Lines Matching defs:of
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32 {\bf Note: As of \eclipse\ release 5.1, the library described
41 domain terms. It has been developed using the kernel of \eclipse\ based
42 on metaterms. It contains the finite domain library of \eclipse. The
56 The computation domain of {\em\bf Conjunto} is finite so set
58 finite set term in the following. Here are defined some of the terms
75 of elements of D. Thus they are both ground sets. S is then called a
81 a set variable {\em S} where each element of {\em WD} is of the
82 form {\em e(s,w)}. {\em s} is a ground set representing a possible value of the
95 \begin{quote} A composition of set domain variables or ground sets together
104 \begin{quote} Any term of the followings: (1) a ground set, (2) a
106 predicates deal with set terms thus with any of the three cases.
136 approximated in terms of the domains of the set variables involved.
138 over set expressions can be approximated in terms of constraints over
152 attaches a domain to the set variable or to a list of set variables
169 The value of the set term {\em S} is equal to
170 the value of the set term {\em S1}.
175 The element {\em E} is an element of {\em S}. If {\em E} is ground it
176 is added to the lower bound of the domain of {\em S}, otherwise the constraint is
178 of {\em S} domain, it fails.
185 it is removed from the upper bound of {\em S}, otherwise the
187 bound of the domain of {\em S}, it is removed from the upper bound and
189 lower bound of {\em S} domain, it fails.
194 The value of the set term {\em S} is a subset of the value of the set
196 inclusion and succeeds or fails. If the lower bound of the domain of {\em
197 S} is not included in the upper bound of {\em S1} domain, it fails.
204 The domains of S and S1 are disjoint (intersection empty).
209 {\em Lsets} is a list of set variables or ground sets. {\em S} is a
210 set term which is the union of all these sets. If {\em S} is a free
212 from the union of the domains or ground sets in {\em Lsets}.
217 {\em Lsets} is a list of set variables of ground sets. All the sets are pairwise
226 If not, the cardinality of S is constrained to be C.
232 {\em W} is the weight of {\em S}. If {\em W} is a free variable, this
234 not, the weight of S is constrained to be W. e.g.
244 possible domain value. If there are several instances of {\em Svar},
253 of set constraints and the propagation mechanism.
281 The first example gives a set of cars from which we know
283 \verb/{renault, bmw, mercedes, peugeot}/ are possible elements of this set. The
285 \verb/Choice/ is the set term resulting from the intersection of the
287 \verb/renault/ is element of \verb/Choice/ and \verb/peugeot/ might be
289 reconsidered if one of the domain of the set terms involved changes.
292 In the second example an additional constraint restricts the cardinality of
294 \verb/Choice/ set to \verb/{peugeot, renault}/. The domain of this
304 is a subset $s'$ of {\em S} whose weight is {\em t}. This also corresponds to
338 % Get rid of a set of elements of the set according to a given delta
375 We state constraints which limit the weight of the set. We apply the
376 ``trim'' heuristics which removes possible elements of the set domain.
379 {\bf conjunto.pl} library makes sure that any modification of an fd
381 labeling procedure refines a set domain by selecting the element of
383 \verb/max_weight(Sub, X),/ and by adding it to the lower bound of the set
394 criteria mainly concern the cardinality or the weight of a set term.
399 \subsection{The ternary Steiner system of order n}
400 A ternary Steiner system of order {\em n} is a set of
402 triplets of distinct elements taking their values between {\em 1} and
408 elements and (ii) the constraint of the problem can be easily written
409 with set constraints saying that any intersection of two set terms
410 contains at most one element. With a finite domain approach, the list of
447 % creates the required number of set variables according to n
451 % initializes the domain of the variables according to n
464 % constrains the cardinality of each set variable to be equal to V (=3)
471 The approach with sets is the following: first we create the number of
474 domain of these set variables we use the fd predicates which allow to
476 is cleaner than enumerating a list of integer between 1 and n. Once
482 in common. The semantics of
487 of the set is ground and some element has been added to the second
503 The {\em subset-sum} example shows that the general principle of solving
513 a set variable for the size of a set domain is exponential in the
514 upper bound cardinality and thus the number of backtracks could be
523 either the goal succeeds or it fails. In case of failure the labeling
527 labeling only concerns a single set, but it can deal with a list of
535 Set constraints propose a new modelling of already solved problems or
539 possible and to make a powerful use of set constraints. The objective
540 of this library is to bring CLP to bear on graph-theorical problems
542 problem, thus leading to a better specification and solving of
550 element as a specific individual but in a collection of elements where
558 access the properties of a set term like its domain, its cardinality,
577 \item {\bf setdom} The representation of the domain itself. As set
581 \item {\bf card} The representation of the set cardinality. The
586 \item {\bf weight} The representation of the set weight. The weight is
594 the lower bound of the set domain is updated.
596 the upper bound of the set domain is updated.
598 any reduction of the domain is inferred.
602 The attribute of a set domain variable can be accessed with the
610 {\bf structures.pl} library, if e.g. {\bf Attr} is the attribute of a
613 arg(del_inst of set, Attr, Dinst)
623 not supposed to access them directly. So we provide a number of
632 bounds of its domain. Otherwise it fails.
637 If {\em Svar} is a set domain variable, it returns the lower bound of
643 If {\em Svar} is a set domain variable, it returns the upper bound of
649 If {\em E} is element of a weighted domain, it returns the weight
655 If {\em Svar} is a set variable, it returns the element of its domain
656 which belongs to the set resulting from the difference of the upper
690 list occurs. For example, if the lower bound of a set variable is modified, two
708 \section{Example of defining a new constraint}
717 Assuming that {\em S} and $S_1$ are specific set variables of the form
725 shows that if one wants to iterate over a ground set (set of known
763 insert_suspension([S,S1], Susp, del_any of set, set)
804 The execution of this constraint is dynamic, {\em i.e.}, the
811 predicate checks that any element of a ground set (which is a set
812 itself in this case) is a subset of at least one element of the second
816 ground set and the upper bound of the second set. If it succeeds then
817 the lower bound of the set variable might not be consistent any more,
824 variable. If so, \verb/check_incl/ is called over the lower bound of
826 bound of the set variable might not be consistent any more. The new
828 bound of the set variable in the lattice acceptation \verb/large_inter/ and
831 lower bound of the first set should be included in the lattice sense
832 in the upper bound of the second one \verb/check//\verb/incl/. If it
835 In the same way, the upper bound of the first set might not be
838 upper bound of the first set \verb/large_inter/. The upper bound of
839 the first set variable is updated as well as the lower bound of the
842 implies an instanciation of one of the two sets. If this is not the
844 any bound of either set domain is changed. The predicate
848 the appropriate lists (woken when any bound is updated) of both set
850 \item the last action \verb/wake/ triggers the execution of all goals that are
858 variable as well as a ground set respectively as an interval of sets or
859 a set. The {\bf setdom} attribute of a set domain variable (metaterm)
860 is printed in the simplified form of just the $glb..lub$ interval, e.g.
873 The \eclipse\ debugger which supports debugging and tracing of finite