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A specification of the range of allowable cardinality values—the size—that a setmay assume.
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Multiplicity specifications may be given for association ends, partswithin composite classes, repetitions of messages, and other purposes.
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See also multiplicity (of association), multiplicity (of class).
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Multiplicity is a constraint on the cardinality (size) of a set.
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In principle, it is a sub-set of the nonnegative integers.
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In practice, it is usually a finite set of integer inter-vals, most often a single interval with a minimum and a maximum value.
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Any setmust be finite, but the upper bound can be finite or unbounded (an unboundedmultiplicity is called “many”).
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The upper bound must be greater than zero; or, atany rate, a multiplicity comprising only zero is not very useful, as it permits onlythe empty set.
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Multiplicity is coded as a string.
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In most cases, a multiplicity may be specified as an integer range—a minimumand a maximum cardinality—but in general, it may be a discontinuous subset ofthe nonnegative integers.
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The set of integers may be infinite—that is, the upperbound may be unlimited (but note that any particular cardinality in the set is fi-nite).
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For most practical purposes, this set of integers can be specified as a finite list ofdisjoint, disconnected integer intervals.
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An interval is a set of contiguous integerscharacterized by its minimum and maximum values.
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Some infinite sets cannot bespecified this way—for example, the set of even integers—but usually little is lostby simply including the gaps.
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See multiplicity (of association) and multiplicity (of class) for specific details ofusing multiplicity with these elements.
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where number is an integer representing an interval of a single size.
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The multiplicity expression consisting of a single star*is equivalent to the expression 0..
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This frequently encountered multiplicityis read “many.
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Two contiguous intervals should be combined into a single interval.
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A multiplicity expression can include variables, but they must resolve to integervalues when the model is complete—that is, they must be parameters or con-stants.
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Multiplicity is not meant to be dynamically evaluated within a run-timescope like a dynamic array bound.
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It is meant to specify the possible range of val-ues (worst case) a set might assume and the application must therefore accommo-date in its data structures and operations.
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The multiplicity may be suppressed on a diagram, but it exists in the underlyingmodel.
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In a finished model, there is no meaning to an “unspecified” multiplicity.
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The list must be a comma-separated list of names of states that can legally occurconcurrently.
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To show a change of class (dynamic classification), the object must be displayedtwice, once with each class.
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The two symbols are connected by a become relation-ship to show that they represent the same object.
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The second compartment shows the attributes for the object and their values as
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The type is redundant with the attribute declaration in the class and may be omit-ted.
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The value is specified as a string that represents the value.
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The name of the object may be omitted.
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In this case, the colon should be keptwith the class name.
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Each symbol that contains an anonymous object denotes adistinct object distinguished by its relationships to other objects.
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The class of the object may be suppressed (together with the colon), but itshould be shown when possible to avoid confusion.
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The attribute value compartment as a whole may be suppressed.
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Attributes whose values are not of interest may be suppressed.
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To show the changes in value of attributes during a computation, show two ver-sions of the same object with a become relationship between them.
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A diagram that shows objects and their relationships at a point in time.
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Also related is a collaboration diagram, whichshows prototypical objects (classifier roles) within a context.
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Tools need not support a separate format for object diagrams.
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” The phrase is useful, however, to characterize a particular usage achievablein various ways.
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An object diagram shows a set of objects and links that represent the state of a sys-tem at a particular moment in time.
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It contains objects with values, not descrip-tors, although they can, of course, be prototypical in many cases.
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To show a generalpattern of objects and relationships that can be instantiated many times, use a col-laboration diagram, which contains descriptors (classifier roles and associationroles) for objects and links.
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If a collaboration diagram is instantiated, it yields anobject diagram.
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An object diagram does not show the evolution of the system over time.
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For thatpurpose, use a collaboration diagram with messages, or a sequence diagram torepresent an interaction.
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An object flow is a kind of control flow with an object flow state as an input or anoutput.
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An object flow is shown as a dashed line from the source entity to the target entity.
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One or both entities may be object flow states, displayed as object symbols.
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If there is no label on the arrow, it is a become relationship.
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See object flow state, become, and copy for examples.
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A state that represents the existence of an object of a particular class at a pointwithin a computation, such as an interaction view or an activity graph.
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Both activity graphs and interaction views represent the flow of control amongoperations in target objects by messages, but messages do not show the flow of theobjects that are arguments to operations.
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This kind of information flow can berepresented in behavioral models using object flow states.
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An object flow state represents an object of a class that exists at a point within acomputation, such as an activity graph or an interaction view.
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The object may bethe output of one activity and the input of many other activities.
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In an activitygraph, it may be the target of a transition (often a fork, the other branch being themain control path), and it may be the source of a completion transition to an ac-tivity.
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When the preceding transition fires, the object flow state becomes active.
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This represents the creation of on object of the class.
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To show the passage of an ob-ject into a state, rather than the creation of a new object, an object flow state can bedeclared as a class in a state, a class-in-state.
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An object flow state must match the type of the result or parameter that it repre-sents.
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If it is the output of an operation, it must match the type of the result.
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If it isthe input of an operation, it must match the type of a parameter.
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In other words, the creation of data in the right form isthe trigger for performing the activity.
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Multiple paths to a transition indicate synchronization.
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Object flow states are usually useful to document input-output relationships forhuman understanding rather than to specify a computation precisely.
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The infor-mation shown by object flow states is already available.
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The production of an event by an activity in an activity graph can be modeled as
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The object flow state is an output of the activity.
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If the activity produces mul-tiple events, the object flow states are targets of a fork.
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An object flow symbol represents the existence of the object in a state of the proce-dure itself and not simply the object itself, as data.
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The object flow symbol (whichrepresents a state) may appear as the target of one transition arrow and as thesource of multiple transition arrows.
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To distinguish these from ordinary transi-tions in an activity diagram, they are drawn as dashed arrows rather than solid ar-rows.
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Figure 13-135 shows object flow states in an activity diagram.
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An object flow stateis created by the completion of an operation.
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For example, Order[Placed] is cre-ated by the completion of Request Service.
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Because that activity is followed by an-other activity, the object flow state Order[Placed] is an output of a fork symbol.
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State Order[Entered], on the other hand, is the result of completing activity TakeOrder, which has no other successor activities.
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Figure 13-136 shows a portion of an activity diagram concerned with building ahouse.
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When the frame has been built, the carpenter is free to work on the roofand the house is ready for the plumbing to be installed.
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These events are modeledas object flow states of signals—Carpenter free and Frame ready.
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As a result ofthese events, the roof can be built and the plumbing can be installed.
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Therefore theobject flow states are shown as inputs of the activities.
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In the model, the produc-tion of an event by the completion of one activity and its use to trigger the next ac-tivity are implicit in the connection of the activities.
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The need for a manifest eventhas been elided.
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An object flow state represents the data flow view of a computation.
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Unlike tradi-tional data flow, however, it exists at a definite point within a control flow model (astate machine or an activity graph), rather than within a data flow model.
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Thisplaces it squarely into an object-oriented framework.
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Object orientation unites thedata structure, control flow, and data flow viewpoints into a single model.
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A line in a sequence diagram that represents the existence of an object over a pe-riod of time.
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An expression that yields a set of objects when evaluated at run time.
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The target of a send action is an object set expression.
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When such an expression isevaluated at run time, it yields a set of objects to which a designated signal is sentin parallel.
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An object set expression may yield a single element, in which case thesend action is an ordinary sequential action.
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It may even yield no element (that is,an empty set) in which case no send occurs.
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Object Constraint Language, a text language for specifying constraints and que-ries.
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For a fulldefinition, see the book [Warmer-99].
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The Object Constrain Language (OCL) is a text language for writing navigationexpressions, Boolean expressions, and other queries.
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It may be used to constructexpressions for constraints, guard conditions, actions, preconditions and postcon-ditions, assertions, and other kinds of UML expressions.
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