1/* $Id$ 2 3 Part of CLP(Q) (Constraint Logic Programming over Rationals) 4 5 Author: Leslie De Koninck 6 E-mail: Leslie.DeKoninck@cs.kuleuven.be 7 WWW: http://www.swi-prolog.org 8 http://www.ai.univie.ac.at/cgi-bin/tr-online?number+95-09 9 Copyright (C): 2006, K.U. Leuven and 10 1992-1995, Austrian Research Institute for 11 Artificial Intelligence (OFAI), 12 Vienna, Austria 13 14 This software is based on CLP(Q,R) by Christian Holzbaur for SICStus 15 Prolog and distributed under the license details below with permission from 16 all mentioned authors. 17 18 This program is free software; you can redistribute it and/or 19 modify it under the terms of the GNU General Public License 20 as published by the Free Software Foundation; either version 2 21 of the License, or (at your option) any later version. 22 23 This program is distributed in the hope that it will be useful, 24 but WITHOUT ANY WARRANTY; without even the implied warranty of 25 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 26 GNU General Public License for more details. 27 28 You should have received a copy of the GNU Lesser General Public 29 License along with this library; if not, write to the Free Software 30 Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 31 32 As a special exception, if you link this library with other files, 33 compiled with a Free Software compiler, to produce an executable, this 34 library does not by itself cause the resulting executable to be covered 35 by the GNU General Public License. This exception does not however 36 invalidate any other reasons why the executable file might be covered by 37 the GNU General Public License. 38*/ 39 40:- module(bb_q, 41 [ 42 bb_inf/3, 43 bb_inf/4, 44 vertex_value/2 45 ]). 46:- use_module(bv_q, 47 [ 48 deref/2, 49 deref_var/2, 50 determine_active_dec/1, 51 inf/2, 52 iterate_dec/2, 53 sup/2, 54 var_with_def_assign/2 55 ]). 56:- use_module(nf_q, 57 [ 58 {}/1, 59 entailed/1, 60 nf/2, 61 nf_constant/2, 62 repair/2, 63 wait_linear/3 64 ]). 65 66% bb_inf(Ints,Term,Inf) 67% 68% Finds the infimum of Term where the variables Ints are to be integers. 69% The infimum is stored in Inf. 70 71bb_inf(Is,Term,Inf) :- 72 bb_inf(Is,Term,Inf,_). 73 74bb_inf(Is,Term,Inf,Vertex) :- 75 wait_linear(Term,Nf,bb_inf_internal(Is,Nf,Inf,Vertex)). 76 77% --------------------------------------------------------------------- 78 79% bb_inf_internal(Is,Lin,Inf,Vertex) 80% 81% Finds an infimum <Inf> for linear expression in normal form <Lin>, where 82% all variables in <Is> are to be integers. 83 84bb_inf_internal(Is,Lin,_,_) :- 85 bb_intern(Is,IsNf), 86 nb_delete(prov_opt), 87 repair(Lin,LinR), % bb_narrow ... 88 deref(LinR,Lind), 89 var_with_def_assign(Dep,Lind), 90 determine_active_dec(Lind), 91 bb_loop(Dep,IsNf), 92 fail. 93bb_inf_internal(_,_,Inf,Vertex) :- 94 nb_current(prov_opt,InfVal-Vertex), 95 {Inf =:= InfVal}, 96 nb_delete(prov_opt). 97 98% bb_loop(Opt,Is) 99% 100% Minimizes the value of Opt where variables Is have to be integer values. 101 102bb_loop(Opt,Is) :- 103 bb_reoptimize(Opt,Inf), 104 bb_better_bound(Inf), 105 vertex_value(Is,Ivs), 106 ( bb_first_nonint(Is,Ivs,Viol,Floor,Ceiling) 107 -> bb_branch(Viol,Floor,Ceiling), 108 bb_loop(Opt,Is) 109 ; nb_setval(prov_opt,Inf-Ivs) % new provisional optimum 110 ). 111 112% bb_reoptimize(Obj,Inf) 113% 114% Minimizes the value of Obj and puts the result in Inf. 115% This new minimization is necessary as making a bound integer may yield a 116% different optimum. The added inequalities may also have led to binding. 117 118bb_reoptimize(Obj,Inf) :- 119 var(Obj), 120 iterate_dec(Obj,Inf). 121bb_reoptimize(Obj,Inf) :- 122 nonvar(Obj), 123 Inf = Obj. 124 125% bb_better_bound(Inf) 126% 127% Checks if the new infimum Inf is better than the previous one (if such exists). 128 129bb_better_bound(Inf) :- 130 nb_current(prov_opt,Inc-_), !, 131 Inf < Inc. 132bb_better_bound(_). 133 134% bb_branch(V,U,L) 135% 136% Stores that V =< U or V >= L, can be used for different strategies within 137% bb_loop/3. 138 139bb_branch(V,U,_) :- {V =< U}. 140bb_branch(V,_,L) :- {V >= L}. 141 142% vertex_value(Vars,Values) 143% 144% Returns in <Values> the current values of the variables in <Vars>. 145 146vertex_value([],[]). 147vertex_value([X|Xs],[V|Vs]) :- 148 rhs_value(X,V), 149 vertex_value(Xs,Vs). 150 151% rhs_value(X,Value) 152% 153% Returns in <Value> the current value of variable <X>. 154 155rhs_value(Xn,Value) :- 156 ( nonvar(Xn) 157 -> Value = Xn 158 ; var(Xn) 159 -> deref_var(Xn,Xd), 160 Xd = [I,R|_], 161 Value is R+I 162 ). 163 164% bb_first_nonint(Ints,Rhss,Eps,Viol,Floor,Ceiling) 165% 166% Finds the first variable in Ints which doesn't have an active integer bound. 167% Rhss contain the Rhs (R + I) values corresponding to the variables. 168% The first variable that hasn't got an active integer bound, is returned in 169% Viol. The floor and ceiling of its actual bound is returned in Floor and Ceiling. 170 171bb_first_nonint([I|Is],[Rhs|Rhss],Viol,F,C) :- 172 ( integer(Rhs) 173 -> bb_first_nonint(Is,Rhss,Viol,F,C) 174 ; Viol = I, 175 F is floor(Rhs), 176 C is ceiling(Rhs) 177 ). 178 179% bb_intern([X|Xs],[Xi|Xis]) 180% 181% Turns the elements of the first list into integers into the second 182% list via bb_intern/3. 183 184bb_intern([],[]). 185bb_intern([X|Xs],[Xi|Xis]) :- 186 nf(X,Xnf), 187 bb_intern(Xnf,Xi,X), 188 bb_intern(Xs,Xis). 189 190 191% bb_intern(Nf,X,Term) 192% 193% Makes sure that Term which is normalized into Nf, is integer. 194% X contains the possibly changed Term. If Term is a variable, 195% then its bounds are hightened or lowered to the next integer. 196% Otherwise, it is checked it Term is integer. 197 198bb_intern([],X,_) :- 199 !, 200 X = 0. 201bb_intern([v(I,[])],X,_) :- 202 !, 203 integer(I), 204 X = I. 205bb_intern([v(1,[V^1])],X,_) :- 206 !, 207 V = X, 208 bb_narrow_lower(X), 209 bb_narrow_upper(X). 210bb_intern(_,_,Term) :- 211 throw(instantiation_error(bb_inf(Term,_),1)). 212 213% bb_narrow_lower(X) 214% 215% Narrows the lower bound so that it is an integer bound. 216% We do this by finding the infimum of X and asserting that X 217% is larger than the first integer larger or equal to the infimum 218% (second integer if X is to be strict larger than the first integer). 219 220bb_narrow_lower(X) :- 221 ( inf(X,Inf) 222 -> Bound is ceiling(Inf), 223 ( entailed(X > Bound) 224 -> {X >= Bound+1} 225 ; {X >= Bound} 226 ) 227 ; true 228 ). 229 230% bb_narrow_upper(X) 231% 232% See bb_narrow_lower/1. This predicate handles the upper bound. 233 234bb_narrow_upper(X) :- 235 ( sup(X,Sup) 236 -> Bound is floor(Sup), 237 ( entailed(X < Bound) 238 -> {X =< Bound-1} 239 ; {X =< Bound} 240 ) 241 ; true 242 ). 243 244 /******************************* 245 * SANDBOX * 246 *******************************/ 247:- multifile 248 sandbox:safe_primitive/1. 249 250sandbox:safe_primitive(bb_q:bb_inf(_,_,_)). 251sandbox:safe_primitive(bb_q:bb_inf(_,_,_,_))