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Model Structuring and Combining UML and VDM++ Views

Model Structuring and Combining UML and VDM++ Views. Peter Gorm Larsen. Agenda. Combining UML and VDM++ Views The Enigma Cipher Example. The CSLaM System. A small system for control speed limitation and monitoring for trains. The CSLaM Requirements.

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Model Structuring and Combining UML and VDM++ Views

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  1. Model Structuring and Combining UML and VDM++ Views Peter Gorm Larsen Model Structuring and Combining UML and VDM++ Views

  2. Agenda • Combining UML and VDM++ Views • The Enigma Cipher Example Model Structuring and Combining UML and VDM++ Views

  3. The CSLaM System • A small system for control speed limitation and monitoring for trains Model Structuring and Combining UML and VDM++ Views

  4. The CSLaM Requirements • The main purpose of the CSLaM system is to provide a continuous train speed monitoring function. This system is intended to be used when temporary speed restrictions are necessary. This is signalled using different types of beacons placed along the track. • The maximum permitted speed is the lower of the maximum speed of which the train is capable and the speed limits imposed by the temporary speed restriction beacons. If the train speed exceeds the maximum permitted speed, various actions are initiated by the train's on-board computer, depending on the severity of the violation. It is ultimately possible for the on-board system to activate the emergency brake automatically if the train's excess speed is too great. The CSLaM system components are: • the on-board control speed limitation (CSL) subsystem; • the trackside beacons; and • the performance monitoring subsystem. Model Structuring and Combining UML and VDM++ Views

  5. The On-board CSL System Model Structuring and Combining UML and VDM++ Views

  6. The CSL Associations class CSL instance variables cabDisplay : CabDisplay; emergencyBrake : EmergencyBrake; onboardComp : OnBoardComp; end CSL Mapping rule 1 There is a one-to-one relationship between classes in UML and classes in VDM++. Mapping rule 2 Every association between two classes at the UML class diagram level must be given a role name Model Structuring and Combining UML and VDM++ Views

  7. Additional basic mapping rules 1 Mapping rule 3: Attributes Attributes inside a UML class are represented as instance variables or values inside the corresponding VDM++ class. The stereotype will indicate the kind, and the default will be instance variables. Mapping rule 4: Functionality Operations inside a UML class are represented as functions and operations in the corresponding VDM++ class, in accordance with the function or operation stereotype, and vice versa. By default the stereotype is operation. Mapping rule 5: Access modifiers All member declarations can have access modifiers at both the UML class diagram; the VDM++ level and the mapping rules for these are one to one. The only exception here is that implementation at the UML class diagram level is considered as private at the VDM++ level. Model Structuring and Combining UML and VDM++ Views

  8. Additional basic mapping rules 2 Mapping rule 6: Static definitions Static member declarations at the VDM++ level correspond to static member declarations at the UML class diagram level, except for operations which cannot be declared static inside Rose. Mapping rule 7: Type definitions Type definitions inside a VDM++ class are simply ignored by the mapping rules because there is no equivalent at the UML class diagram level. This just means that type definitions will only be kept at the VDM++ level. Model Structuring and Combining UML and VDM++ Views

  9. The Beacon Classes 1 • Announcement Beacon: This announces a limitation beacon. The information provided by the beacon is the target speed that must be respected when the limitation beacon is met. Several announcement beacons might be met successively. • Limitation Beacon: The speed restriction is valid as soon as the head of the train reaches the beacon. If a limitation beacon is not preceded by an announcement beacon, a ground fault is raised. • Cancel Beacon: This beacon cancels all announcements present. If no announcement is available, the cancel beacon is ignored. This beacon is used when a speed restriction is announced before a track switch and is not needed in some branches after the switch. • End Beacon: This ends the speed restriction area. The speed restriction is no longer valid as soon as the tail of the train reaches the end beacon. Model Structuring and Combining UML and VDM++ Views

  10. The Beacon Classes 2 class AnnounceBeacon is subclass of Beacon … end AnnounceBeacon Mapping rule 8: Inheritance There is a one-to-one relationship between inheritance in UML class diagrams and inheritance in VDM++. Model Structuring and Combining UML and VDM++ Views

  11. Multiplicity of Associations Mapping rule 9: Association Multiplicity The multiplicity of an association determines its type at the VDM++ level. With “0..n” multiplicity and an ordered constraint the association is modelled as a sequence of object reference types using the sequence type constructor. Model Structuring and Combining UML and VDM++ Views

  12. Qualified Associations class Supervisor instance variables driverInfo: map DriverCard to Driver := {|->}; trainInfo : map TrainId to CSL := {|->}; types public TrainId = token; end Supervisor Mapping rule 10: Qualified Associations Qualified associations use a type (or a class name) as the qualifier and are modelled as a mapping from the qualifier type to the object reference type it is going to (possibly with further multiplicity). Model Structuring and Combining UML and VDM++ Views

  13. Monitoring Driver Performance class CSL instance variables driverCard: [DriverCard] := nil; faults : set of Fault := {}; end CSL Mapping rule 11: Collection Associations The multiplicity of an association determines its type at the VDM++ level. “0 .. n” multiplicity is modelled as an unordered collection of object reference types using the set type constructor. Mapping rule 12: Optional Associations The multiplicity of an association determines its type at the VDM++ level. Unspecified (or with 1) multiplicity is simply modelled as an object reference type. “0 .. 1” multiplicity is modelled as an optional type. Model Structuring and Combining UML and VDM++ Views

  14. Agenda • Combining UML and VDM++ Views • The Enigma Cipher Example Model Structuring and Combining UML and VDM++ Views

  15. The Enigma Cipher • Used by the Germans during the Second World War • Encryption and decryption • Cracked by ”bombes” by the Allies at Bletchley Park • More powerful cypher system cracked by ”Colossus” • Influenced the outcome of the war • Some believe that Alan Turing was involved in the worlds first computer Model Structuring and Combining UML and VDM++ Views

  16. Basic principles of Encryption • Around 1400 Leon Alberti invented the cipher disk • Substition of letters in a monalphabetic fashion • Caesar ciphers have an encoding distance • Distance of 4 would make A -> E and B -> F • Alberti invented a polyalphabetic cipher • Coding distance implemented by a code word e.g. LEON • Now L -> A for the first letter, E -> A for the second letter • Enigma was made of a plugboard, a set of rotors and a reflector • The plugboard replaces letters • The rotors are jointly called a scambler • The reflector is responsible for making it symmetric Model Structuring and Combining UML and VDM++ Views

  17. The Structure of the Enigma Model Structuring and Combining UML and VDM++ Views

  18. Initial UML Class Diagram Model Structuring and Combining UML and VDM++ Views

  19. The Revised Enigma UML Model Model Structuring and Combining UML and VDM++ Views

  20. class Alphabet instance variables alph : seq of char := []; inv AlphabetInv(alph) functions AlphabetInv: seq of char -> bool AlphabetInv (palph) == len palph mod 2 = 0 and card elems palph = len palph operations public Alphabet: seq of char ==> Alphabet Alphabet (pa) == alph := pa pre AlphabetInv(pa); public GetChar: nat ==> char GetChar (pidx) == return alph(pidx) pre pidx in set inds alph; public GetIndex: char ==> nat GetIndex (pch) == let pidx in set {i | i in set inds alph & alph(i) = pch} in return pidx pre pch in set elems alph; public GetIndices: () ==> set of nat GetIndices () == return inds alph; public GetSize: () ==> nat GetSize () == return len alph; public Shift: nat * nat ==> nat Shift (pidx, poffset) == if pidx + poffset > len alph thenreturn pidx + poffset - len alph else return pidx + poffset pre pidx in set inds alph and poffset <= len alph; public Shift: nat ==> nat Shift (pidx) == Shift(pidx, 1) end Alphabet The Alphabet Class Model Structuring and Combining UML and VDM++ Views

  21. The Component Class class Component instance variables protected next : [Component] := nil; protected alph : Alphabet operations public Successors: () ==> set of Component Successors () == if next = nil then return {self} else return {self} union next.Successors(); public SetNext: Component ==> () SetNext (pcom) == next := pcom pre next = nil and self not in set pcom.Successors(); public Substitute: nat ==> nat Substitute (-) == is subclass responsibility; public Rotate: () ==> () Rotate () == skip; public Rotate: nat ==> () Rotate (-) == skip end Component Model Structuring and Combining UML and VDM++ Views

  22. The Configuration Class 1 class Configuration is subclass of Component instance variables protected config: inmap nat to nat; Plugboard {2|->3,3|->2} Rotor {1|->2,2|->1,3|->4,4|->3} Reflector {1|->2,3|->4} Model Structuring and Combining UML and VDM++ Views

  23. The Configuration Class 2 operations protected Encode: nat ==> nat Encode (penc) == if penc in set dom config then return config(penc) else return penc; protected Decode: nat ==> nat Decode (pdec) == let invcfg = inverse config in if pdec in set dom invcfg then return invcfg(pdec) else return pdec; public Substitute: nat ==> nat Substitute(pidx) == return Decode(next.Substitute(Encode(pidx))) pre next <> nil end Configuration Model Structuring and Combining UML and VDM++ Views

  24. The Reflector Class class Reflector is subclass of Configuration instance variables inv ReflectorInv(next, config, alph) functions ReflectorInv: [Component] * inmap nat to nat * Alphabet -> bool ReflectorInv (pnext, pconfig, palph) == pnext = nil and dom pconfig inter rng pconfig = {} and dom pconfig union rng pconfig = palph.GetIndices() operations public Reflector: nat * Alphabet * inmap nat to nat ==> Reflector Reflector (psp, pa, pcfg) == atomic (alph := pa; config := {pa.Shift(i, psp-1) |-> pa.Shift(pcfg(i), psp-1) | i in set dom pcfg}) pre psp in set pa.GetIndices() and ReflectorInv(next, pcfg, pa); public Substitute: nat ==> nat Substitute (pidx) == if pidx in set dom config then Encode(pidx) else Decode(pidx) end Reflector Model Structuring and Combining UML and VDM++ Views

  25. The Rotor Class 1 class Rotor is subclass of Configuration instance variables latch_pos : nat; latch_lock : bool := false; inv RotorInv(latch_pos, config, alph) functions RotorInv: nat * inmap nat to nat * Alphabet -> bool RotorInv (platch_pos, pconfig, palph) == let ainds = palph.GetIndices() in platch_pos in set ainds and dom pconfig = ainds and rng pconfig = ainds and exists x in set dom pconfig & x <> pconfig(x) operations public Rotor: nat * nat * Alphabet * inmap nat to nat ==> Rotor Rotor (psp, plp, pa, pcfg) == atomic (latch_pos := pa.Shift(plp,psp-1); alph := pa; config := {pa.Shift(i,psp-1) |-> pa.Shift(pcfg(i),psp-1) | i in set dom pcfg}) pre psp in set pa.GetIndices() and RotorInv(plp, pcfg, pa); Model Structuring and Combining UML and VDM++ Views

  26. The Rotor Class 2 public Rotate: () ==> () Rotate () == (-- propagate the rotation to the next component and tell it where our latch position is next.Rotate(latch_pos); -- update our own latch position and take the alphabet size into account if latch_pos = alph.GetSize() then latch_pos := 1 else latch_pos := latch_pos+1; -- update the transpositioning relation by shifting all indices one position config := {alph.Shift(i) |-> alph.Shift(config(i)) | i in set dom config}; -- remember the rotation latch_lock := true) preisofclass(Rotor,next) orisofclass(Reflector,next); public Rotate: nat ==> () Rotate (ppos) == -- compare the latch position and the lock if ppos = latch_pos and not latch_lock -- perform the actual rotation then Rotate() -- otherwise reset the lock else latch_lock := false pre ppos in set alph.GetIndices(); end Rotor Model Structuring and Combining UML and VDM++ Views

  27. The Plugboard Class class Plugboard is subclass of Configuration instance variables inv PlugboardInv(config, alph) functions PlugboardInv: inmap nat to nat * Alphabet -> bool PlugboardInv (pconfig, palph) == dom pconfig subset palph.GetIndices() operations public Plugboard: Alphabet * inmap nat to nat ==> Plugboard Plugboard (pa, pcfg) == atomic (alph := pa; config := pcfg munion inverse pcfg) pre dom pcfg inter rng pcfg = {} and PlugboardInv(pcfg, pa); public Substitute: nat ==> nat Substitute (pidx) == (next.Rotate(); Configuration`Substitute(pidx)) pre pidx in set alph.GetIndices() and (isofclass(Rotor,next) orisofclass(Reflector,next)) end Plugboard Model Structuring and Combining UML and VDM++ Views

  28. Redefining Substitute Model Structuring and Combining UML and VDM++ Views

  29. The SimpleEnigma Class class SimpleEnigma is subclass of Component values refcfg : inmap nat to nat = {1 |-> 3, 2 |-> 4}; rotcfg : inmap nat to nat = {1 |-> 2, 2 |-> 4, 3 |-> 3, 4 |-> 1}; pbcfg : inmap nat to nat = {2 |-> 3} operations public SimpleEnigma: () ==> SimpleEnigma SimpleEnigma () == (dcl cp : Component ; alph := new Alphabet("ABCD"); next := new Reflector(4,alph,refcfg); cp := new Rotor(3,3,alph,rotcfg); cp.SetNext(next); next := cp; cp := new Rotor(2,2,alph,rotcfg); cp.SetNext(next); next := cp; cp := new Rotor(1,1,alph,rotcfg); cp.SetNext(next); next := cp; cp := new Plugboard(alph,pbcfg); cp.SetNext(next); next := cp); public Keystroke : char ==> char Keystroke (pch) == let pidx = alph.GetIndex(pch) in return alph.GetChar(next.Substitute(pidx)) preisofclass(Plugboard,next) end SimpleEnigma Model Structuring and Combining UML and VDM++ Views

  30. The VDMUnit Framework Model Structuring and Combining UML and VDM++ Views

  31. The TestSuite Class class TestSuite is subclass of Test instance variables tests : seq of Test := []; operations public Run: () ==> () Run () == (dcl ntr : TestResult := new TestResult(); Run(ntr); ntr.Show()); public Run: TestResult ==> () Run (result) == for test in tests do test.Run(result); public AddTest: Test ==> () AddTest(test) == tests := tests ^ [test]; end TestSuite Model Structuring and Combining UML and VDM++ Views

  32. class TestCase is subclass of Test instance variables name : seq of char operations public TestCase: seq of char ==> TestCase TestCase(nm) == name := nm; public GetName: () ==> seq of char GetName () == return name; protected AssertTrue: bool ==> () AssertTrue (pb) == if not pb then exit <FAILURE>; protected AssertFalse: bool ==> () AssertFalse (pb) == if pb then exit <FAILURE>; The TestCase Class public Run: TestResult ==> () Run (ptr) == trap <FAILURE> with ptr.AddFailure(self) in (SetUp(); RunTest(); TearDown()); protected SetUp: () ==> () SetUp () == is subclass responsibility; protected RunTest: () ==> () RunTest () == is subclass responsibility; protected TearDown: () ==> () TearDown () == is subclass responsibility end TestCase Model Structuring and Combining UML and VDM++ Views

  33. The TestResult Class class TestResult instance variables failures : seq of TestCase := [] operations public AddFailure: TestCase ==> () AddFailure (ptst) == failures := failures ^ [ptst]; public Print: seq of char ==> () Print (pstr) == def - = new IO().echo(pstr ^ "\n") in skip; public Show: () ==> () Show () == if failures = [] then Print ("No failures detected") else for failure in failures do Print (failure.GetName() ^ " failed") end TestResult Model Structuring and Combining UML and VDM++ Views

  34. Enigma Unit Tests Model Structuring and Combining UML and VDM++ Views

  35. Summary • What have I presented today? • The rules for mappings between VDM++ and UML • Illustrated by a small Control Speed Limitation and Monitoring (CSLaM) example for trains • Worked on turning CSLaM into a distributed real-time model • Illustrated the Enigma example in VDM++ • What do you need to do now? • Read chapters 9 and 10 of the book • Start your distributed real time model for your project Model Structuring and Combining UML and VDM++ Views

  36. Quote of the day Science is a differential equation. Religion is a boundary condition. Alan Turing (1912 - 1954) Model Structuring and Combining UML and VDM++ Views

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