Composite Objects in VDMSL

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Composite Objects in VDM-SL
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Learning Outcomes

• Identify when it is appropriate to use a
  composite object type
• Use the composite object operators (make,
  selection and mu)
• Add an invariant to a composite object type
• Use the composite object type to help model
  systems in VDM-SL
• Use a letin clause to simplify expressions in
  VDM-SL

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So far
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.. we have always associated a single type with
each item of data in our VDM specifications.
temp ? robot Status permission
Aircraft-set
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Composite Types..
.. allow us to associate more than one type
with an object.
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Defining Composite Object Types
types
TypeName

fieldname1
Type1
fieldname2
Type2

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The Time Type
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types
TypeName

fieldname1
Type1
fieldname2
Type2

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types
Time

fieldname1
Type1
fieldname2
Type2

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types
Time

hour
Type1
fieldname2
Type2

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types
Time

hour
Type1
minute
Type2

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types
Time

hour
Type1
minute
Type2
second
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types
?
Time

hour
minute
Type2
second
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types
?
Time

hour
minute
?
second
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types
?
Time

hour
minute
?
second
?
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This Time type can now be used like any other
type in your specification
someTime Time
importantTimes Time-set
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Composite object operators
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The make function
The make function that creates a new object of a
given composite type.
mk-CompositeObjectTypeName (parameter list)
Returning to the Time example
someTime mk-Time ( )
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, 20
, 44
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someTime mk-Time (36, 20, 44)
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someTime mk-Time (36, 20, 44)
This should not be a valid time value?
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someTime mk-Time (36, 20, 44)
Add an invariant to your object definition to
make these times invalid!
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Time hour ? minute ? second ? inv
mk-Time (h, m, s) ?
h lt 24 ? m lt 60 ? s lt 60
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Composite object selectors
We can refer to a particular field of a composite
object by using a selector operator. Individual
fields are selected by the dot operator '.'
followed by the name of a field. For example
someTime.minute someTime.hour
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16
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The mu function
The mu function returns one composite object from
another but with one or more fields changed.
newTime ? (someTime, hour ? 15)
thisTime ? (someTime, minute ? 0, second ? 0)
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The DiskScanner class
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The DiskScanner class
TRACKS
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The DiskScanner class
SECTORS
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The DiskScanner class
BLOCKS
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DiskScanner damagedBlocks Block
addBlock(Integer, Integer) removeBlock
(Integer, Integer) isDamaged(Integer, Integer)
Boolean getBadSectors(Integer) Integer
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DiskScanner damagedBlocks Block
addBlock(Integer, Integer) removeBlock
(Integer, Integer) isDamaged(Integer, Integer)
Boolean getBadSectors(Integer) Integer
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Analysing the Block type further
Block track Integer sector Integer
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Specifying the data model in VDM-SL
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types state DiskScanner
of damagedBlocks init mk-DiskScanner (dB)
? end
Block track sector
?
?
Block-set
dB
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DiskScanner damagedBlocks Block
addBlock(Integer, Integer) removeBlock
(Integer, Integer) isDamaged(Integer, Integer)
Boolean getBadSectors(Integer) Integer
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addBlock (
) ext pre post
trackIn ?, sectorIn ?
wr
damagedBlocks Block-set
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addBlock (
) ext pre post
trackIn ?, sectorIn ?
wr
damagedBlocks Block-set
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addBlock (
) ext pre post
trackIn ?, sectorIn ?
wr
damagedBlocks Block-set
mk-Block (trackIn, sectorIn) ? damagedBlocks
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DiskScanner damagedBlocks Block
addBlock(Integer, Integer) removeBlock
(Integer, Integer) isDamaged(Integer, Integer)
Boolean getBadSectors(Integer) Integer
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removeBlock (
) ext pre post
trackIn ?, sectorIn ?
wr
damagedBlocks Block-set
mk-Block (trackIn, sectorIn) ? damagedBlocks
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DiskScanner damagedBlocks Block
addBlock(Integer, Integer) removeBlock
(Integer, Integer) isDamaged(Integer, Integer)
Boolean getBadSectors(Integer) Integer
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isDamaged (
) ext pre post
trackIn ?, sectorIn ?
query ?
damagedBlocks Block-set
rd
TRUE
query
?
mk-Block (trackIn, sectorIn) ? damagedBlocks
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DiskScanner damagedBlocks Block
addBlock(Integer, Integer) removeBlock
(Integer, Integer) isDamaged(Integer, Integer)
Boolean getBadSectors(Integer) Integer
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getBadSectors ( )
ext pre post
trackIn ?
list ?-set
rd
damagedBlocks Block-set
TRUE

?

b ? damagedBlocks
b.sector
?
?
list
b.track trackIn
?
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A process management system
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timeout
admit
terminate
dispatch
block
wakeup
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ProcessManagament running ID waiting
Process admit(ID) dispatch() timeOut() block()
wakeUp(ID) terminate()
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ProcessManagament running ID waiting
Process admit(ID) dispatch() timeOut() block()
wakeUp(ID) terminate()
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ProcessManagament running ID waiting
Process admit(ID) dispatch() timeOut() block()
wakeUp(ID) terminate()
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id ID status Status
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id ID status Status
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READY BLOCKED
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Specifying the types in VDM-SL
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types
ID
TOKEN
Status
ltREADYgt ltBLOCKEDgt
ID
Process

id
Status
status
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Specifying the state in VDM-SL
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state ProcessManagement of running waiting inv
mk-ProcessManagement (run, wait) ?
init mk-ProcessManagement (run, wait) ?
end
ID
Process-set
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state ProcessManagement of running waiting inv
mk-ProcessManagement (run, wait) ?
init mk-ProcessManagement (run, wait) ?
end
ID
Process
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state ProcessManagement of running waiting inv
mk-ProcessManagement (run, wait) ? init
mk-ProcessManagement (run, wait) ?
end
ID
Process
run nil ? wait
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state ProcessManagement of running waiting inv
mk-ProcessManagement (run, wait) ? init
mk-ProcessManagement (run, wait) ?
end
ID
Process
run nil ? wait
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state ProcessManagement of running waiting inv
mk-ProcessManagement (run, wait) ? init
mk-ProcessManagement (run, wait) ?
end
ID
Process
P2
run nil ? wait
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state ProcessManagement of running waiting inv
mk-ProcessManagement (run, wait) ? (

) (

) init
mk-ProcessManagement (run, wait) ?
end
ID
Process
no waiting id should match the running id
?
the ids in the waiting queue should be unique
run nil ? wait
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no waiting id should match the running id
P2
run
wait
?
??p ? elems wait ? p.id run
run nil
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no waiting id should match the running id
P2
run
wait
?
??i ? inds wait ? wait(i).id run
run nil
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the ids in the waiting queue should be unique
P2
run
wait
card elems wait len wait
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the ids in the waiting queue should be unique
P2
run
wait
? i,j ? inds wait ? i ? j ? wait(i).id ?
wait(j).id
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state ProcessManagement of running waiting inv
mk-ProcessManagement (run, wait) ? (

) (

) init
mk-ProcessManagement (run, wait) ?
end
ID
Process
??i ? inds wait ? wait(i).id run
run nil
?
?
? i,j ? inds wait ? i ? j ? wait(i).id ?
wait(j).id
run nil ? wait
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Specifying a findPos function
P6
3
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Specifying a findPos function
findPos(qIn Process, idIn ID) pos ? pre ?p
? elems qIn ? p.id idIn post qIn(pos).id
idIn
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Specifying a findNext function
2
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Specifying a findNext function
qIn Process
findNext( ) pre post
pos ?
?p ? elems qIn ? p.status ltREADYgt
?
qIn(pos).status ltREADYgt
??i ? 1,,pos-1 ? qIn(i).status ltREADYgt
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Specifying a remove function
2
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Specifying a remove function
remove(qIn Process, posIn ?) qOut
Process pre posIn ? inds qIn post qOut
qIn(1,, posIn-1) qIn(posIn1,,len qIn)
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ProcessManagament running ID waiting
Process admit(ID) dispatch() timeOut() block()
wakeUp(ID) terminate()
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admit( idIn ID) ext pre post
waiting Process
wr
running ID
rd
(running nil ? idIn ? running ) ?
?p ? elems waiting ? p.id ? idIn
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ProcessManagament running ID waiting
Process admit(ID) dispatch() timeOut() block()
wakeUp(ID) terminate()
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dispatch() ext pre post
running ID
wr
waiting Process
wr
running nil ?
?p ? elems waiting ? p.status ltREADYgt
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ProcessManagament running ID waiting
Process admit(ID) dispatch() timeOut() block()
wakeUp(ID) terminate()
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timeOut() ext pre post
running ID
wr
waiting Process
wr
running ? nil
? running nil
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ProcessManagament running ID waiting
Process admit(ID) dispatch() timeOut() block()
wakeUp(ID) terminate()
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block() ext pre post
running ID
wr
waiting Process
wr
running ? nil
? running nil
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ProcessManagament running ID waiting
Process admit(ID) dispatch() timeOut() block()
wakeUp(ID) terminate()
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wakeUp( idIn ID) ext pre post
waiting Process
wr
waiting(findPos(waiting, idIn)).status
ltBLOCKEDgt
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ProcessManagament running ID waiting
Process admit(ID) dispatch() timeOut() block()
wakeUp(ID) terminate()
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terminate() ext pre post
running ID
wr
running ? nil
running nil
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The letin clause
A letin clause takes the following general form
let name sub-expression in expression(name)
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Re-writing postcondition of dispatch
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Nested letin clauses