :- negate(Lit,NLit), negateAll( Lits, NLits ),!. negate( -Var, Var) :- !. negate( Var, -Var) :- !. subsetOfSize(0,_,[]) :- !. subsetOfSize(N,[X|L],[X|S]) :- N1 is N-1, length(L,Leng), Leng>=N1, subsetOfSize(N1,L,S). subsetOfSize(N,[_|L], S ) :- length(L,Leng), Leng>=N, subsetOfSize( N,L,S). %%%%%%% Express equivalence between a variable and a disjunction or conjunction of literals === % Express that Var is equivalent to the disjunction of Lits: expressOr( Var, Lits ) :- symbolicOutput(1), write( Var ), write(' <--> or('), write(Lits), write(')'), nl, !. expressOr( Var, Lits ) :- member(Lit,Lits), negate(Lit,NLit), writeOneClause([ NLit, Var ]), fail. expressOr( Var, Lits ) :- negate(Var,NVar), writeOneClause([ NVar | Lits ]),!. %% expressOr(a,[x,y]) genera 3 clausulas (como en la Transformación de Tseitin): %% a == x v y %% x -> a -x v a %% y -> a -y v a %% a -> x v y -a v x v y % Express that Var is equivalent to the conjunction of Lits: expressAnd( Var, Lits) :- symbolicOutput(1), write( Var ), write(' <--> and('), write(Lits), write(')'), nl, !. expressAnd( Var, Lits) :- member(Lit,Lits), negate(Var,NVar), writeOneClause([ NVar, Lit ]), fail. expressAnd( Var, Lits) :- findall(NLit, (member(Lit,Lits), negate(Lit,NLit)), NLits), writeOneClause([ Var | NLits]), !. %%%%%%% main: ================================================================================= main:- current_prolog_flag(os_argv, Argv), nth0(1, Argv, InputFile), main(InputFile), !. main:- write('Usage: $ ./ or ?- main().'), nl, halt. main(InputFile):- symbolicOutput(1), !, consult(InputFile), writeClauses, halt. % print the clauses in symbolic form and halt Prolog main(InputFile):- consult(InputFile), initClauseGeneration, tell(clauses), writeClauses, told, % generate the (numeric) SAT clauses and call the solver tell(header), writeHeader, told, numVars(N), numClauses(C), write('Generated '), write(C), write(' clauses over '), write(N), write(' variables. '),nl, shell('cat header clauses > infile.cnf',_), write('Calling solver....'), nl, shell('kissat -v infile.cnf > model', Result), % if sat: Result=10; if unsat: Result=20. treatResult(Result),!. treatResult(20) :- write('Unsatisfiable'), nl, halt. treatResult(10) :- write('Solution found: '), nl, see(model), symbolicModel(M), seen, displaySol(M), nl,nl,halt. treatResult( _) :- write('cnf input error. Wrote anything strange in your cnf?'), nl,nl, halt. initClauseGeneration:- %initialize all info about variables and clauses: retractall(numClauses( _)), retractall(numVars( _)), retractall(varNumber(_,_,_)), assert(numClauses( 0 )), assert(numVars( 0 )), !. writeOneClause([]) :- symbolicOutput(1),!, nl. writeOneClause([]) :- countClause, write(0), nl. writeOneClause([Lit|C]) :- w(Lit), writeOneClause(C),!. w(-Var) :- symbolicOutput(1), satVariable(Var), write(-Var), write(' '),!. w( Var) :- symbolicOutput(1), satVariable(Var), write( Var), write(' '),!. w(-Var) :- satVariable(Var), var2num(Var,N), write(-), write(N), write(' '),!. w( Var) :- satVariable(Var), var2num(Var,N), write(N), write(' '),!. w( Lit) :- told, write('ERROR: generating clause with undeclared variable in literal '), write(Lit), nl,nl, halt. % given the symbolic variable V, find its variable number N in the SAT solver: :- dynamic(varNumber / 3). var2num(V,N) :- hash_term(V,Key), existsOrCreate(V,Key,N),!. existsOrCreate(V,Key,N) :- varNumber(Key,V,N),!. % V already existed with num N existsOrCreate(V,Key,N) :- newVarNumber(N), assert(varNumber(Key,V,N)), !. % otherwise, introduce new N for V writeHeader :- numVars(N),numClauses(C), write('p cnf '),write(N), write(' '),write(C),nl. countClause :- retract( numClauses(N0) ), N is N0+1, assert( numClauses(N) ),!. newVarNumber(N) :- retract( numVars( N0) ), N is N0+1, assert( numVars(N) ),!. % Getting the symbolic model M from the output file: symbolicModel(M) :- get_code(Char), readWord(Char,W), symbolicModel(M1), addIfPositiveInt(W,M1,M),!. symbolicModel([]). addIfPositiveInt(W,L,[Var|L]) :- W = [C|_], between(48,57,C), number_codes(N,W), N>0, varNumber(_,Var,N),!. addIfPositiveInt(_,L,L). readWord( 99,W) :- repeat, get_code(Ch), member(Ch,[-1,10]), !, get_code(Ch1), readWord(Ch1,W),!. % skip line starting w/ c readWord(115,W) :- repeat, get_code(Ch), member(Ch,[-1,10]), !, get_code(Ch1), readWord(Ch1,W),!. % skip line starting w/ s readWord( -1,_) :-!, fail. %end of file readWord(C, []) :- member(C,[10,32]), !. % newline or white space marks end of word readWord(Char,[Char|W]) :- get_code(Char1), readWord(Char1,W), !. %%%%%%% =======================================================================================