% Boolean tests from Daniel Diaz % 931127 adapted to Eclipse and CHRs by Thom Fruehwirth, ECRC %From diaz@margaux.inria.fr Tue Nov 23 18:59:17 1993 % %I send you 3 programs schur.pl, pigeon.pl and queens.pl and a file %b_bips.pl containing the necessary built-ins and libraries. %---schur.pl--- /*-------------------------------------------------------------------------*/ /* Benchmark (Boolean) INRIA Rocquencourt - ChLoE Project */ /* */ /* Name : bschur.pl */ /* Title : Schur's lemma */ /* Original Source: Giovanna Dore - Italy */ /* Adapted by : Daniel Diaz - INRIA France */ /* Date : January 1993 */ /* */ /* Color the integers 1,2...,N with 3 colors so that there is no monochrome*/ /* triplets (x,y,z) where x+y=z. Solution iff N<=13. */ /* The solution is a list [ [Int11,Int12,Int13],..., [IntN1,IntN2,IntN3] ] */ /* where Intij is 1 if the integer i is colored with the color j. */ /* */ /* Solution: */ /* N=4 [[0,0,1],[0,1,0],[0,0,1],[1,0,0]] */ /* [[0,0,1],[0,1,0],[0,1,0],[0,0,1]] */ /* ... */ /* N=13 [[0,0,1],[0,1,0],[0,1,0],[0,0,1],[1,0,0],[1,0,0],[0,0,1],[1,0,0], */ /* [1,0,0],[0,0,1],[0,1,0],[0,1,0],[0,0,1]] (first solution) */ /*-------------------------------------------------------------------------*/ bschur:- write('N ?'), read(N), cputime( Starttime), (schur(N,A), % write(A), nl, fail ; write('No more solutions'), nl), cputime( Cputime), Y is Cputime-Starttime, write('time : '), write(Y), nl. cputime( Ts) :- statistics( runtime, [Tm,_]), Ts is Tm/1000. schur(N,A):- create_array(N,3,A), for_each_line(A,only1), pair_constraints(A,A), !, % labeling. array_labeling(A). pair_constraints([],_):- !. pair_constraints([_],_):- !. pair_constraints([_,[K1,K2,K3]|A2],[[I1,I2,I3]|A1]):- and0(I1,K1), and0(I2,K2), and0(I3,K3), triplet_constraints(A2,A1,[I1,I2,I3]), pair_constraints(A2,A1). triplet_constraints([],_,_). triplet_constraints([[K1,K2,K3]|A2],[[J1,J2,J3]|A1],[I1,I2,I3]):- and0(I1,J1,K1), and0(I2,J2,K2), and0(I3,J3,K3), triplet_constraints(A2,A1,[I1,I2,I3]). %--- pigeon.pl --- /*-------------------------------------------------------------------------*/ /* Benchmark (Boolean) INRIA Rocquencourt - ChLoE Project */ /* */ /* Name : bpigeon.pl */ /* Title : pigeon-hole problem */ /* Originated from: */ /* Adapted by : Daniel Diaz - INRIA France */ /* Date : January 1993 */ /* */ /* Put N pigeons in M pigeon-holes. Solution iff N<=M. */ /* The solution is a list [ [Pig11,...,Pig1m], ... ,[Pign1,...,Pignm] ] */ /* where Pigij = 1 if the pigeon i is in the pigeon-hole j */ /* */ /* Solution: */ /* N=2 M=3 [[0,0,1],[0,1,0]] */ /* [[0,0,1],[1,0,0]] */ /* [[0,1,0],[0,0,1]] */ /* [[0,1,0],[1,0,0]] */ /* [[1,0,0],[0,0,1]] */ /* [[1,0,0],[0,1,0]] */ /*-------------------------------------------------------------------------*/ bpigeon:- write('N ?'), read(N), write('M ?'), read(M), cputime( Starttime), (bpigeon(N,M,A), % write(A), nl, fail ; write('No more solutions'), nl), cputime( Cputime), Y is Cputime-Starttime, write('time : '), write(Y), nl. bpigeon(N,M,A):- create_array(N,M,A), for_each_line(A,only1), for_each_column(A,atmost1), !, array_labeling(A). %--- queens.pl --- /*-------------------------------------------------------------------------*/ /* Benchmark (Boolean) INRIA Rocquencourt - ChLoE Project */ /* */ /* Name : bqueens.pl */ /* Title : N-queens problem */ /* Original Source: Daniel Diaz - INRIA France */ /* Adapted by : */ /* Date : January 1993 */ /* */ /* Put N queens on an NxN chessboard so that there is no couple of queens */ /* threatening each other. */ /* The solution is a list [ [Que11,...,Que1N], ... ,[QueN1,...,QueNN] ] */ /* where Queij is 1 if the the is a queen on the ith line an jth row. */ /* */ /* Solution: */ /* N=4 [[0,0,1,0], [[0,1,0,0], */ /* [1,0,0,0], [0,0,0,1], */ /* [0,0,0,1], and [1,0,0,0], */ /* [0,1,0,0]] [0,0,1,0]] */ /* */ /* N=8 [[0,0,0,0,0,0,0,1], (first solution) */ /* [0,0,0,1,0,0,0,0], */ /* [1,0,0,0,0,0,0,0], */ /* [0,0,1,0,0,0,0,0], */ /* [0,0,0,0,0,1,0,0], */ /* [0,1,0,0,0,0,0,0], */ /* [0,0,0,0,0,0,1,0], */ /* [0,0,0,0,1,0,0,0]] */ /*-------------------------------------------------------------------------*/ bqueens:- write('N ?'), read(N), cputime( Starttime), (bqueens(N,A), % write(A), nl, fail ; write('No more solutions'), nl), cputime( Cputime), Y is Cputime-Starttime, write('time : '), write(Y), nl. bqueens(N,A):- create_array(N,N,A), for_each_line(A,only1), for_each_column(A,only1), for_each_diagonal(A,N,N,atmost1), !, array_labeling(A). %--- b_bips.pl --- %I also use the following shorthands: and0(X,Y):- and(X,Y,0). % delay([X,Y],and(X,Y,0)). or1(X,Y):- or(X,Y,1). and0(X,Y,Z):- and(X,Y,XY), and(XY,Z,0). % delay([X,Y,Z],( % and(X,Y,XY), % and(XY,Z,0))). or1(X,Y,Z):- or(X,Y,XY), or(XY,Z,1). /*-------------------------------------------------------------------------*/ /* Prolog to Wam Compiler INRIA Rocquencourt - ChLoE Project */ /* Version 1.0 - C Run-time Daniel Diaz - 1991 */ /* Extended to FD Constraints (July 1992) */ /* */ /* Built-In: B predicates (booleans) */ /* */ /* b_bips.pl */ /*-------------------------------------------------------------------------*/ /* Symbolic constraints */ %:- public only_one/1, at_least_one/1, at_most_one/1. %only_one(L):- card(1,1,L). %at_most_one(L):- card(0,1,L). only_one(L):- at_least_one(L), at_most_one(L). at_least_one(L):- at_least_one1(L,1). at_least_one1([X],X). at_least_one1([X|L],R):- at_least_one1(L,R1), or(X,R1,R). at_most_one([]). at_most_one([X|L]):- not_two(L,X), at_most_one(L). not_two([],_). not_two([X1|L],X):- and0(X1,X), not_two(L,X). /* Array procedures */ %:- public create_array/3, for_each_line/2, for_each_column/2, for_each_diagonal/4, array_labeling/1. /*---------------------------------------------------------*/ /* */ /* An array NL x NC elements is represented as follows : */ /* A = [L_1, ..., L_NL] with L_i = [X_i_1, ..., X_i_NC] */ /* Hence : */ /* A = [ [X_1_1,..., X_1_NC], ..., [X_NL_1,..., X_NL_NC] ] */ /*---------------------------------------------------------*/ % create_array(NL,NC,A) % NL: nb of lines NC:nb of columns A:array % creates an array (with unbound variables) create_array(NL,NC,A):- create_array1(0,NL,NC,A), !. create_array1(NL,NL,_,[]). create_array1(I,NL,NC,[L|A]):- create_one_line(0,NC,L), I1 is I+1, create_array1(I1,NL,NC,A). create_one_line(NC,NC,[]). create_one_line(J,NC,[_|L]):- J1 is J+1, create_one_line(J1,NC,L). % for_each_line(A,P) % A:array P: program atom % calls: array_prog(P,L) for each line L (L is a list) for_each_line([],_). for_each_line([L|A],P):- array_prog(P,L), for_each_line(A,P). % for_each_column(A,P) % A:array P: program atom % calls: array_prog(P,L) for each column L (L is a list) for_each_column([[]|_],_):- !. for_each_column(A,P):- create_column(A,C,A1), array_prog(P,C), for_each_column(A1,P). create_column([],[],[]). create_column([[X|L]|A],[X|C],[L|A1]):- create_column(A,C,A1). % for_each_diagonal(A,NL,NC,P) % A:array NL: nb of lines % NC:nb of columns P: program atom % calls: array_prog(P,L) for each diagonal D (D is a list) for_each_diagonal(A,NL,NC,P):- NbDiag is 2*(NL+NC-1), % numbered from 0 to NbDiag-1 create_lst_diagonal(0,NbDiag,LD), fill_lst_diagonal(A,0,NL,NC,LD,LD1), !, for_each_line(LD1,P). create_lst_diagonal(NbDiag,NbDiag,[]). create_lst_diagonal(I,NbDiag,[[]|LD]):- I1 is I+1, create_lst_diagonal(I1,NbDiag,LD). fill_lst_diagonal([],_,_,_,LD,LD). fill_lst_diagonal([L|A],I,NL,NC,LD,LD2):- I1 is I+1, fill_lst_diagonal(A,I1,NL,NC,LD,LD1), one_list(L,I,NL,0,NC,LD1,LD2). one_list([],_,_,_,_,LD,LD). one_list([X|L],I,NL,J,NC,LD,LD3):- J1 is J+1, one_list(L,I,NL,J1,NC,LD,LD1), NoDiag1 is I+J, NoDiag2 is I+NC-J+NL+NC-2, add_in_lst_diagonal(0,NoDiag1,X,LD1,LD2), add_in_lst_diagonal(0,NoDiag2,X,LD2,LD3). add_in_lst_diagonal(NoDiag,NoDiag,X,[D|LD],[[X|D]|LD]). add_in_lst_diagonal(K,NoDiag,X,[D|LD],[D|LD1]):- K1 is K+1, add_in_lst_diagonal(K1,NoDiag,X,LD,LD1). array_prog(only1,L):- !, only_one(L). array_prog(atmost1,L):- !, at_most_one(L). array_labeling([]). array_labeling([L|A]):- label_bool(L), array_labeling(A). %--- end ---