A Formal Semantics of UML Sequence Diagram - UNU-IIST - United ...

More documents

Recommendations

Info

and edges represent links and passing messages. Since asequence diagram is defined as a sequence of messages, weshould give formal definition of messages.Definition 1 A message is a tuple:wheremsg = (ob i : C i , ob j : C j , action, order)• ob i is the source object of the message with class typeC i , of course the source of message can also be anactor.• ob j is the target object of the message with class typeC j .• action is a guarded method call of the form g → act ,where g is a Boolean expression of attributes of sourceobject ob i , and possibly public variables, and actionis either a command without method calls (an internalaction) or a method call ob j .m().• order is the order number of the message in the correspondingsequence diagram structure tree. All the ordernumbers of messages in the sequence diagram constructa partial order. The order number of a messageis given according to its position in the tree. The rootnode is corresponding to the starting object or actor ofa sequence diagram. Then the first layer branches withorder number is 1, 2, , 3, · · · , n. From the u-th nodeob u of first layer object nodes, perhaps there are mnodes. The corresponding order numbers of branchesare u.1, u.2, · · · , u.m. The u.v is the v-th branchesfrom the node object ob u . Given the sequence diagramexample in Figure 2, the corresponding structure treewith ordered messages is shown in Figure 7.We now look at how composite diagrams can be constructedfrom basic diagrams by using programming language-likeconstructs.obi : Cig -> m()obj : Cjg -> m()Figure 3. Basic activation notationobi : Ciobj : Cj• The activation notation of a basic message in sequencediagram is shown in Figure 3.• The iterative notation of messages is shown in Figure4. The corresponding ordered tree can be constructedin the figure.• The special messages such as create object anddestroy are shown in Figure 5.• And the branching choice case of messages can bedealt as shown in Figure 6.obi : Cig -> m()u.v.1: * g1 -> n1()u.v : g -> m()obk : Ckobj : Cjobi : Ci* g1 -> n1()g2 -> n2()obj : Cjobk : Ckobk : Cku.v.2: g2 -> n2()Figure 4. Iteration notationA complicate sequence diagram can be constructed byabove basic notations. For sequence diagram of Figure 2,we can easily derive its corresponding message orderedstructure tree as shown in Figure 7.The ordered structure tree presents the hierarchical relationshipsamong the messages. And the execution of messages(i.e. execution of the method represented by the message)in the sequence diagram must follow the traversingrule of first root then son trees from left to right. For onethread sequence diagram, there is only one token to denotecontrol right of invoking message. In the beginning of anexecution of the sequence diagram, the token is in the actor’shand. When the source of message wants to invokea message, the source object or actor must hold the token.When the message is invoked, the token should be passedthe target of message. The source of message will wait untilthe target return the token, it can invoke another messageor return the token to the previous source which invoked itbefore. We consider that the execution of a sequence diagramfrom the start to termination is the process of the token4
obi : Ciobi : Ciobj : Cjobj=new Cj()obj : Cjb1 -> m()destroy()b2 -> n()obi : Ciobi : Ciu.v: obj=new Cj()u.v+1: destroy()u.v: b1 -> m()u.v+1: b2 -> n()obj : Cjobj : CjFigure 5. Create and destroy notationsobj : Cjobj : Cjtraversing from the root node of the hierarchical tree to subtreesfrom left to right, finally the token return back to theroot.If the order of the messages given in one thread sequencediagram is not conformed to a hierarchical structure tree,then the diagram is not well-formed. For example, the sequencediagram shown in Figure 8 is illegal because afterthe first message getName() finished, the thread controlpoint is returned the actor CampaignManager, the nextmessage ∗getCost() can be invoked by object : Campaignin the system.Figure 6. Branching choice notationCampaign Manager1: getName() 2: listCampaigns() 3: checkCapaingnBudget():Client2.1: *getCampaignDetails():Client:Campaign3.1: *getCost() 3.2: getOverheads()4 Computational Model:Campaign:Advert:CampaignWe use a notation similar to a transition or action system[13] to combine the models of class diagrams and themodel of sequence diagrams together to model a design ofa system. A system is defined by a tuple (α, Φ, Θ, P ) where• α denotes the set of program variables known to theprogram.• P is a set of operations, each of which is a predicatethat relates the initial values of program variables. Thepredicate is of the form p(x) ⊢ R(x, x ′ ) (called a designin [9]):p(x) ⊢ R(x, x ′ ) def= ok ∧ p(x) ⇒ ok ′ ∧ R(x, x ′ )where x and x ′ represent the initial and final valuesof x respectively; ok asserting that the operation isstarted well and ok ′ means that the operation terminated;p(x) is called the precondition, and R(x, x ′ ) thepost-condition or the transition relation.Figure 7. Sequence diagram structure tree• Θ is a predicate over α, called the initial condition anddefines the initial state(s) of the system.• Φ is a predicate over α, called the invariant. It must betrue in any initial state and preserved by each operationin P .An action only changes a subset of variables declared inα. The normal form of a design is thus a framed design ofthe form V : (p ⊢ R), that denotes p ⊢ R ∧ (w ′ = w),where V and w are subsets of α, and w = α − V . Whenthere is no confusion, we will omit the frame in a design byassuming that a variable x can be changed by a design onlyif its primed version x ′ occurs in the design.The above model has to take into account the followingOO aspects.1. A sequence diagram is composed from a number of5
Page 6 and 7: ¡CampaignManagergetName()¡¡¡¡
Page 8 and 9: e simply defined as follows since t

A Formal Semantics of UML Sequence Diagram - UNU-IIST - United ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?