/* Part of SWI-Prolog Author: Tom Schrijvers E-mail: tom.schrijvers@cs.kuleuven.ac.be WWW: http://www.swi-prolog.org Copyright (c) 2004-2013, K.U.Leuven All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Simple integer solver that keeps track of upper and lower bounds % % Author: Tom Schrijvers % E-mail: tom.schrijvers@cs.kuleuven.ac.be % Copyright: 2004, K.U.Leuven % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Todo: % - reduce redundant propagation work % - other labelling functions % - abs, mod, ... % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% :- module(bounds, [ op(760,yfx,(#<=>)), op(750,xfy,(#=>)), op(750,yfx,(#<=)), op(740,yfx,(#\/)), op(730,yfx,(#\)), op(720,yfx,(#/\)), op(710, fy,(#\)), op(700,xfx,(#>)), op(700,xfx,(#<)), op(700,xfx,(#>=)), op(700,xfx,(#=<)), op(700,xfx,(#=)), op(700,xfx,(#\=)), op(700,xfx,(in)), op(550,xfx,(..)), (#>)/2, (#<)/2, (#>=)/2, (#=<)/2, (#=)/2, (#\=)/2, (#<=>)/2, (#=>)/2, (#<=)/2, (#/\)/2, (#\/)/2, (#\)/2, (#\)/1, (in)/2, label/1, labeling/2, all_different/1, sum/3, lex_chain/1, indomain/1, check/1, tuples_in/2, serialized/2 ]). :- use_module(library('clp/clp_events')). /** Simple integer solver that keeps track of upper and lower bounds @deprecated No longer maintained. Please use clpfd.pl @author Tom Schrijvers */ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % exported predicates X #>= Y :- parse_expression(X,RX), parse_expression(Y,RY), geq(RX,RY,yes). X #=< Y :- parse_expression(X,RX), parse_expression(Y,RY), leq(RX,RY,yes). X #= Y :- parse_expression(X,RX), parse_expression(Y,RX). X #\= Y :- parse_expression(X,RX), parse_expression(Y,RY), neq(RX,RY,yes). X #> Y :- Z #= Y + 1, X #>= Z. X #< Y :- Y #> X. X in L .. U :- ( is_list(X) -> domains(X,L,U) ; domain(X,L,U) ). L #<=> R :- reify(L,B), reify(R,B). L #=> R :- reify(L,BL), reify(R,BR), myimpl(BL,BR). R #<= L :- reify(L,BL), reify(R,BR), myimpl(BL,BR). L #/\ R :- call(L), call(R). L #\/ R :- reify(L,BL), reify(R,BR), myor(BL,BR,1). L #\ R :- reify(L,BL), reify(R,BR), myxor(BL,BR,1). #\ C :- reify(C,B), mynot(B,1). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% reify(B,R) :- var(B), !, R = B. reify(B,R) :- number(B), !, R = B. reify(X #>= Y,B) :- parse_expression(X,XR), parse_expression(Y,YR), reified_geq(XR,YR,B). reify(X #> Y,B) :- parse_expression(X,XR), Z #= Y + 1, reified_geq(XR,Z,B). reify(X #=< Y,B) :- parse_expression(X,XR), parse_expression(Y,YR), reified_geq(YR,XR,B). reify(X #< Y,B) :- reify(Y #> X,B). reify(X #= Y,B) :- parse_expression(X,XR), parse_expression(Y,YR), reified_eq(XR,YR,B). reify(X #\= Y,B) :- parse_expression(X,XR), parse_expression(Y,YR), reified_neq(XR,YR,B). reify((X #/\ Y),B) :- reify(X,BX), reify(Y,BY), myand(BX,BY,B). reify((X #\/ Y),B) :- reify(X,BX), reify(Y,BY), myor(BX,BY,B). reify((X #\ Y),B) :- reify(X,BX), reify(Y,BY), myxor(BX,BY,B). reify(#\ C, B) :- reify(C,BC), mynot(BC,B). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% check(X #= Y) :- parse_expression(X,XR), parse_expression(Y,YR), check_eq(XR,YR). check(X #=< Y) :- parse_expression(X,XR), parse_expression(Y,YR), check_leq(XR,YR). check(X #>= Y) :- parse_expression(X,XR), parse_expression(Y,YR), check_leq(YR,XR). check(X #< Y) :- parse_expression(X,XR), parse_expression(Y,YR), check_lt(XR,YR). check(X #> Y) :- parse_expression(X,XR), parse_expression(Y,YR), check_lt(YR,XR). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% parse_expression(Expr,Result) :- ( var(Expr) -> Result = Expr ; number(Expr) -> Result = Expr ; Expr = (L + R) -> parse_expression(L,RL), parse_expression(R,RR), myplus(RL,RR,Result,yes) ; Expr = (L * R) -> parse_expression(L,RL), parse_expression(R,RR), mytimes(RL,RR,Result,yes) ; Expr = (L - R) -> parse_expression(L,RL), parse_expression(R,RR), mytimes(-1,RR,RRR,yes), myplus(RL,RRR,Result,yes) ; Expr = (- E) -> parse_expression(E,RE), mytimes(-1,RE,Result,yes) ; Expr = max(L,R) -> parse_expression(L,RL), parse_expression(R,RR), mymax(RL,RR,Result,yes) ; Expr = min(L,R) -> parse_expression(L,RL), parse_expression(R,RR), mymin(RL,RR,Result,yes) ; Expr = L mod R -> parse_expression(L,RL), parse_expression(R,RR), mymod(RL,RR,Result,yes) ; Expr = abs(E) -> parse_expression(E,RE), myabs(RE,Result,yes) ; Expr = (L / R) -> parse_expression(L,RL), parse_expression(R,RR), mydiv(RL,RR,Result,yes) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% indomain(Var) :- ( var(Var) -> bounds(Var,L,U), between(L,U,Var) ; true ). label(Vs) :- labeling([], Vs). labeling(Options, Vars) :- label(Options, leftmost, none, Vars). label([Option|Options], Selection, Optimisation, Vars) :- ( selection(Option) -> label(Options, Option, Optimisation, Vars) ; optimization(Option) -> label(Options, Selection, Option, Vars) ; label(Options, Selection, Optimisation, Vars) ). label([], Selection, Optimisation, Vars) :- ( Optimisation == none -> label(Vars, Selection) ; optimize(Vars, Selection, Optimisation) ). label([],_) :- !. label(Vars,Selection) :- select_var(Selection,Vars,Var,RVars), indomain(Var), label(RVars,Selection). selection(ff). selection(min). selection(max). selection(leftmost). optimization(min(_)). optimization(max(_)). select_var(leftmost,[Var|Vars],Var,Vars). select_var(min,[V|Vs],Var,RVars) :- find_min(Vs,V,Var), delete_eq([V|Vs],Var,RVars). select_var(max,[V|Vs],Var,RVars) :- find_max(Vs,V,Var), delete_eq([V|Vs],Var,RVars). select_var(ff,[V|Vs],Var,RVars) :- find_ff(Vs,V,Var), delete_eq([V|Vs],Var,RVars). find_min([],Var,Var). find_min([V|Vs],CM,Min) :- ( min_lt(V,CM) -> find_min(Vs,V,Min) ; find_min(Vs,CM,Min) ). find_max([],Var,Var). find_max([V|Vs],CM,Max) :- ( max_gt(V,CM) -> find_max(Vs,V,Max) ; find_max(Vs,CM,Max) ). find_ff([],Var,Var). find_ff([V|Vs],CM,FF) :- ( ff_lt(V,CM) -> find_ff(Vs,V,FF) ; find_ff(Vs,CM,FF) ). ff_lt(X,Y) :- bounds(X,LX,UX), bounds(Y,LY,UY), UX - LX < UY - LY. min_lt(X,Y) :- bounds(X,LX,_), bounds(Y,LY,_), LX < LY. max_gt(X,Y) :- bounds(X,_,UX), bounds(Y,_,UY), UX > UY. bounds(X,L,U) :- ( var(X) -> get(X,L,U,_) ; X = L, X = U ). delete_eq([],_,[]). delete_eq([X|Xs],Y,List) :- ( X == Y -> List = Xs ; List = [X|Tail], delete_eq(Xs,Y,Tail) ). optimize(Vars, Selection, Opt) :- copy_term(Vars-Opt, Vars1-Opt1), once(label(Vars1, Selection)), functor(Opt1, Direction, _), maplist(arg(1), [Opt,Opt1], [Expr,Expr1]), optimize(Direction, Selection, Vars1, Vars, Expr1, Expr). optimize(Direction, Selection, Vars0, Vars, Expr0, Expr) :- Val0 is Expr0, copy_term(Vars-Expr, Vars1-Expr1), ( Direction == min -> Tighten = (Expr1 #< Val0) ; % max Tighten = (Expr1 #> Val0) ), ( Tighten, label(Vars1, Selection) -> optimize(Direction, Selection, Vars1, Vars, Expr1, Expr) ; Vars = Vars0, Expr = Expr0 ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% all_different([]). all_different([X|Xs]) :- different(Xs,X), all_different(Xs). different([],_). different([Y|Ys],X) :- neq(X,Y,yes), different(Ys,X). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% sum(Xs,Op,Value) :- sum1(Xs,0,Op,Value). sum1([],Sum,Op,Value) :- call(Op,Sum,Value). sum1([X|Xs],Acc,Op,Value) :- NAcc #= Acc + X, sum1(Xs,NAcc,Op,Value). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % contributed by Markus Triska lex_le([],[]). lex_le([V1|V1s], [V2|V2s]) :- V1 #=< V2, ( integer(V1) -> ( integer(V2) -> (V1 == V2 -> lex_le(V1s,V2s) ; true ) ; freeze(V2,lex_le([V1|V1s],[V2|V2s])) ) ; freeze(V1,lex_le([V1|V1s],[V2|V2s])) ). lex_chain([]). lex_chain([L|Ls]) :- lex_chain_lag(Ls, L). lex_chain_lag([], _). lex_chain_lag([L|Ls], Prev) :- lex_le(Prev, L), lex_chain_lag(Ls, L). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% domain(X,L,U) :- ( var(X) -> get(X,XL,XU,Exp), NL is max(L,XL), NU is min(U,XU), put(X,NL,NU,Exp) ; % nonvar(X) -> X >= L, X =< U ). domains([],_,_). domains([V|Vs],L,U) :- domain(V,L,U), domains(Vs,L,U). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% leq(X,Y,New) :- geq(Y,X,New). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% geq(X,Y,New) :- ( X == Y -> true ; nonvar(X) -> ( nonvar(Y) -> X >= Y ; get(Y,YL,YU,Exp) -> NYU is min(X,YU), put(Y,YL,NYU,Exp) ) ; nonvar(Y) -> get(X,XL,XU,Exp) -> NXL is max(Y,XL), put(X,NXL,XU,Exp) ; get(X,XL,XU,ExpX), get(Y,YL,YU,ExpY), XU >= YL, ( XL > YU -> true ; XU == YL -> X = Y ; member(leq(Z,State),ExpX), Y == Z -> set_passive(State), X = Y ; ( New == yes -> active_state(State), put(Y,YL,YU,[leq(X,State)|ExpY]), ExpX1 = [geq(Y,State)|ExpX] ; ExpX1 = ExpX ), NXL is max(XL,YL), put(X,NXL,XU,ExpX1), ( get(Y,YL2,YU2,ExpY2) -> NYU is min(YU2,XU), put(Y,YL2,NYU,ExpY2) ; true ) ) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% neq(X,Y,New) :- X \== Y, ( nonvar(X) -> ( nonvar(Y) -> true ; get(Y,L,U,Exp), ( L == X -> NL is L + 1, put(Y,NL,U,Exp) ; U == X -> NU is U - 1, put(Y,L,NU,Exp) ; L > X -> true ; U < X -> true ; ( New == yes -> active_state(State), put(Y,L,U,[neq(X,State)|Exp]) ; true ) ) ) ; nonvar(Y) -> neq(Y,X,New) ; get(X,XL,XU,XExp), get(Y,YL,YU,YExp), ( XL > YU -> true ; YL > XU -> true ; ( New == yes -> active_state(State), put(X,XL,XU,[neq(Y,State)|XExp]), put(Y,YL,YU,[neq(X,State)|YExp]) ; true ) ) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% myplus(X,Y,Z,New) :- ( nonvar(X) -> ( nonvar(Y) -> Z is X + Y ; nonvar(Z) -> Y is Z - X ; get(Z,ZL,ZU,ZExp), get(Y,YL,YU,YExp), ( New == yes -> ZExp1 = [myplus2(Y,X)|ZExp], YExp1 = [myplus(X,Z)|YExp], put(Y,YL,YU,YExp1) ; ZExp1 = ZExp ), NZL is max(ZL,X+YL), NZU is min(ZU,X+YU), put(Z,NZL,NZU,ZExp1), ( get(Y,YL2,YU2,YExp2) -> % JW: YL2 and YU2? NYL is max(YL2,NZL-X), NYU is min(YU2,NZU-X), put(Y,NYL,NYU,YExp2) ; Z is X + Y ) ) ; nonvar(Y) -> myplus(Y,X,Z,New) ; nonvar(Z) -> get(X,XL,XU,XExp), get(Y,YL,YU,YExp), ( New == yes -> XExp1 = [myplus(Y,Z)|XExp], YExp1 = [myplus(X,Z)|YExp], put(Y,YL,YU,YExp1) ; XExp1 = XExp ), NXL is max(XL,Z-YU), NXU is min(XU,Z-YL), put(X,NXL,NXU,XExp1), ( get(Y,YL2,YU2,YExp2) -> NYL is max(YL2,Z-NXU), NYU is min(YU2,Z-NXL), put(Y,NYL,NYU,YExp2) ; X is Z - Y ) ; get(X,XL,XU,XExp), get(Y,YL,YU,YExp), get(Z,ZL,ZU,ZExp), ( New == yes -> XExp1 = [myplus(Y,Z)|XExp], YExp1 = [myplus(X,Z)|YExp], ZExp1 = [myplus2(X,Y)|ZExp], put(Y,YL,YU,YExp1), put(Z,ZL,ZU,ZExp1) ; XExp1 = XExp ), NXL is max(XL,ZL-YU), NXU is min(XU,ZU-YL), put(X,NXL,NXU,XExp1), ( get(Y,YL2,YU2,YExp2) -> NYL is max(YL2,ZL-NXU), NYU is min(YU2,ZU-NXL), put(Y,NYL,NYU,YExp2) ; NYL = Y, NYU = Y ), ( get(Z,ZL2,ZU2,ZExp2) -> NZL is max(ZL2,NXL+NYL), NZU is min(ZU2,NXU+NYU), put(Z,NZL,NZU,ZExp2) ; true ) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % X * Y = Z div(X,Y,Z) :- ( max_inf(X) -> ( Y >= 0 -> Z = X ; min_inf(Z) ) ; min_inf(X) -> ( Y >= 0 -> Z = X ; max_inf(Z) ) ; Y \== 0 -> Z is X / Y ; X >= 0 -> max_inf(Z) ; X < 0 -> min_inf(Z) ). mytimes(X,Y,Z,New) :- ( nonvar(X) -> (nonvar(Y) -> Z is X * Y ; X == 0 -> Z = 0 ; nonvar(Z) -> 0 is Z mod X, Y is Z / X ; get(Y,YL,YU,YExp), get(Z,ZL,ZU,ZExp), NZL is max(ZL,min(X * YL,X*YU)), NZU is min(ZU,max(X * YU,X*YL)), ( New == yes -> YExp1 = [mytimes(X,Z)|YExp], put(Y,YL,YU,YExp1), put(Z,NZL,NZU,[mytimes2(X,Y)|ZExp]) ; put(Z,NZL,NZU,ZExp) ), ( get(Y,YL2,YU2,YExp2) -> min_divide(ZL,ZU,X,X,NYLT), max_divide(ZL,ZU,X,X,NYUT), NYL is max(YL2,ceiling(NYLT)), NYU is min(YU2,floor(NYUT)), put(Y,NYL,NYU,YExp2) ; Z is X * Y ) ) ; nonvar(Y) -> mytimes(Y,X,Z,New) ; nonvar(Z) -> get(X,XL,XU,XExp), get(Y,YL,YU,YExp), min_divide(Z,Z,YL,YU,TNXL), max_divide(Z,Z,YL,YU,TNXU), NXL is max(XL,ceiling(TNXL)), NXU is min(XU,floor(TNXU)), ( New == yes -> YExp1 = [mytimes(X,Z)|YExp], put(Y,YL,YU,YExp1), put(X,NXL,NXU,[mytimes(Y,Z)|XExp]) ; put(X,NXL,NXU,XExp) ), ( get(Y,YL2,YU2,YExp2) -> min_divide(Z,Z,NXL,NXU,NYLT), max_divide(Z,Z,NXL,NXU,NYUT), NYL is max(YL2,ceiling(NYLT)), NYU is min(YU2,floor(NYUT)), put(Y,NYL,NYU,YExp2) ; ( Y \== 0 -> 0 is Z mod Y, X is Z / Y ; Z = 0 ) ) ; get(X,XL,XU,XExp), get(Y,YL,YU,YExp), get(Z,ZL,ZU,ZExp), min_divide(ZL,ZU,YL,YU,TXL), NXL is max(XL,ceiling(TXL)), max_divide(ZL,ZU,YL,YU,TXU), NXU is min(XU,floor(TXU)), ( New == yes -> put(Y,YL,YU,[mytimes(X,Z)|YExp]), put(Z,ZL,ZU,[mytimes2(X,Y)|ZExp]), put(X,NXL,NXU,[mytimes(Y,Z)|XExp]) ; put(X,NXL,NXU,XExp) ), ( get(Y,YL2,YU2,YExp2) -> min_divide(ZL,ZU,XL,XU,TYL), NYL is max(YL2,ceiling(TYL)), max_divide(ZL,ZU,XL,XU,TYU), NYU is min(YU2,floor(TYU)), put(Y,NYL,NYU,YExp2) ; NYL = Y, NYU = Y ), ( get(Z,ZL2,ZU2,ZExp2) -> min_times(NXL,NXU,NYL,NYU,TZL), NZL is max(ZL2,TZL), max_times(NXL,NXU,NYL,NYU,TZU), NZU is min(ZU2,TZU), put(Z,NZL,NZU,ZExp2) ; true ) ). max_times(L1,U1,L2,U2,Max) :- Max is max(max(L1*L2,L1*U2),max(U1*L2,U1*U2)). min_times(L1,U1,L2,U2,Min) :- Min is min(min(L1*L2,L1*U2),min(U1*L2,U1*U2)). max_divide(L1,U1,L2,U2,Max) :- ( L2 =< 0 , U2 >= 0 -> max_inf(Max) ; div(L1,L2,DLL), div(L1,U2,DLU), div(U1,L2,DUL), div(U1,U2,DUU), Max is max(max(DLL,DLU),max(DUL,DUU)) ). min_divide(L1,U1,L2,U2,Min) :- ( L2 =< 0 , U2 >= 0 -> min_inf(Min) ; div(L1,L2,DLL), div(L1,U2,DLU), div(U1,L2,DUL), div(U1,U2,DUU), Min is min(min(DLL,DLU),min(DUL,DUU)) ). mydiv(X,Y,Z,New) :- ( Y == 0 -> fail ; true ), ( nonvar(X) -> ( nonvar(Y) -> Z is X // Y ; get(Y,YL,YU,YExp), ( New == yes -> put(Y,YL,YU,[mydiv3(X,Z)|YExp]) ; true ), ( nonvar(Z) -> % TODO: cover this true ; get(Z,ZL,ZU,ZExp), ( YL =< 0, YU >= 0 -> NZL is max(-abs(X),ZL), NZU is min(abs(X),ZU) ; X >= 0, YL > 0 -> NZL is max(X // YU, ZL), NZU is min(X // YL, ZU) ; % TODO: cover more cases NZL = ZL, NZU = ZU ), ( New == yes -> put(Z,NZL,NZU,[mydiv2(X,Y)|ZExp]) ; put(Z,NZL,NZU,ZExp) ) ) ) ; nonvar(Y) -> get(X,XL,XU,XExp), ( nonvar(Z) -> (Z >= 0, Y >= 0 -> NXL is max(Z*Y,XL), NXU is min((Z+1)*Y - 1,XU) ; % TODO: cover more cases NXL = XL, NXU = XU ), ( New == yes -> put(X,NXL,NXU,[mydiv(Y,Z)|XExp]) ; put(X,NXL,NXU,XExp) ) ; get(Z,ZL,ZU,ZExp), ( XL >= 0, Y >= 0 -> NZL is max(XL // Y,ZL), NZU is min(XU // Y,ZU), NXL is max(Y*NZL, XL), NXU is min((NZU+1)*Y - 1, XU) ; % TODO: cover more cases NZL is max(-max(abs(XL),abs(XU)),ZL), NZU is min(max(abs(XL),abs(XU)),ZU), NXL = XL, NXU = XU ), ( New == yes -> put(X,NXL,NXU,[mydiv(Y,Z)|XExp]), put(Z,NZL,NZU,[mydiv2(X,Y)|ZExp]) ; put(X,NXL,NXU,XExp), ( nonvar(Z) -> true ; put(Z,NZL,NZU,ZExp) ) ) ) ; nonvar(Z) -> get(X,XL,XU,XExp), get(Y,YL,YU,YExp), (YL >= 0, XL >= 0 -> NXL is max(YL*Z,XL), NXU is min(YU*(Z + 1) - 1,XU) ; % TODO: cover more cases NXL = XL, NXU = XU ), ( New == yes -> put(X,NXL,NXU,[mydiv(Y,Z)|XExp]), put(Y,YL,YU,[mydiv3(X,Z)|YExp]) ; put(X,NXL,NXU,XExp) ) ; get(X,XL,XU,XExp), get(Y,YL,YU,YExp), get(Z,ZL,ZU,ZExp), ( New == yes -> put(Y,YL,YU,[mydiv3(X,Z)|YExp]), put(Z,ZL,ZU,[mydiv2(X,Y)|ZExp]), put(X,XL,XU,[mydiv(Y,Z)|XExp]) ; true ) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% mymax(X,Y,Z,New) :- ( nonvar(X) -> ( nonvar(Y) -> Z is max(X,Y) ; nonvar(Z) -> ( Z == X -> geq(X,Y,yes) ; Z > X -> Y = Z %; Z < X % fail ) ; get(Y,YL,YU,YExp), get(Z,ZL,ZU,ZExp), ( YL >= X -> Z = Y ; X >= YU -> Z = X ; X < ZL -> Y = Z ; ( New == yes -> put(Y,YL,YU,[mymax(X,Z)|YExp]) ; true ), NZL is max(ZL,X), NZU is min(ZU,YU), ( New == yes -> put(Z,NZL,NZU,[mymax2(X,Y)|ZExp]) ; put(Z,NZL,NZU,ZExp) ), ( get(Y,YL2,YU2,YExp2) -> NYU is min(YU2,NZU), put(Y,YL2,NYU,YExp2) ; true ) ) ) ; nonvar(Y) -> mymax(Y,X,Z,New) ; nonvar(Z) -> get(X,XL,XU,XExp), get(Y,YL,YU,YExp), ( XU < Z -> Y = Z ; % XU >= Z -> YU < Z -> X = Z ; % YU >= Z XL > YU -> Z = X ; YL > XU -> Z = Y ; ( New == yes -> put(Y,YL,YU,[mymax(X,Z)|YExp]), put(X,XL,Z,[mymax(Y,Z)|XExp]) ; put(X,XL,Z,XExp) ), ( get(Y,YL2,YU2,YExp2) -> NYU is min(YU2,Z), put(Y,YL2,NYU,YExp2) ; true ) ) ; X == Y -> Z = X ; Z == X -> geq(X,Y,yes) ; Z == Y -> geq(Y,X,yes) ; get(X,XL,XU,XExp), get(Y,YL,YU,YExp), get(Z,ZL,ZU,ZExp), NZL is max(ZL,max(XL,YL)), NZU is min(ZU,max(XU,YU)), ( New == yes -> put(X,XL,XU,[mymax(Y,Z)|XExp]), put(Y,YL,YU,[mymax(X,Z)|YExp]), put(Z,NZL,NZU,[mymax2(X,Y)|ZExp]) ; put(Z,NZL,NZU,ZExp) ), ( get(X,XL2,XU2,XExp2) -> ( XU2 < NZL -> Y = Z ; YU < NZL -> X = Z ; YU < XL2 -> X = Z ; XU2 < YL -> Y = Z ; NXU is min(XU2,NZU), put(X,XL2,NXU,XExp2), ( get(Y,YL2,YU2,YExp2) -> NYU is min(YU2,NZU), put(Y,YL2,NYU,YExp2) ; mymax(Y,X,Z,no) ) ) ; mymax(X,Y,Z,no) ) ). mymin(X,Y,Z,New) :- ( nonvar(X) -> ( nonvar(Y) -> Z is min(X,Y) ; nonvar(Z) -> ( Z == X -> leq(X,Y,yes) ; Z < X -> Y = Z %; Z > X % fail ) ; get(Y,YL,YU,YExp), get(Z,ZL,ZU,ZExp), ( YL >= X -> Z = X ; X >= YU -> Z = Y ; X > ZU -> Y = Z ; ( New == yes -> put(Y,YL,YU,[mymin(X,Z)|YExp]) ; true ), NZL is max(ZL,YL), NZU is min(ZU,X), ( New == yes -> put(Z,NZL,NZU,[mymin2(X,Y)|ZExp]) ; put(Z,NZL,NZU,ZExp) ), ( get(Y,YL2,YU2,YExp2) -> NYL is max(YL2,NZL), put(Y,NYL,YU2,YExp2) ; true ) ) ) ; nonvar(Y) -> mymin(Y,X,Z,New) ; nonvar(Z) -> get(X,XL,XU,XExp), get(Y,YL,YU,YExp), ( XL > Z -> Y = Z ; % XL =< Z -> YL > Z -> X = Z ; % YL =< Z XU =< YL -> Z = X ; YU =< XL -> Z = Y ; ( New == yes -> put(Y,YL,YU,[mymin(X,Z)|YExp]), put(X,Z,XU,[mymin(Y,Z)|XExp]) ; put(X,Z,XU,XExp) ), ( get(Y,YL2,YU2,YExp2) -> NYL is max(YL2,Z), put(Y,NYL,YU2,YExp2) ; true ) ) ; X == Y -> Z = X ; Z == X -> leq(X,Y,yes) ; Z == Y -> leq(Y,X,yes) ; get(X,XL,XU,XExp), get(Y,YL,YU,YExp), get(Z,ZL,ZU,ZExp), NZL is max(ZL,min(XL,YL)), NZU is min(ZU,min(XU,YU)), ( New == yes -> put(X,XL,XU,[mymin(Y,Z)|XExp]), put(Y,YL,YU,[mymin(X,Z)|YExp]), put(Z,NZL,NZU,[mymin2(X,Y)|ZExp]) ; put(Z,NZL,NZU,ZExp) ), ( get(X,XL2,XU2,XExp2) -> ( XL2 > NZU -> Y = Z ; YL > NZU -> X = Z ; YU < XL2 -> Y = Z ; XU2 < YL -> X = Z ; NXL is max(XL2,NZL), put(X,NXL,XU2,XExp2), ( get(Y,YL2,YU2,YExp2) -> NYL is max(YL2,NZL), put(Y,NYL,YU2,YExp2) ; mymin(Y,X,Z,no) ) ) ; mymin(X,Y,Z,no) ) ). myabs(X,Y,New) :- ( nonvar(X) -> Y is abs(X) ; nonvar(Y) -> Y >= 0, get(X,LX,UX,ExpX), ( UX < Y -> X is (-Y) ; LX > (-Y) -> X = Y ; NLX is (-Y), ( New == yes -> put(X,NLX,Y,[myabs(Y)|ExpX]) ; put(X,NLX,Y,ExpX) ) ) ; get(X,LX,UX,ExpX), get(Y,LY,UY,ExpY), UY > 0, ( New == yes -> put(X,LX,UX,[myabs(Y)|ExpX]) ; true ), ( LX =< 0, UX >= 0 -> NLY is max(0,LY) ; NLY is max(min(abs(LX),abs(UX)),max(LY,0)) ), NUY is min(UY,max(abs(LX),abs(UX))), ( New == yes -> put(Y,NLY,NUY,[myabs2(X)|ExpY]) ; put(Y,NLY,NUY,ExpY) ), ( var(X) -> get(X,LX2,UX2,ExpX2), ( LX2 == LX, UX2 == UX -> ( NLY == 0 -> NLX is max(LX,(-NUY)), NUX is min(UX,NUY) ; LX > (-NLY) -> NLX is max(LX,NLY), NUX is min(UX,NUY) ; NLX is max((-NUY),LX), ( UX < NLY -> NUX is min((-NLY),UX) ; NUX is min(NUY,UX) ) ), put(X,NLX,NUX,ExpX2) ; true ) ; true ) ). mymod(X,Y,Z,New) :- % Z is X mod Y ( nonvar(X) -> ( nonvar(Y) -> Z is X mod Y ; nonvar(Z) -> get(Y,YL,YU,YExp), ( Z > 0 -> ( X == Z -> no_overlap(-X,X,YL,YU,NYL,NYU), ( New == yes -> put(Y,NYL,NYU,[mymod2(X,Z)|YExp]) ; put(Y,NYL,NYU,YExp) ) ; % Z < X no_overlap(-Z,Z,YL,YU,YL1,YU1), in_between(-X,X,YL1,YU1,NYL,NYU), ( New == yes -> put(Y,NYL,NYU,[mymod2(X,Z)|YExp]) ; put(Y,NYL,NYU,YExp) ) ) ; Z < 0 -> ( X == Z -> no_overlap(X,-X,YL,YU,NYL,NYU), ( New == yes -> put(Y,NYL,NYU,[mymod2(X,Z)|YExp]) ; put(Y,NYL,NYU,YExp) ) ; % Z < X no_overlap(Z,-Z,YL,YU,YL1,YU1), in_between(X,-X,YL1,YU1,NYL,NYU), ( New == yes -> put(Y,NYL,NYU,[mymod2(X,Z)|YExp]) ; put(Y,NYL,NYU,YExp) ) ) ; % Z == 0 ( X == 0 -> no_overlap(0,0,YL,YU,NYL,NYU),% Y \== 0 ( New == yes -> put(Y,NYL,NYU,[mymod2(X,Z)|YExp]) ; put(Y,NYL,NYU,YExp) ) ; % X \== 0 PX is abs(X), in_between(-PX,PX,YL,YU,NYL,NYU),% |Y| < |X| ( New == yes -> put(Y,NYL,NYU,[mymod2(X,Z)|YExp]) ; put(Y,NYL,NYU,YExp) ) ) ) ; % var(Y), var(Z) ( New == yes -> get(Y,YL,YU,YExp), get(Z,ZL,ZU,ZExp), put(Y,YL,YU,[mymod2(X,Z)|YExp]), put(Z,ZL,ZU,[mymod3(X,Y)|ZExp]) ; true ) ) ; nonvar(Y) -> Y \== 0, ( nonvar(Z) -> get(X,XL,XU,XExp), ( Z > 0 -> NXL is max(XL,1), ( New == yes -> put(X,NXL,XU,[mymod1(Y,Z)|XExp]) ; put(X,NXL,XU,XExp) ) ; Z < 0 -> NXU is min(XU,-1), ( New == yes -> put(X,XL,NXU,[mymod1(Y,Z)|XExp]) ; put(X,XL,NXU,XExp) ) ; ( New == yes -> put(X,XL,XU,[mymod1(Y,Z)|XExp]) ; put(X,XL,XU,XExp) ) ) ; ( New == yes -> get(X,XL,XU,XExp), get(Z,ZL,ZU,ZExp), put(X,XL,XU,[mymod1(Y,Z)|XExp]), put(Z,ZL,ZU,[mymod3(X,Y)|ZExp]) ; true ) ) ; nonvar(Z) -> ( New == yes -> get(X,XL,XU,XExp), get(Y,YL,YU,YExp), put(X,XL,XU,[mymod1(Y,Z)|XExp]), put(Y,YL,YU,[mymod2(X,Z)|YExp]) ; true ) ; ( New == yes -> get(X,XL,XU,XExp), get(Y,YL,YU,YExp), get(Z,ZL,ZU,ZExp), put(X,XL,XU,[mymod1(Y,Z)|XExp]), put(Y,YL,YU,[mymod2(X,Z)|YExp]), put(Z,ZL,ZU,[mymod3(X,Y)|ZExp]) ; true ) ). no_overlap(XL,XU,YL,YU,NYL,NYU) :- ( XL =< YL -> NYL is XU + 1, NYU = YU ; YU =< XU -> NYU is XL - 1, NYL is YL ; NYL = YL, NYU = YU ). in_between(XL,XU,YL,YU,NYL,NYU) :- ( XL >= YL -> NYL is XL + 1 ; NYL = YL ), ( XU =< YU -> NYU is XU -1 ; NYU = YU ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % TODO % trigger reified constraints when geq is added reified_geq(X,Y,B) :- ( var(B) -> ( nonvar(X) -> ( nonvar(Y) -> ( X >= Y -> B = 1 ; B = 0 ) ; get(Y,L,U,Expr), ( X >= U -> B = 1 ; X < L -> B = 0 ; put(Y,L,U,[reified_leq(X,B)|Expr]), get(B,BL,BU,BExpr), put(B,BL,BU,[reified_geq2(X,Y)|BExpr]), B in 0..1 ) ) ; nonvar(Y) -> get(X,L,U,Expr), ( L >= Y -> B = 1 ; U < Y -> B = 0 ; put(X,L,U,[reified_geq(Y,B)|Expr]), get(B,BL,BU,BExpr), put(B,BL,BU,[reified_geq2(X,Y)|BExpr]), B in 0..1 ) ; get(X,XL,XU,XExpr), get(Y,YL,YU,YExpr), ( XL >= YU -> B = 1 ; XU < YL -> B = 0 ; member(geq(Z,_State),XExpr), Z == Y -> B = 1 ; put(X,XL,XU,[reified_geq(Y,B)|XExpr]), put(Y,YL,YU,[reified_leq(X,B)|YExpr]), get(B,BL,BU,BExpr), put(B,BL,BU,[reified_geq2(X,Y)|BExpr]), B in 0..1 ) ) ; B == 1 -> X #>= Y ; B == 0 -> X #< Y ). check_leq(X,Y) :- ( nonvar(X) -> ( nonvar(Y) -> X =< Y ; bounds(Y,L,_), X =< L ) ; ( nonvar(Y) -> bounds(X,_,U), U =< Y ; bounds(X,_,UX), bounds(Y,LY,_), UX =< LY ) ). check_lt(X,Y) :- ( nonvar(X) -> ( nonvar(Y) -> X < Y ; bounds(Y,L,_), X < L ) ; ( nonvar(Y) -> bounds(X,_,U), U < Y ; bounds(X,_,UX), bounds(Y,LY,_), UX < LY ) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% reified_eq(X,Y,B) :- ( var(B) -> ( nonvar(X) -> ( nonvar(Y) -> ( X == Y -> B = 1 ; B = 0 ) ; get(Y,L,U,Expr), ( L > X -> B = 0 ; U < X -> B = 0 ; put(Y,L,U,[reified_eq(X,B)|Expr]), get(B,BL,BU,BExpr), put(B,BL,BU,[reified_eq2(X,Y)|BExpr]), B in 0..1 ) ) ; nonvar(Y) -> reified_eq(Y,X,B) ; X == Y -> B = 1 ; get(X,XL,XU,XExpr), get(Y,YL,YU,YExpr), ( XL > YU -> B = 0 ; YL > XU -> B = 0 ; member(neq(Z,_),XExpr), Z == Y -> B = 0 ; put(X,XL,XU,[reified_eq(Y,B)|XExpr]), put(Y,YL,YU,[reified_eq(X,B)|YExpr]), get(B,BL,BU,BExpr), put(B,BL,BU,[reified_eq2(X,Y)|BExpr]), B in 0..1 ) ) ; B == 1 -> X #= Y ; B == 0 -> X #\= Y ). check_eq(X,Y) :- X == Y. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% reified_neq(X,Y,B) :- mynot(B,B1), reified_eq(X,Y,B1). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% mynot(B1,B2) :- ( nonvar(B1) -> ( B1 == 1 -> B2 = 0 ; B1 == 0 -> B2 = 1 ) ; nonvar(B2) -> mynot(B2,B1) ; get(B1,L1,U1,Expr1), get(B2,L2,U2,Expr2), put(B2,L2,U2,[mynot(B1)|Expr2]), put(B1,L1,U1,[mynot(B2)|Expr1]), B1 in 0..1, B2 in 0..1 ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% myimpl(B1,B2) :- ( nonvar(B1) -> ( B1 == 1 -> B2 = 1 ; B1 == 0 -> B2 in 0..1 ) ; nonvar(B2) -> ( B2 == 0 -> B1 = 0 ; B2 == 1 -> B1 in 0..1 ) ; get(B1,L1,U1,Expr1), get(B2,L2,U2,Expr2), put(B1,L1,U1,[myimpl(B2)|Expr1]), put(B2,L2,U2,[myimpl2(B1)|Expr2]), B1 in 0..1, B2 in 0..1 ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% myand(X,Y,Z) :- ( nonvar(X) -> ( X == 1 -> Y in 0..1, Y = Z ; X == 0 -> Y in 0..1, Z = 0 ) ; nonvar(Y) -> myand(Y,X,Z) ; nonvar(Z) -> ( Z == 1 -> X = 1, Y = 1 ; Z == 0 -> X in 0..1, Y in 0..1, X + Y #=< 1 ) ; get(X,LX,UX,ExpX), get(Y,LY,UY,ExpY), get(Z,LZ,UZ,ExpZ), put(X,LX,UX,[myand(Y,Z)|ExpX]), put(Y,LY,UY,[myand(X,Z)|ExpY]), put(Z,LZ,UZ,[myand2(X,Y)|ExpZ]), [X,Y,Z] in 0..1 ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% myor(X,Y,Z) :- ( nonvar(X) -> ( X == 0 -> Y in 0..1, Y = Z ; X == 1 -> Y in 0..1, Z = 1 ) ; nonvar(Y) -> myor(Y,X,Z) ; nonvar(Z) -> ( Z == 0 -> X = 0, Y = 0 ; Z == 1 -> X in 0..1, Y in 0..1, X + Y #>= 1 ) ; get(X,LX,UX,ExpX), get(Y,LY,UY,ExpY), get(Z,LZ,UZ,ExpZ), put(X,LX,UX,[myor(Y,Z)|ExpX]), put(Y,LY,UY,[myor(X,Z)|ExpY]), put(Z,LZ,UZ,[myor2(X,Y)|ExpZ]), [X,Y,Z] in 0..1 ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% myxor(X,Y,Z) :- ( nonvar(X) -> ( X == 0 -> Y in 0..1, Y = Z ; X == 1 -> mynot(Y,Z) ) ; nonvar(Y) -> myxor(Y,X,Z) ; nonvar(Z) -> ( Z == 0 -> X = Y, [X,Y] in 0..1 ; Z == 1 -> X in 0..1, Y in 0..1, X + Y #= 1 ) ; get(X,LX,UX,ExpX), get(Y,LY,UY,ExpY), get(Z,LZ,UZ,ExpZ), put(X,LX,UX,[myxor(Y,Z)|ExpX]), put(Y,LY,UY,[myxor(X,Z)|ExpY]), put(Z,LZ,UZ,[myxor2(X,Y)|ExpZ]), [X,Y,Z] in 0..1 ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% get(X,L,U,Exp) :- ( get_attr(X,bounds,Attr) -> Attr = bounds(L,U,Exp) ; var(X) -> min_inf(L), max_inf(U), Exp = [] ). put(X,L,U,Exp) :- L =< U, ( L == U -> X = L, trigger_exps(Exp,X) ; ( get_attr(X,bounds,Attr) -> put_attr(X,bounds,bounds(L,U,Exp)), Attr = bounds(OldL,OldU,_), ( OldL == L, OldU == U -> true ; %format('\t~w in ~w .. ~w\n',[X,L,U]), trigger_exps(Exp,X), notify(X,bounds) ) ; %format('\t~w in ~w .. ~w\n',[X,L,U]), put_attr(X,bounds,bounds(L,U,Exp)), notify(X,bounds) ) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % SWI-Prolog 5.7.x has unbounded arithmetic. What to do? min_inf(Inf) :- ( current_prolog_flag(min_integer,MInf) -> Inf is MInf + 1 ; Inf = -9223372036854775807 ). max_inf(Inf) :- ( current_prolog_flag(max_integer,Inf) -> true ; Inf = 9223372036854775807 ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% attr_unify_hook(bounds(L,U,Exp),Other) :- ( get(Other,OL,OU,OExp) -> NL is max(L,OL), NU is min(U,OU), append(Exp,OExp,NExp), check_neqs(NExp,Other), put(Other,NL,NU,NExp) ; % nonvar(Other) -> Other >= L, Other =< U, trigger_exps(Exp,Other) ). check_neqs([],_). check_neqs([E|Es],X) :- ( E = neq(Y,_), X == Y -> fail ; check_neqs(Es,X) ). trigger_exps([],_). trigger_exps([E|Es],X) :- trigger_exp(E,X), trigger_exps(Es,X). trigger_exp(geq(Y,State),X) :- ( is_active(State) -> geq(X,Y,no) ; true ). trigger_exp(leq(Y,State),X) :- ( is_active(State) -> leq(X,Y,no) ; true ). trigger_exp(neq(Y,State),X) :- ( is_active(State) -> neq(X,Y,no) ; true ). trigger_exp(myplus(Y,Z),X) :- myplus(X,Y,Z,no). trigger_exp(myplus2(A,B),X) :- myplus(A,B,X,no). trigger_exp(mytimes(Y,Z),X) :- mytimes(X,Y,Z,no). trigger_exp(mytimes2(A,B),X) :- mytimes(A,B,X,no). trigger_exp(mymax(Y,Z),X) :- mymax(X,Y,Z,no). trigger_exp(mymax2(X,Y),Z) :- mymax(X,Y,Z,no). trigger_exp(mymin(Y,Z),X) :- mymin(X,Y,Z,no). trigger_exp(mymin2(X,Y),Z) :- mymin(X,Y,Z,no). trigger_exp(reified_leq(X,B),Y) :- reified_geq(X,Y,B). trigger_exp(reified_geq(Y,B),X) :- reified_geq(X,Y,B). trigger_exp(reified_geq2(X,Y),B) :- reified_geq(X,Y,B). trigger_exp(reified_eq(Y,B),X) :- reified_eq(X,Y,B). trigger_exp(reified_eq2(X,Y),B) :- reified_eq(X,Y,B). trigger_exp(mynot(Y),X) :- mynot(X,Y). trigger_exp(myimpl(Y),X) :- myimpl(X,Y). trigger_exp(myimpl2(X),Y) :- myimpl(X,Y). trigger_exp(myand(Y,Z),X) :- myand(X,Y,Z). trigger_exp(myand2(X,Y),Z) :- myand(X,Y,Z). trigger_exp(myor(Y,Z),X) :- myor(X,Y,Z). trigger_exp(myor2(X,Y),Z) :- myor(X,Y,Z). trigger_exp(myxor(Y,Z),X) :- myxor(X,Y,Z). trigger_exp(myxor2(X,Y),Z) :- myxor(X,Y,Z). trigger_exp(myabs(Y),X) :- myabs(X,Y,no). trigger_exp(myabs2(X),Y) :- myabs(X,Y,no). trigger_exp(mymod1(Y,Z),X) :- mymod(X,Y,Z,no). trigger_exp(mymod2(X,Z),Y) :- mymod(X,Y,Z,no). trigger_exp(mymod3(X,Y),Z) :- mymod(X,Y,Z,no). trigger_exp(mydiv(Y,Z),X) :- mydiv(X,Y,Z,no). trigger_exp(mydiv2(A,B),X) :- mydiv(A,B,X,no). trigger_exp(mydiv3(A,B),X) :- mydiv(A,X,B,no). trigger_exp(rel_tuple(Relation,Tuple), _) :- ( ground(Tuple) -> memberchk(Tuple, Relation) ; relation_unifiable(Relation, Tuple, Us), Us \= [], ( Us = [Single] -> Single = Tuple ; ( Us == Relation -> true ; tuple_domain(Tuple, Us) ) ) ). trigger_exp(serialized(Duration,Left,Right), X) :- myserialized(Duration, Left, Right, X). memberchk_eq(X,[Y|Ys],Z) :- ( X == Y -> Z = Y ; memberchk_eq(X,Ys,Z) ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% tuples_in(Tuples, Relation) :- ground(Relation), bind_unique(Tuples, Relation), approx_tuples_domain(Tuples, Relation), tuples_freeze(Tuples, Relation). bind_unique([], _). bind_unique([Tuple|Ts], Relation) :- relation_unifiable(Relation, Tuple, Us), Us \= [], ( Us = [Single] -> Single = Tuple ; true ), bind_unique(Ts, Relation). % The following predicates find component-wise extrema in the relation. relation_mins_maxs(Relation, Mins, Maxs) :- Relation = [R|_], relation_mins_maxs(Relation, R, Mins, R, Maxs). relation_mins_maxs([], Mins, Mins, Maxs, Maxs). relation_mins_maxs([R|Rs], Mins0, Mins, Maxs0, Maxs) :- components_mins_maxs(R, Mins0, Mins1, Maxs0, Maxs1), relation_mins_maxs(Rs, Mins1, Mins, Maxs1, Maxs). components_mins_maxs([], [], [], [], []). components_mins_maxs([C|Cs], [Min0|Mins0], [Min|Mins], [Max0|Maxs0], [Max|Maxs]) :- Min is min(Min0, C), Max is max(Max0, C), components_mins_maxs(Cs, Mins0, Mins, Maxs0, Maxs). % Approximate the domains of each tuple variable for all tuples. % Heuristics: Take component-wise mins/maxs of the relation. approx_tuples_domain(Tuples, Relation) :- relation_mins_maxs(Relation, Mins, Maxs), constrain_domains(Tuples, Mins, Maxs). constrain_domains([], _, _). constrain_domains([Tuple|Tuples], Mins, Maxs) :- constrain_domain(Tuple, Mins, Maxs), constrain_domains(Tuples, Mins, Maxs). constrain_domain([], [], []). constrain_domain([T|Ts], [Min|Mins], [Max|Maxs]) :- T in Min..Max, constrain_domain(Ts, Mins, Maxs). tuple_domain(Tuple, Relation) :- relation_mins_maxs(Relation, Mins, Maxs), constrain_domain(Tuple, Mins, Maxs). % Set up the attributes for each tuple variable. % Attributes are rel_tuple(Rel, Tuple) terms: % Rel: the relation of which Tuple must be an element % Tuple: the tuple to which this variable belongs % Note that the variable is itself part of the Tuple of its attribute. tuple_freeze([], _, _). tuple_freeze([T|Ts], Tuple, Relation) :- ( var(T) -> get(T, L, U, Exp), put(T, L, U, [rel_tuple(Relation,Tuple)|Exp]) ; true ), tuple_freeze(Ts, Tuple, Relation). tuples_freeze([], _). tuples_freeze([Tuple|Tuples], Relation) :- tuple_freeze(Tuple, Tuple, Relation), tuples_freeze(Tuples, Relation). % Find all tuples in the relation that can unify with Tuple, not % taking into account attributes (like constraints), as that would % trigger attr_unify_hook recursively. relation_unifiable([], _, []). relation_unifiable([R|Rs], Tuple, Us) :- ( unifiable(R, Tuple, _) -> Us = [R|Rest] ; Rest = Us ), relation_unifiable(Rs, Tuple, Rest). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % serialized/2; see Dorndorf et al. 2000, "Constraint Propagation % Techniques for the Disjunctive Scheduling Problem" % attribute: serialized(Duration, Left, Right) % Left and Right are lists of Start-Duration pairs representing % other tasks occupying the same resource % Currently implements 2-b-consistency serialized(Starts, Durations) :- pair_up(Starts, Durations, SDs), serialize(SDs, []). pair_up([], [], []). pair_up([A|As], [B|Bs], [A-B|ABs]) :- pair_up(As, Bs, ABs). % store attributes for serialized/2 constraint serialize([], _). serialize([Start-Duration|SDs], Left) :- ( var(Start) -> get(Start, L, U, Exp), put(Start, L, U, [serialized(Duration,Left,SDs)|Exp]) ; true ), myserialized(Duration, Left, SDs, Start), serialize(SDs, [Start-Duration|Left]). % consistency check / propagation myserialized(Duration, Left, Right, Start) :- myserialized(Left, Start, Duration), myserialized(Right, Start, Duration). earliest_start_time(Start, EST) :- ( var(Start) -> get(Start, EST, _, _) ; EST = Start ). latest_start_time(Start, LST) :- ( var(Start) -> get(Start, _, LST, _) ; LST = Start ). myserialized([], _, _). myserialized([S_I-D_I|SDs], S_J, D_J) :- ( var(S_I) -> serialize_lower_bound(S_I, D_I, Start, D_J), ( var(S_I) -> % STILL variable? serialize_upper_bound(S_I, D_I, Start, D_J) ; true ) ; var(S_J) -> serialize_lower_bound(S_J, D_J, S, D_I), ( var(S_J) -> serialize_upper_bound(S_J, D_J, S, D_I) ; true ) ; ( S_I + D_I =< S_J -> true ; S_J + D_J =< S_I -> true ; fail ) ), myserialized(SDs, S_J, D_J). serialize_lower_bound(I, D_I, J, D_J) :- get(I, EST_I, U, Exp), latest_start_time(J, LST_J), ( EST_I + D_I > LST_J -> earliest_start_time(J, EST_J), EST is max(EST_I, EST_J+D_J), put(I, EST, U, Exp) ; true ). serialize_upper_bound(I, D_I, J, D_J) :- get(I, L, LST_I, Exp), earliest_start_time(J, EST_J), ( EST_J + D_J > LST_I -> latest_start_time(J, LST_J), LST is min(LST_I, LST_J-D_I), put(I, L, LST, Exp) ; true ). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% active_state(state(active)). is_active(state(active)). set_passive(State) :- setarg(1,State,passive). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% attr_portray_hook(bounds(L,U,_),_) :- write(L..U).