UML-B: Formal Modeling and Design Aided by UML

1
UML-B Formal Modeling and Design Aided by
UML
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B-Specification

• -state model based, formal specification
• -3steps(specification,implementation and
  implementation)
• -for refinement it requires refinement relation
  

3
0.. 1
UML-B model
NAME

ltltcreategtgtadd(numbNUMB) ltltdestroygtgt remove() Lookup() numb
NUMB


pbook
1
Operation Guard action
add Numberan(pbook) Pbooknumb
Remove - -
lookup - numbpbook
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Difficulties Translating from UML to B

• B is not object-oriented
• Restrictions on B component and variable access
• Simultaneous calls to several operations of
  another machine are not allowed
• UML-B profile
• -uses stereotypes
• -defines tagged values(invariants,guards etc)

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UML-B Model Architecture

• Class Diagrams
• -attributes
• -associations

CELL
powerlevel INT
PHONE
ltltconstantgtgt threshold HOLD
current
0..
0..1
1
0..
cellChannels
dspChannels
0..
0..
CHANNEL
broadcasting BOOL
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• TRANSLATION OF uB
• -OCLdefmyExpressionintegera ?
  select(ocllsTypeOf(S)).x ? sum()
• -uBSi.(i e C ? i e S ? i e a?i.x)
• BEHAVIOUR
• - Invariants
• instance invariants
• class invariants
• - Operation Specification
• - Initialization
• - Appearance and Disappearance of class
  instances
• - subroutines

PHONE
startCall(ttCHANNEL) success
CHANNEL
inUseBOOLFALSE
channels

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SPECIALIZATION OF CLASSES
CBCH


TRAFFIC
Callkind CALLKIND

ACCESS


CHANNEL
broadcasting BOOL FALSE

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BEHAVIOURAL SPECIFICATION BY STATE MACHINE

• State Dependant Invariants
• Example of state Machine Behaviour specification

Inc / bx bx1
Inc / bx bx10
new BB
Non_Zero
Zero
Dec bx1
Dec bxgt1

• State machine decision point

s2
G2 /A2
E1 G1 /A1
s1
s3
G4 /A4
G3 /A3
s4
G5 /A5
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G8/A8
s8
E10G10/A10
s10
s9
G9/A9
E5G5/A5
s5
G7/A7
s7
s6
E6G6/A6
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Alternative Semantics for UML-B State Machines
s1
s2
REFINEMENT
refines
ltltrefinementgtgt cellphone1
ltltmachinegtgt cellphone
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Refinement in UML-B
current
PHONE
CELL
PowerlevelINT
TRChannel
cellTRChannels
CBChannel
cellCBChannel
cellASChannles
ASChannels
CBCH
TRAFFIC
ACCESS
callkindCALLKIND
CHANNEL
broadcastingBOOLFALSE
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Refinement Relation
CLASS REFINEMENT_ RELATION
PHONE ChannelsCBChannel U ASChannels
CELL cellChannelscellChannel U cellTRChannels U cellASChannels