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yap-6.3/packages/gecode/clpfd.yap

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update docs
2014-09-11 20:06:57 +01:00
/**
@defgroup Gecode_and_ClPbBFDbC Programming Finite Domain Constraints in YAP/Gecode
@ingroup Gecode
@{
The gecode/clp(fd) interface is designed to use the GECODE functionality
in a more CLP like style. It requires
~~~~~{.prolog}
:- use_module(library(gecode/clpfd)).
~~~~~
Several example programs are available with the distribution.
Integer variables are declared as:
+ _V_ in _A_.. _B_
declares an integer variable _V_ with range _A_ to _B_.
+ _Vs_ ins _A_.. _B_
declares a set of integer variabless _Vs_ with range _A_ to _B_.
+ boolvar( _V_)
declares a boolean variable.
+ boolvars( _Vs_)
declares a set of boolean variable.
Constraints supported are:
*/
more doxygen fixes
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syntax errors
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:- module(gecode_clpfd, [
distributed config && float library
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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(705, xfx, where),
op(700, xfx, #>),
op(700, xfx, #<),
op(700, xfx, #>=),
op(700, xfx, #=<),
op(700, xfx, #=),
op(700, xfx, #\=),
op(700, xf, #>),
op(700, xf, #<),
op(700, xf, #>=),
op(700, xf, #=<),
op(700, xf, #=),
op(700, xf, #\=),
op(700, xfx, in),
op(700, xfx, ins),
op(500, yfx, '<=>'),
op(500, yfx, '=>'),
op(450, xfx, ..), % should bind more tightly than \/
(#>)/2,
(#<)/2,
(#>=)/2,
(#=<)/2,
(#=)/2,
(#\=)/2,
(#>)/1,
(#<)/1,
(#>=)/1,
(#=<)/1,
(#=)/1,
(#\=)/1,
(#<==>)/2,
(#==>)/2,
(#<==)/2,
(#\)/1,
(#\/)/2,
(#/\)/2,
in/2 ,
ins/2,
boolvar/1,
boolvars/1,
all_different/1,
all_distinct/1,
all_distinct/2,
maximize/1,
minimize/1,
sum/3,
lex_chain/1,
minimum/2,
min/2,
maximum/2,
max/2,
scalar_product/4,
element/2,
extensional_constraint/2,
in_relation/2,
clause/4,
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 */
]).
more doxygen fixes
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/** @pred _X_ #< _B_ is det
reified implication
As an example. consider finding out the people who wanted to sit
next to a friend and that are are actually sitting together:
~~~~~{.prolog}
preference_satisfied(X-Y, B) :-
abs(X - Y) #= 1 #<==> B.
~~~~~
Note that not all constraints may be reifiable.
*/
/** @pred _X_ #< _Y_ is semidet
smaller or equal
Arguments to this constraint may be an arithmetic expression with <tt>+</tt>,
<tt>-</tt>, <tt>\\*</tt>, integer division <tt>/</tt>, <tt>min</tt>, <tt>max</tt>, <tt>sum</tt>,
<tt>count</tt>, and
<tt>abs</tt>. Boolean variables support conjunction (/\), disjunction (\/),
implication (=>), equivalence (<=>), and xor. The <tt>sum</tt> constraint allows a two argument version using the
`where` conditional, in Zinc style.
The send more money equation may be written as:
~~~~~{.prolog}
1000*S + 100*E + 10*N + D +
1000*M + 100*O + 10*R + E #=
10000*M + 1000*O + 100*N + 10*E + Y,
~~~~~
This example uses `where` to select from
column _I_ the elements that have value under _M_:
~~~~~{.prolog}
OutFlow[I] #= sum(J in 1..N where D[J,I]<M, X[J,I])
~~~~~
The <tt>count</tt> constraint counts the number of elements that match a
certain constant or variable (integer sets are not available).
*/
/** @pred _X_ #<==> _B_ is det
reified equivalence
*/
/** @pred _X_ #= _Y_ is semidet
equality
*/
/** @pred _X_ #=< _Y_ is semidet
smaller
*/
/** @pred _X_ #==> _B_ is det
Reified implication
*/
/** @pred _X_ #> _Y_ is semidet
larger
*/
/** @pred _X_ #>= _Y_ is semidet
larger or equal
*/
/** @pred _X_ #\= _Y_ is semidet
disequality
*/
/** @pred all_different( _Vs_ )
Verifies whether all elements of a list are different.
*/
/** @pred labeling( _Opts_, _Xs_)
performs labeling, several variable and value selection options are
available. The defaults are `min` and `min_step`.
Variable selection options are as follows:
+ leftmost
choose the first variable
+ min
choose one of the variables with smallest minimum value
+ max
choose one of the variables with greatest maximum value
+ ff
choose one of the most constrained variables, that is, with the smallest
domain.
Given that we selected a variable, the values chosen for branching may
be:
+ min_step
smallest value
+ max_step
largest value
+ bisect
median
+ enum
all value starting from the minimum.
*/
/** @pred scalar_product(+ _Cs_, + _Vs_, + _Rel_, ? _V_ )
The product of constant _Cs_ by _Vs_ must be in relation
_Rel_ with _V_ .
*/
distributed config && float library
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:- use_module(library(gecode)).
:- use_module(library(maplist)).
fix arena initialization
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syntax errors
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:- reexport(library(matrix), [(<==)/2, op(600, xfx, '<=='),
op(700, xfx, in),
op(700, xfx, ins),
op(450, xfx, ..), % should bind more tightly than \/
op(710, xfx, of),
foreach/2, foreach/4, of/2]).
distributed config && float library
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% build array of constraints
%
syntax errors
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matrix:array_extension(_.._ , gecode_clpfd:build).
distributed config && float library
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build( I..J, _, Size, L) :-
length( L, Size ),
L ins I..J.
matrix:rhs_opaque(X) :- constraint(X).
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( element(_, _) ). %2,
constraint( fd_var(_) ). %1,
constraint( fd_inf(_, _) ). %2,
constraint( fd_sup(_, _) ). %2,
constraint( fd_size(_, _) ). %2,
constraint( fd_dom(_, _) ). %2
constraint( clause(_, _, _, _) ). %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, _).
( A #= ) :-
get_home(Env),
check(A, NA),
post( rel(NA, (#=)), Env, _).
update docs
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/** @pred _X_ #= is det
all elements of _X_ must take the same value
*/
distributed config && float library
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( A #\= ) :-
get_home(Env),
check(A, NA),
post( rel(NA, (#\=)), Env, _).
update docs
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/** @pred _X_ #< is det
elements of _X_ must be decreasing or equal
*/
distributed config && float library
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( A #< ) :-
get_home(Env),
check(A, NA),
post( rel(NA, (#<)), Env, _).
update docs
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/** @pred _X_ #> is det
elements of _X_ must be increasing
*/
distributed config && float library
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( A #> ) :-
get_home(Env),
check(A, NA),
post( rel(NA, (#>)), Env, _).
update docs
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/** @pred _X_ #=< is det
elements of _X_ must be decreasing
*/
distributed config && float library
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( A #=< ) :-
get_home(Env),
check(A, NA),
post( rel(NA, (#=<) ), Env, _).
update docs
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/** @pred _X_ #>= is det
elements of _X_ must be increasinga or equal
*/
distributed config && float library
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( A #>= ) :-
get_home(Env),
check(A, NA),
post( rel(NA, (#>=)), Env, _).
sum( L, Op, V) :-
get_home( Env ),
check(L, NL),
check(V, NV),
post( rel(sum(NL), Op, NV), Env, _).
fix arena initialization
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( ( A #<==> VBool )) :-
distributed config && float library
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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).
boolvar( X ) :-
get_home(Space-Map),
m(X, NX, 0, 1, Map),
NX := boolvar( Space ).
boolvars( Xs ) :-
get_home(Space-Map),
maplist(lm(0, 1, Map), Xs, NXs),
length(Xs, N),
NXs := boolvars( Space, N ).
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, _ ).
element( V, Xs ) :-
get_home(Env),
check(Xs, NXs),
check(V, NV),
post( element( NV, NXs ), 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(Xs, NXs),
post(in_dfa(NXs, S0, Ts, Fs), Env, _ ).
clause( and, Ps, Ns, V ) :-
get_home(Env),
check(Ps, NPs),
check(Ns, NNs),
check(V, NV),
post(clause( 'BOT_AND', NPs, NNs, NV), Env, _ ).
clause( or, Ps, Ns, V ) :-
get_home(Env),
check(Ps, NPs),
check(Ns, NNs),
check(V, NV),
post(clause( 'BOT_OR', NPs, NNs, NV), Env, _ ).
labeling(Opts, Xs) :-
get_home(Space-Map),
foldl2( processs_lab_opt, Opts, 'INT_VAR_SIZE_MIN', BranchVar, 'INT_VAL_MIN', BranchVal),
term_variables(Xs, Vs),
check( Vs, X1s ),
( X1s == [] -> true ;
maplist(ll(Map), X1s, NXs),
Space += branch(NXs, BranchVar, BranchVal) ).
processs_lab_opt(leftmost, _, 'INT_VAR_NONE', BranchVal, BranchVal).
processs_lab_opt(min, _, 'INT_VAR_SIZE_MIN', BranchVal, BranchVal).
processs_lab_opt(max, _, 'INT_VAR_SIZE_MAX', BranchVal, BranchVal).
processs_lab_opt(ff, _, 'INT_VAR_DEGREE_MIN', BranchVal, BranchVal).
processs_lab_opt(min_step, BranchVar, BranchVar, _, 'INT_VAL_MIN').
processs_lab_opt(max_step, BranchVar, BranchVar, _, 'INT_VAL_MIN').
processs_lab_opt(bisect, BranchVar, BranchVar, _, 'INT_VAL_MED').
processs_lab_opt(enum, BranchVar, BranchVar, _, 'INT_VALUES_MIN').
maximize(V) :-
get_home(Space-Map),
l(V, I, Map),
Space += maximize(I).
minimize(V) :-
get_home(Space-Map),
l(V, I, Map),
Space += minimize(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 = sum(_,_) -> V = NV ;
V = '[]'(Indx, Mat) -> NV <== '[]'(Indx, Mat) ;
V = '$matrix'(_, _, _, _, C) -> C =.. [_|L], maplist(check, L, NV) ;
V = A+B -> check(A,NA), check(B, NB), NV = NB+NA ;
V = A-B -> check(A,NA), check(B, NB), NV = NB-NA ;
arith(V, _) -> V =.. [C|L], maplist(check, L, NL), NV =.. [C|NL] ;
constraint(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,Z] #<
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) ).
% 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) ).
% 2 #\= B -> reverse
post( rel( A, Op, B), Space-Map, Reify) :-
( var(A) ; integer(A) ), !,
reverse_arith_op( Op, ROp ),
post( rel( B, ROp, A), Space-Map, Reify).
% A is never unbound
% [A,B,C,D] #< 3
post( rel( A, Op, B ), Space-Map, Reify):-
checklist( var, A ), !,
maplist(ll(Map), A, IL ),
( var(B) -> l(B, IB, Map) ; integer(B) -> IB = B ; equality(B, NB, Space-Map), l(NB, IB, Map) ), !,
gecode_arith_op( Op, GOP ),
(var(Reify) -> Space += rel(IL, GOP) ;
Space += rel(IL, GOP, IB) ).
% sum([A,B,C]) #= X
post( rel( sum(L), Op, Out), Space-Map, Reify):- !,
checklist( var, L ), !,
maplist(ll(Map), L, IL ),
( var(Out) -> l(Out, IOut, Map) ; integer(Out) -> IOut = Out ; equality(Out, NOut, Space-Map), l(NOut, IOut, Map) ),
gecode_arith_op( Op, GOP ),
(var(Reify) ->
Space += linear(IL, GOP, IOut);
Space += linear(IL, GOP, IOut, Reify)
).
% count([A,B,C], 3) #= X
post( rel( count(X, Y), Op, Out), Space-Map, Reify):- !,
( checklist( var, X ) -> maplist(ll(Map), X, IX ) ),
( var(Y) -> l(Y, IY, Map) ; integer(Y) -> IY = Y ; equality(Y, NY, Space-Map), l(NY, IY, Map) ),
( var(Out) -> l(Out, IOut, Map) ; integer(Out) -> IOut = Out ; equality(Out, NOut, Space-Map), l(NOut, IOut, Map) ), !,
gecode_arith_op( Op, GOP ),
(var(Reify) ->
Space += count(IX, IY, GOP, IOut);
Space += count(IX, IY, GOP, IOut, Reify)
).
% sum([I in 0..N-1, M[I]]) #= X
post( rel( sum(Foreach, Cond), Op, Out), Space-Map, Reify):- !,
( var(Out) -> l(Out, IOut, Map) ; integer(Out) -> IOut = Out ; equality(Out, NOut, Space-Map), l(NOut, IOut, Map) ),
cond2list( Foreach, Cond, Cs, L),
maplist(ll(Map), [Out|L], [IOut|IL] ),
gecode_arith_op( Op, GOP ),
(L = [] -> true ;
var(Reify) ->
Space += linear(Cs, IL, GOP, IOut);
Space += linear(Cs, IL, GOP, IOut, Reify)
).
post( rel(A1+A2, Op, B), Space-Map, Reify):-
( nonvar(B) ; B = _ + _ ; B = _-_), !,
linearize(A1+A2, 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(A1-A2, Op, B), Space-Map, Reify):-
( nonvar(B) ; B = _ + _ ; B = _-_), !,
linearize(A1-A2, 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):-
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):-
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):-
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)))
).
post(element(V, Xs), Space-Map, Reify) :-
l(V, IV, Map),
maplist(ll(Map), Xs, IXs),
(var(Reify) ->
Space += element(IV, IXs)
;
Space += element(IV, IXs, Reify)
).
post(clause( Type, Ps, Ns, V), Space-Map, Reify) :-
(integer(V) -> V = IV ; l(V, IV, Map) ),
maplist(ll(Map), Ps, IPs),
maplist(ll(Map), Ns, INs),
(var(Reify) ->
Space += clause(Type, IPs, INs, IV)
;
Space += clause(Type, IPs, INs, IV, Reify)
).
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' ).
reverse_arith_op( (#=) , (#=) ).
reverse_arith_op( (#\=) , (#\=) ).
reverse_arith_op( (#>) , (#<) ).
reverse_arith_op( (#>=) , (#=<) ).
reverse_arith_op( (#<) , (#>) ).
reverse_arith_op( (#=<) , (#>=) ).
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('/\\'(_,_), (/\)).
arith('\\/'(_,_), (\/)).
arith('=>'(_,_), (=>)).
arith('<=>'(_,_), (<=>)).
arith(xor(_,_), xor).
arith(abs(_), abs).
arith(min(_), min).
arith(max(_), max).
arith(min(_,_), min).
arith(max(_,_), max).
arith((_ * _), times).
arith((_ / _), div).
arith(sum(_), sum).
arith(sum(_,_), sum).
arith(count(_,_), count).
% 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(sum( V ), NV, Env) :-
maplist( equality_l(Env), V, VA ),
new_arith(sum, VA, NV, Env).
equality(sum( C, G ), NV, Env) :-
new_arith(sum, C, G, NV, Env).
equality('/\\'( V1 , V2), NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( (/\), V1A, V2A, NV, Env).
equality('\\/'( V1 , V2), NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( (\/), V1A, V2A, NV, Env).
equality('<=>'( V1 , V2), NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( (<=>), V1A, V2A, NV, Env).
equality('=>'( V1 , V2), NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( (=>), V1A, V2A, NV, Env).
equality('xor'( V1 , V2), NV, Env) :-
equality(V1, V1A, Env),
equality(V2, V2A, Env),
new_arith( (xor), 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( sum, V, NV, Space-Map) :-
foldl2( sum_l(Map), V, 0, Max, 0, Min),
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
maplist(ll(Map), V, X),
Space += linear(X, 'IRT_EQ', 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).
new_arith( sum, Foreach, Cond, NV, Space-Map) :-
cond2list( Foreach, Cond, Cs, V),
foldl2( sum_l(Map), V, 0, Max, 0, Min),
NX := intvar(Space, Min, Max),
m(NV, NX, Min, Max, Map),
maplist(ll(Map), V, X),
Space += linear(Cs, X, 'IRT_EQ', NX).
new_arith( (/\), V1, V2, NV, Space-Map) :-
l(V1, X1, Map),
l(V2, X2, Map),
NX := boolvar(Space),
m(NV, NX, 0, 1, Map),
Space += rel(X1, 'BOT_AND', X2, NX).
new_arith( (\/), V1, V2, NV, Space-Map) :-
l(V1, X1, Map),
l(V2, X2, Map),
NX := boolvar(Space),
m(NV, NX, 0, 1, Map),
Space += rel(X1, 'BOT_OR', X2, NX).
new_arith( (=>), V1, V2, NV, Space-Map) :-
l(V1, X1, Map),
l(V2, X2, Map),
NX := boolvar(Space),
m(NV, NX, 0, 1, Map),
Space += rel(X1, 'BOT_IMP', X2, NX).
new_arith( (<=>), V1, V2, NV, Space-Map) :-
l(V1, X1, Map),
l(V2, X2, Map),
NX := boolvar(Space),
m(NV, NX, 0, 1, Map),
Space += rel(X1, 'BOT_EQV', X2, NX).
new_arith( xor, V1, V2, NV, Space-Map) :-
l(V1, X1, Map),
l(V2, X2, Map),
NX := boolvar(Space),
m(NV, NX, 0, 1, Map),
Space += rel(X1, 'BOT_XOR', 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).
sum_l(Map, V, Min0, Min, Max0, Max) :-
l(V, _, Min1, Max1, Map),
Min is Min0 + Min1,
Max is 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).
syntax errors
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user:term_expansion( ( H :- B), (H :- (gecode_clpfd:init_gecode(Space, Me), NB, gecode_clpfd:close_gecode(Space, Vs, Me)) ) ) :-
distributed config && float library
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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_done, false),
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),
b_setval(gecode_done, true),
CVs := val(SolSpace,IVs).
intvar(Map, V) :-
l(V, _IV, Map).
get_home(Home) :-
b_getval(gecode_space, Home).
cond2list((List where Goal), El, Cs, Vs) :- !,
foreach( List, add_el(Goal, El), ([])-([]), Cs-Vs ).
cond2list(List, El, Cs, Vs) :- !,
foreach( List, add_el(true, El), ([])-([]), Cs-Vs ).
add_el(G0, El, Cs-Vs, [C|Cs]-[V|Vs]) :-
call(G0), !,
E <== El,
( var(E) -> C = 1, E = V ; E = C*V, integer(C), var(V) -> true ; E = V*C, integer(C), var(V) ).
add_el(_G0, _El, Cs-Vs, Cs-Vs).
% An attributed variable with attribute value Domain has been
% assigned the value Y
attr_unify_hook(_, _) :-
b_getval(gecode_done, true), !.
attr_unify_hook(v(IV1,_,_), Y) :-
syntax errors
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( get_attr(Y, gecode_clpfd, v(IV2,_,_))
distributed config && float library
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->
nb_getval(gecode_space, Space-_),
( IV1 == IV2 -> true ;
Space += rel(IV1, 'IRT_EQ', IV2) )
; var(Y)
-> true
; integer(Y) ->
nb_getval(gecode_space, Space-_),
Space += rel(IV1, 'IRT_EQ', Y)
).
% Translate attributes from this module to residual goals
attribute_goals(X) -->
syntax errors
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{ get_attr(X, gecode_clpfd, v(_,A,B)) },
distributed config && float library
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[X in A..B].
m(X, Y, A, B, _Map) :-
syntax errors
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put_attr(X, gecode_clpfd, v(Y, A, B)).
distributed config && float library
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/*
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(V, IV, _) :-
syntax errors
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get_attr(V, gecode_clpfd, v(IV, _, _)).
distributed config && float library
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/*
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(V, IV, A, B, _) :-
syntax errors
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get_attr(V, gecode_clpfd, v(IV, A, B)).
distributed config && float library
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/*
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).
update docs
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/**
@}
*/
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