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yap-6.3/library/gecode/clpfd.yap
Vítor Santos Costa efddaab558 sudoku and for
2013-09-21 23:23:42 +01:00

842 lines
22 KiB
Prolog

:- module(clpfd, [
op(100, yf, []),
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(700, xfx, ins),
op(450, xfx, ..), % should bind more tightly than \/
(#>)/2,
(#<)/2,
(#>=)/2,
(#=<)/2,
(#=)/2,
(#\=)/2,
(#<==>)/2,
(#==>)/2,
(#<==)/2,
(#\)/1,
(#\/)/2,
(#/\)/2,
in/2 ,
ins/2,
all_different/1,
all_distinct/1,
all_distinct/2,
maximize/1,
sum/3,
lex_chain/1,
minimum/2,
min/2,
maximum/2,
max/2,
scalar_product/4,
extensional_constraint/2,
in_relation/2,
dfa/4,
in_dfa/2,
in_dfa/4, /*
tuples_in/2, */
labeling/2 /*,
label/1,
indomain/1,
serialized/2,
global_cardinality/2,
global_cardinality/3,
circuit/1,
element/3,
automaton/3,
automaton/8,
transpose/2,
zcompare/3,
chain/2,
fd_var/1,
fd_inf/2,
fd_sup/2,
fd_size/2,
fd_dom/2 */
]).
:- use_module(library(gecode)).
:- use_module(library(maplist)).
:- reexport(library(matrix), [(<==)/2, for/2, for/4]).
constraint( (_ #> _) ).
constraint( (_ #< _) ).
constraint( (_ #>= _) ).
constraint( (_ #=< _) ).
constraint( (_ #= _) ).
constraint( (_ #\= _) ).
constraint( (_ #\ _) ).
constraint( (_ #<==> _) ).
constraint( (_ #==> _) ).
constraint( (_ #<== _) ).
constraint( (_ #\/ _) ).
constraint( (_ #/\ _) ).
constraint( in(_, _) ). %2,
constraint( ins(_, _) ). %2,
constraint( all_different(_) ). %1,
constraint( all_distinct(_) ). %1,
constraint( all_distinct(_,_) ). %1,
constraint( sum(_, _, _) ). %3,
constraint( scalar_product(_, _, _, _) ). %4,
constraint( min(_, _) ). %2,
constraint( minimum(_, _) ). %2,
constraint( max(_, _) ). %2,
constraint( maximum(_, _) ). %2,
constraint( in_relation(_, _) ). %2,
constraint( in_dfa(_, _) ). %2,
constraint( in_dfa(_, _, _, _) ). %2,
constraint( tuples_in(_, _) ). %2,
constraint( labeling(_, _) ). %2,
constraint( label(_) ). %1,
constraint( indomain(_) ). %1,
constraint( lex_chain(_) ). %1,
constraint( serialized(_, _) ). %2,
constraint( global_cardinality(_, _) ). %2,
constraint( global_cardinality(_, _, _) ). %3,
constraint( circuit(_) ). %1,
constraint( element(_, _, _) ). %3,
constraint( automaton(_, _, _) ). %3,
constraint( automaton(_, _, _, _, _, _, _, _) ). %8,
constraint( transpose(_, _) ). %2,
constraint( zcompare(_, _, _) ). %3,
constraint( chain(_, _) ). %2,
constraint( fd_var(_) ). %1,
constraint( fd_inf(_, _) ). %2,
constraint( fd_sup(_, _) ). %2,
constraint( fd_size(_, _) ). %2,
constraint( fd_dom(_, _) ). %2
process_constraints((B0,B1), (NB0, NB1), Env) :-
process_constraints(B0, NB0, Env),
process_constraints(B1, NB1, Env).
process_constraints(B, B, env(_Space)) :-
constraint(B), !.
process_constraints(B, B, _Env).
% process_constraint(B, NB, Space).
( A #= B) :-
get_home(Env),
check(A, NA),
check(B, NB),
post( rel(NA, (#=), NB), Env, _).
( A #\= B) :-
get_home(Env),
check(A, NA),
check(B, NB),
post( rel(NA, (#\=), NB), Env, _).
( A #< B) :-
get_home(Env),
check(A, NA),
check(B, NB),
post( rel(NA, (#<), NB), Env, _).
( A #> B) :-
get_home(Env),
check(A, NA),
check(B, NB),
post( rel(NA, (#>), NB), Env, _).
( A #=< B) :-
get_home(Env),
check(A, NA),
check(B, NB),
post( rel(NA, (#=<), NB), Env, _).
( A #>= B) :-
get_home(Env),
check(A, NA),
check(B, NB),
post( rel(NA, (#>=), NB), Env, _).
sum( L, Op, V) :-
get_home( Env ),
check(L, NL),
check(V, NV),
post( rel(sum(NL), Op, NV), Env, _).
( A #<==> VBool) :-
get_home(Space-Map),
check(A, NA),
check(VBool, NVBool),
Bool := boolvar(Space),
m( NVBool, Bool, 0, 1, Map),
Space += reify(Bool, 'RM_EQV', R),
post(NA, Space-Map, R).
( A #==> VBool) :-
get_home(Space-Map),
check(A, NA),
check(VBool, NVBool),
Bool := boolvar(Space),
m( NVBool, Bool, 0, 1, Map),
Space += reify(Bool, 'RM_IMP', R),
post(NA, Space-Map, R).
( A #<== VBool) :-
get_home(Space-Map),
check(A, NA),
check(VBool, NVBool),
Bool := boolvar(Space),
m( NVBool, Bool, 0, 1, Map),
Space += reify(Bool, 'RM_PMI', R),
post(NA, Space-Map, R).
'#\\'(A) :-
get_home(Space-Map),
check(A, NA),
B := boolvar(Space),
Space += reify(B, 'RM_EQV', R),
Space += rel(B, 'BOT_EQV', 0),
post(NA, Space-Map, R).
( A1 #\/ A2 ) :-
get_home(Space-Map),
check(A1, NA1),
check(A2, NA2),
B1 := boolvar(Space),
B2 := boolvar(Space),
Space += reify(B1, 'RM_EQV', R1),
Space += reify(B2, 'RM_EQV', R2),
post(NA1, Space-Map, R1),
post(NA2, Space-Map, R2),
Space += rel(B1, B2, 'BOT_OR', 1).
( A1 #/\ A2 ) :-
get_home(Space-Map),
check(A1, NA1),
check(A2, NA2),
B1 := boolvar(Space),
B2 := boolvar(Space),
Space += reify(B1, 'RM_EQV', R1),
Space += reify(B2, 'RM_EQV', R2),
post(NA1, Space-Map, R1),
post(NA2, Space-Map, R2),
Space += rel(B1, B2, 'BOT_AND', 1).
( X in A..B) :-
get_home(Space-Map),
check(A, NA),
check(B, NB),
m(X, NX, NA, NB, Map),
NX := intvar(Space, NA, NB).
( Xs ins A..B) :-
get_home(Space-Map),
check(A, NA),
check(B, NB),
maplist(lm(NA, NB, Map), Xs, NXs),
length(Xs, N),
NXs := intvars(Space, N, NA, NB).
all_different( Xs ) :-
get_home(Env),
check(Xs, NXs),
post( all_different( NXs ), Env, _ ).
all_distinct( Xs ) :-
get_home(Env),
check(Xs, NXs),
post( all_distinct( NXs ), Env, _ ).
all_distinct( Cs, Xs ) :-
get_home(Env),
check(Xs, NXs),
post( all_distinct( Cs, NXs ), Env, _ ).
scalar_product( Cs, Vs, Rels, X ) :-
get_home(Env),
check(Vs, NVs),
post( scalar_product( Cs, NVs, Rels, X ), Env, _ ).
lex_chain( Cs ) :-
get_home(Env),
check(Cs, NCs),
post( rel( NCs, '#=<' ), Env, _ ).
minimum( V, Xs ) :-
get_home(Env),
check(Xs, NXs),
check(V, NV),
post( rel( min(NXs), (#=), NV ), Env, _ ).
min( Xs, V ) :-
get_home(Env),
check(Xs, NXs),
check(V, NV),
post( rel( min(NXs), (#=), NV ), Env, _ ).
maximum( V, Xs ) :-
get_home(Env),
check(Xs, NXs),
check(V, NV),
post( rel( max(NXs), (#=), NV ), Env, _ ).
max( Xs, V ) :-
get_home(Env),
check(Xs, NXs),
check(V, NV),
post( rel( max(NXs), (#=), NV ), Env, _ ).
in_relation( Xs, Rel ) :-
get_home(Env),
check(Xs, NXs),
post(in_tupleset(NXs, Rel), Env, _ ).
in_dfa( Xs, Rel ) :-
get_home(Env),
check(Xs, NXs),
post(in_dfa(NXs, Rel), Env, _ ).
in_dfa( Xs, S0, Ts, Fs ) :-
get_home(Env),
check(NXs, NXs),
post(in_dfa(Xs, S0, Ts, Fs), Env, _ ).
labeling(_Opts, Xs) :-
get_home(Space-Map),
maplist(ll(Map), Xs, NXs),
Space += branch(NXs, 'INT_VAR_SIZE_MIN', 'INT_VAL_MIN').
maximize(V) :-
get_home(Space-Map),
l(V, I, Map),
Space += maximize(I).
extensional_constraint( Tuples, TupleSet) :-
TupleSet := tupleset( Tuples ).
dfa( S0, Transitions, Finals, DFA) :-
DFA := dfa( S0, Transitions, Finals ).
check(V, NV) :-
( var(V) -> V = NV ;
number(V) -> V = NV ;
is_list(V) -> maplist(check, V, NV) ;
V = '[]'(Indx, Mat) -> NV <== '[]'(Indx, Mat) ;
arith(V, _) -> V =.. [C|L], maplist(check, L, NL), NV =.. [C|NL] ).
post( ( A #= B), Env, Reify) :-
post( rel( A, (#=), B), Env, Reify).
post( ( A #\= B), Env, Reify) :-
post( rel( A, (#\=), B), Env, Reify).
post( ( A #> B), Env, Reify) :-
post( rel( A, (#>), B), Env, Reify).
post( ( A #< B), Env, Reify) :-
post( rel( A, (#<), B), Env, Reify).
post( ( A #>= B), Env, Reify) :-
post( rel( A, (#>=), B), Env, Reify).
post( ( A #=< B), Env, Reify) :-
post( rel( A, (#=<), B), Env, Reify).
% X #< Y
% X #< 2
post( rel( A, Op, B), Space-Map, Reify):-
var(A),
( var(B) -> l(B, IB, Map) ; integer(B) -> IB = B ), !,
l(A, IA, Map),
gecode_arith_op( Op, GOP ),
(var(Reify) -> Space += rel(IA, GOP, IB) ;
Space += rel(IA, GOP, IB, Reify) ).
post( rel( A, Op), Space-Map, Reify):-
( var( A ) -> l(A, IA, Map) ; checklist( var, A ) -> maplist(ll(Map), A, IA ) ),
gecode_arith_op( Op, GOP ),
(var(Reify) -> Space += rel(IA, GOP) ;
Space += rel(IA, GOP, Reify) ).
% 2 #\= B
post( rel( A, Op, B), Space-Map, Reify):-
var(B), integer(A), !,
l(B, IB, Map),
gecode_arith_op( Op, GOP ),
(var(Reify) -> Space += rel(A, GOP, IB) ;
Space += rel(A, GOP, IB, Reify) ).
% sum([A,B,C]) #= X
post( rel( sum(L), Op, Out), Space-Map, Reify):-
checklist( var, L ),
( var(Out) -> l(Out, IOut, Map) ; integer(Out) -> IOut = Out ), !,
var(Out), !,
maplist(ll(Map), [Out|L], [IOut|IL] ),
gecode_arith_op( Op, GOP ),
(var(Reify) ->
Space += linear(IL, GOP, IOut);
Space += linear(IL, GOP, IOut, Reify)
).
% [A,B,C,D] #< 3
post( rel( A, Op, B ), Space-Map, Reify):-
checklist( var, A ), !,
( var(B) -> l(B, IB, Map) ; integer(B) -> IB = B ), !,
maplist(ll(Map), A, IL ),
gecode_arith_op( Op, GOP ),
(var(Reify) -> Space += rel(IL, GOP) ;
Space += rel(IL, GOP, IB) ).
post( rel( A, Op, B), Space-Map, Reify):-
var( A ), !,
( var(B) -> l(B, IB, Map) ; integer(B) -> IB = B ),
l(A, IA, Map),
gecode_arith_op( Op, GOP ),
(var(Reify) -> Space += rel(IA, GOP, IB) ;
Space += rel(IA, GOP, IB, Reify) ).
post( rel( A, Op, B), Space-Map, Reify):-
checklist( var, A ),
( var(B) -> l(B, IB, Map) ; integer(B) -> IB = B ), !,
maplist(ll(Map), A, IL ),
gecode_arith_op( Op, GOP ),
(var(Reify) -> Space += rel(IL, GOP, IB) ;
Space += rel(IL, GOP, IB, Reify) ).
post( rel(A, Op, B), Space-Map, Reify):-
( nonvar(A), ( A = _+_ ; A = _-_ ) ;
nonvar(B), ( B = _ + _ ; B = _-_) ), !,
linearize(A, 1, As, Bs, CAs, CBs, 0, A0, Space-Map),
linearize(B, -1, Bs, [], CBs, [], A0, B0, Space-Map),
gecode_arith_op( Op, GOP ),
(var(Reify) ->
( checklist(is_one, CAs) ->
Space += linear(As, GOP, B0);
Space += linear(CAs, As, GOP, B0)
)
;
( checklist(is_one, CAs) ->
Space += linear(As, GOP, B0, Reify);
Space += linear(CAs, As, GOP, B0, Reify)
)
).
post( rel(A, Op, B), Space-Map, Reify):-
nonvar(A),
arith(A, Name),
A =.. [_Op,A1],
is_list(A1), !,
( _Op = min -> true ; _Op = max ),
maplist(equality_l( Space-Map), A1, NA1),
maplist(in_c_l( Space-Map), NA1, VA1),
equality(B, B1, Space-Map),
out_c(Name, VA1, B1, Op, Space-Map, Reify).
post( rel(A, Op, B), Space-Map, Reify):-
nonvar(A),
arith(A, Name),
A =.. [_Op,A1], !,
equality(A1, NA1, Space-Map),
in_c(NA1, VA1, Space-Map), !,
equality(B, B1, Space-Map),
out_c(Name, VA1, B1, Op, Space-Map, Reify).
post( rel(A, Op, B), Space-Map, Reify):-
nonvar(A),
arith(A, Name),
A =.. [_Op,A1,A2], !,
equality(A1, NA1, Space-Map),
in_c(NA1, VA1, Space-Map),
equality(A2, NA2, Space-Map),
in_c(NA2, VA2, Space-Map),
equality(B, B1, Space-Map),
out_c(Name, VA1, VA2, B1, Op, Space-Map, Reify).
post( scalar_product(Cs, L, Op, Out), Space-Map, Reify):-
var(Out), !,
maplist(ll(Map), [Out|L], [IOut|IL] ),
gecode_arith_op( Op, GOP ),
(var(Reify) ->
Space += linear(Cs, IL, GOP, IOut);
Space += linear(Cs, IL, GOP, IOut, Reify)
).
post( scalar_product(Cs, L, Op, Out), Space-Map, Reify):-
integer(Out), !,
maplist(ll(Map), L, IL ),
gecode_arith_op( Op, GOP ),
(var(Reify) ->
Space += linear(Cs, IL, GOP, Out);
Space += linear(Cs, IL, GOP, Out, Reify)
).
post( all_different( Xs ), Space-Map, Reify) :-
maplist(ll(Map), Xs, NXs),
(var(Reify) ->
Space += distinct(NXs)
;
throw(error(domain(not_reifiable),all_different( Xs )))
).
post( all_distinct( Xs ), Space-Map, Reify) :-
maplist(ll(Map), Xs, NXs),
(var(Reify) ->
Space += distinct(NXs)
;
throw(error(domain(not_reifiable),all_distinct( Xs )))
).
post( all_distinct( Cs , Xs ), Space-Map, Reify) :-
maplist(ll(Map), Xs, NXs),
(var(Reify) ->
Space += distinct(Cs,NXs)
;
throw(error(domain(not_reifiable),all_distinct( Cs , Xs )))
).
post(in_tupleset(Xs, Tuples), Space-Map, Reify) :-
is_list( Tuples ), !,
TS := tupleset( Tuples ),
maplist(ll(Map), Xs, IXs),
(var(Reify) ->
Space += extensional(IXs, TS)
;
throw(error(domain(not_reifiable),in_relation(Xs, Tuples)))
).
post(in_tupleset(Xs, TS), Space-Map, Reify) :-
maplist(ll(Map), Xs, IXs),
(var(Reify) ->
Space += extensional(IXs, TS)
;
throw(error(domain(not_reifiable),in_relation(Xs, TS)))
).
post(in_dfa(Xs, S0, Trs, Fs), Space-Map, Reify) :-
TS := dfa( S0, Trs, Fs ),
maplist(ll(Map), Xs, IXs),
(var(Reify) ->
Space += extensional(IXs, TS)
;
throw(error(domain(not_reifiable),in_dfa(Xs, S0, Trs, Fs)))
).
post(in_dfa(Xs, TS), Space-Map, Reify) :-
maplist(ll(Map), Xs, IXs),
(var(Reify) ->
Space += extensional(IXs, TS)
;
throw(error(domain(not_reifiable),in_dfa(Xs, TS)))
).
gecode_arith_op( (#=) , 'IRT_EQ' ).
gecode_arith_op( (#\=) , 'IRT_NQ' ).
gecode_arith_op( (#>) , 'IRT_GR' ).
gecode_arith_op( (#>=) , 'IRT_GQ' ).
gecode_arith_op( (#<) , 'IRT_LE' ).
gecode_arith_op( (#=<) , 'IRT_LQ' ).
linearize(V, C, [A|As], As, [C|CAs], CAs, I, I, _-Map) :-
var(V), !,
l(V, A, Map).
linearize(A+B, C, As, Bs, CAs, CBs, I, IF, Env) :-
linearize(A, C, As, A1s, CAs, CA1s, I, I1, Env),
linearize(B, C, A1s, Bs, CA1s, CBs, I1, IF, Env).
linearize(A-B, C, As, Bs, CAs, CBs, I, IF, Env) :-
NC is -C,
linearize(A, C, As, A1s, CAs, CA1s, I, I1, Env),
linearize(B, NC, A1s, Bs, CA1s, CBs, I1, IF, Env).
linearize(A, C, As, As, CAs, CAs, I, IF, _) :-
integer(A), !,
IF is I-C*A.
linearize(A, C, As, As, CAs, CAs, I, IF, _) :-
ground(A),
catch( (B is eval(A)), _, fail ), !,
IF is I-C*B.
linearize(C1*B, C, As, Bs, CAs, CBs, I, IF, Env) :-
integer(C1), !,
NC is C*C1,
linearize(B, NC, As, Bs, CAs, CBs, I, IF, Env).
linearize(B*C1, C, As, Bs, CAs, CBs, I, IF, Env) :-
integer(C1), !,
NC is C*C1,
linearize(B, NC, As, Bs, CAs, CBs, I, IF, Env).
linearize(AC, C, [A|Bs], Bs, [C|CBs], CBs, I, I, Env) :-
arith(AC, _),
equality(AC, V, Env),
Env = _-Map,
l(V, A, Map).
arith(abs(_), abs).
arith(min(_), min).
arith(max(_), max).
arith(min(_,_), min).
arith(max(_,_), max).
arith((_ * _), times).
arith((_ / _), div).
arith((_ mod _), mod).
% replace abs(min(A,B)-max(A,B)) by
% min(A,B,A1), max(A,B,A2), linear([1,-1],[A1,B1],=,A3), abs(A3,AN)
equality(V, V, _Env) :-
var( V ), !.
equality(V, V, _Env) :-
integer( V ), !.
equality(abs(V), NV, Env) :-
equality(V, VA, Env),
new_arith(abs, VA, NV, Env).
equality(min(V), NV, Env) :-
maplist( equality_l(Env), V, VA ),
new_arith(min, VA, NV, Env).
equality(max(V), NV, Env) :-
maplist( equality_l(Env), V, VA ),
new_arith(max, VA, NV, Env).
equality(V1+V2, NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( plus, V1A, V2A, NV, Env).
equality(V1-V2, NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( minus, V1A, V2A, NV, Env).
equality(V1*V2, NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( times, V1A, V2A, NV, Env).
equality(V1/V2, NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( div, V1A, V2A, NV, Env).
equality(V1 mod V2, NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( (mod), V1A, V2A, NV, Env).
equality(max( V1 , V2), NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( (max), V1A, V2A, NV, Env).
equality(min( V1 , V2), NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( (min), V1A, V2A, NV, Env).
equality_l(Env, V0, V) :-
equality(V0, V, Env).
% abs(X) #= 3
out_c(Name, A1, B, Op, Space-Map, Reify) :-
integer(B), !,
new_arith( Name, A1, NB, Space-Map),
gecode_arith_op( Op, BOP ),
l(NB, IB, Map),
( var(Reify) ->
Space += rel(IB, BOP, B)
;
Space += rel(IB, BOP, B, Reify)
).
% abs(X) #= Cin[..]
out_c(Name, A1, B, (#=), Space-Map, Reify) :-
var(Reify),
l(B, IB, Map), !,
l(A1, IA1, Map),
G =.. [Name, IA1, IB],
Space += G.
% abs(X) #= NEW
out_c(Name, A1, B, (#=), Space-Map, Reify) :-
var(Reify), !,
new_arith( Name, A1, B, Space-Map).
% abs(X) #> NEW
out_c(Name, A1, B, Op, Space-Map, Reify) :-
l(B, IB0, Map), !,
new_arith( Name, A1, NB, Space-Map),
l(NB, IB, Map),
gecode_arith_op( Op, BOP ),
(
nonvar(Reify) ->
Space += rel(IB, BOP, IB0)
;
Space += rel(IB, BOP, IB0, Reify)
).
% X*Y #= 3
out_c(Name, A1, A2, B, Op, Space-Map, Reify) :-
integer(B), !,
new_arith( Name, A1, A2, NB, Space-Map),
l(NB, IB, Map),
gecode_arith_op( Op, BOP ),
( var(Reify) ->
Space += rel(IB, BOP, B)
;
Space += rel(IB, BOP, B, Reify)
).
% X*Y #= Cin[..]
out_c(Name, A1, A2, B, (#=), Space-Map, Reify) :-
var(Reify),
l(B, IB, Map), !,
l(A1, IA1, Map),
l(A2, IA2, Map),
G =.. [Name, IA1, IA2, IB],
Space += G.
% abs(X) #= NEW, cannot be reified
out_c(Name, A1, A2, B, (#=), Space-Map, Reify) :-
var(Reify), !,
new_arith( Name, A1, A2, B, Space-Map).
% min(X,Y) #= Cin[..] <=>
out_c(Name, A1, A2, B, Op, Space-Map, Reify) :-
l(B, IB0, Map), !,
new_arith( Name, A1, A2, NB, Space-Map),
l(NB, IB, Map),
gecode_arith_op( Op, BOP ),
( var(Reify) ->
Space += rel(IB, BOP, IB0)
;
Space += rel(IB, BOP, IB0, Reify)
).
new_arith( abs, V, NV, Space-Map) :-
l(V, X, Min0, Max0, Map),
( Min0 < 0 ->
( Max0 < 0 -> Min is -Max0, Max is -Min0 ;
Min = 0 , Max is max( -Min0, Max0 ) )
;
Min = Min0, Max = Max0
),
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
Space += abs(X, NX).
new_arith( min, V, NV, Space-Map) :-
V = [V1|RV],
l(V1, _X1, Min0, Max0, Map),
foldl2( min_l(Map), RV, Max0, Max, Min0, Min),
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
maplist(ll(Map), V, X),
Space += min(X, NX).
new_arith( max, V, NV, Space-Map) :-
V = [V1|RV],
l(V1, _X1, Min0, Max0, Map),
foldl2( max_l(Map), RV, Max0, Max, Min0, Min),
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
maplist(ll(Map), V, X),
Space += min(X, NX).
new_arith( minus, V1, V2, NV, Space-Map) :-
l(V1, X1, Min1, Max1, Map),
l(V2, X2, Min2, Max2, Map),
Min is Min1-Max2,
Max is Max1-Min2,
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
Space += linear([1,-1], [X1,X2], 'IRT_EQ', NX).
new_arith( plus, V1, V2, NV, Space-Map) :-
l(V1, X1, Min1, Max1, Map),
l(V2, X2, Min2, Max2, Map),
Min is Min1+Min2,
Max is Max1+Max2,
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
Space += linear([1,1], [X1,X2], 'IRT_EQ', NX).
new_arith( min, V1, V2, NV, Space-Map) :-
l(V1, X1, Min1, Max1, Map),
l(V2, X2, Min2, Max2, Map),
Min is min(Min1,Min2),
Max is min(Max1,Max2),
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
Space += min(X1, X2, NX).
new_arith( max, V1, V2, NV, Space-Map) :-
l(V1, X1, Min1, Max1, Map),
l(V2, X2, Min2, Max2, Map),
Min is max(Min1,Min2),
Max is max(Max1,Max2),
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
Space += max(X1, X2, NX).
new_arith( times, V1, V2, NV, Space-Map) :-
l(V1, X1, Min1, Max1, Map),
l(V2, X2, Min2, Max2, Map),
min_times(Min1,Min2,Max1,Max2,Min),
max_times(Min1,Min2,Max1,Max2,Max),
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
Space += times(X1, X2, NX).
new_arith( (div), V1, V2, NV, Space-Map) :-
l(V1, X1, Min1, Max1, Map),
l(V2, X2, Min2, Max2, Map),
min_div(Min1,Min2,Max1,Max2,Min),
max_div(Min1,Min2,Max1,Max2,Max),
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
Space += div(X1, X2, NX).
new_arith( (mod), V1, V2, NV, Space-Map) :-
l(V1, X1, _Min1, Max1, Map),
l(V2, X2, _Min2, Max2, Map),
Min is 0,
Max is min(abs(Max1), Max2-1),
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
Space += mod(X1, X2, NX).
min_times(Min1,Min2,Max1,Max2,Min) :-
Min is min(Min1*Min2, min(Min1*Max2, min(Max1*Min2, Max1*Max2))).
max_times(Min1,Min2,Max1,Max2,Max) :-
Max is max(Min1*Min2, max(Min1*Max2, max(Max1*Min2, Max1*Max2))).
min_div(Min1,Min20,Max1,Max20,Min) :-
( Min20 == 0 -> Min2 = 1 ; Min2 = Min20),
( Max20 == 0 -> Max2 = -1; Max2 = Max20),
Min is min(Min1 div Min2, min(Min1 div Max2, min(Max1 div Min2, Max1 div Max2))).
max_div(Min1,Min20,Max1,Max20,Max) :-
( Min20 == 0 -> Min2 = 1 ; Min2 = Min20),
( Max20 == 0 -> Max2 = -1; Max2 = Max20),
Max is max(Min1 div Min2, max(Min1 div Max2, max(Max1 div Min2, Max1 div Max2))).
min_l(Map, V, Min0, Min, Max0, Max) :-
l(V, _, Min1, Max1, Map),
Min is min(Min0, Min1),
Max is min(Max0, Max1).
max_l(Map, V, Min0, Min, Max0, Max) :-
l(V, _, Min1, Max1, Map),
Min is max(Min0, Min1),
Max is max(Max0, Max1).
in_c(A, A, _y) :-
var(A), !.
in_c(C, A, Space-Map) :-
integer(C),
Min is C-1,
NX := intvar(Space, Min, C),
m(A, NX, Min, C, Map),
Space += rel(NX, 'IRT_EQ', C).
in_c_l(Env, V, IV) :-
in_c(V, IV, Env).
user:term_expansion( ( H :- B), (H :- (clpfd:init_gecode(Space, Me), NB, clpfd:close_gecode(Space, Vs, Me)) ) ) :-
process_constraints(B, NB, Env),
term_variables(H, Vs),
nonvar( Env ), !,
Env = env( Space ).
init_gecode(Space, old) :-
nb_current(gecode_space, Space), nonvar(Space), !.
init_gecode(Space-Map, new) :-
Space := space,
b_setval(gecode_space, Space-Map).
close_gecode(_Space, _Vs, old) :- !.
close_gecode(Space-Map, Vs0, new) :-
term_variables(Vs0, Vs),
selectlist(intvar(Map), Vs, CVs),
maplist(ll(Map), CVs, IVs),
SolSpace := search(Space),
CVs := val(SolSpace,IVs).
intvar(Map, V) :-
l(V, _IV, Map).
get_home(Home) :-
b_getval(gecode_space, Home).
m(NV, OV, NA, NB, Vs) :-
var(Vs), !,
Vs = [v(NV,OV,NA,NB)|_].
m(NV, OV, NA, NB, [_|Vs]) :-
m(NV, OV, NA, NB, Vs).
lm(A, B, Map, X, Y) :-
m(X, Y, A, B, Map).
l(_NV, _OV, Vs) :-
var(Vs), !,
fail.
l(NV, OV, [v(V, OV, _A, _B)|_Vs]) :-
V == NV, !.
l(NV, OV, [_|Vs]) :-
l(NV, OV, Vs).
ll(Map, X, Y) :-
l(X, Y, Map).
l(_NV, _OV, _, _, Vs) :-
var(Vs), !,
fail.
l(NV, OV, A, B, [v(V, OV, A, B)|_Vs]) :-
V == NV, !.
l(NV, OV, A, B, [_|Vs]) :-
l(NV, OV, A, B, Vs).
is_one(1).