Content • Inheritance • Abstract syntax Software Design, Modelling and Analysis in UML • Liskov Substitution Principle • Well-typedness with inheritance • Subset-semantics vs. uplink-semantics Lecture 22: Meta-Modelling Inheritance • Meta-Modelling • Idea • Experiment : can we model classes ? • Revisit the UML 2.x standard 2017-02-07 (vs. experiment ) • Meta Object Facility (MOF) • The principle illustrated (once again) Prof. Dr. Andreas Podelski, Dr. Bernd Westphal • And That’s It! • The map – in hindsight. Albert-Ludwigs-Universität Freiburg, Germany – 22 – 2017-02-07 – Scontent – • Educational objectives – useful questions . – 22 – 2017-02-07 – main – – 22 – 2017-02-07 – main – • Any open questions? 2 /41 3 /41 Abstract Syntax Inheritance: Concrete Syntax Desired Semantics of Specialisation: Subtyping A signature with inheritance is a tuple Common graphical representations (of ⊳ = { ( C, D 1 ) , ( C, D 2 ) } ): There is a classical description of what one expects from sub-types , which is closely related to inheritance in object-oriented approaches: S = ( T , C , V, atr , E , F, mth , ⊳ ) C C C The principle of type substitutability : where Liskov Substitution Principle (LSP) Liskov (1988); Liskov and Wing (1994). • ( T , C , V, atr , E ) is a signature with signals and behavioural features D 1 D 2 D 1 D 2 D 1 D 2 ( F/ mth are methods, analogous to V/ atr attributes), and Mapping Concrete to Abstract Syntax by Example: • ⊳ ⊆ ( C × C ) ∪ ( E × E ) is an acyclic generalisation relation, i.e. C ⊳ + C for no C ∈ C . C 0 x : Int In the following (for simplicity), we assume that all attribute (method) names are of the form C :: v and C :: f for some C ∈ C ∪ E (“ fully qualified names ”). Read C ⊳ D as... D C 1 x : Int • D inherits from C , • C is a generalisation of D , • D is a specialisation of C , – 22 – 2017-02-07 – Ssyntax – – 22 – 2017-02-07 – Ssyntax – – 22 – 2017-02-07 – Slsp – • C is a super-class of D , C 2 • D is a sub-class of C , • ... Note : we can have multiple inheritance . 4 /41 5 /41 6 /41
Desired Semantics of Specialisation: Subtyping Static Sub-Typing Session 0,1 FrontEnd itsSession dump () There is a classical description of what one expects from sub-types , which is closely related to inheritance in object-oriented approaches: VIPSession The principle of type substitutability : Liskov Substitution Principle (LSP) Liskov (1988); Liskov and Wing (1994). “If for each object o S of type S Domain Inclusion vs. Uplink Semantics In FrontEnd’s there is an object o T of type T state machine: such that for all programs P defined in terms of T the behavior of P is unchanged when o S is substituted for o T / itsSession := new Session s 0 then S is a subtype of T .” / itsSession . dump () s 2 s 3 In other words: Fischer and Wehrheim (2000) s 1 “An instance of the sub-type shall be usable / itsSession := new VIPSession whenever an instance of the supertype was expected, without a client being able to tell the difference .” – 22 – 2017-02-07 – Sinhessence – – 22 – 2017-02-07 – Sinhessence – – 22 – 2017-02-07 – Slsp – 6 /41 7 /41 8 /41 System States with Inheritance Inheritance and State-Machines: Example Inheritance and State-Machines: Example Wanted : a formal representation of “if C ⊳ ∗ D then D ‘ is a ’ C ”, that is, • • /n ! F /n ! F SM A : s 1 s 2 SM A : s 1 s 2 (i) D has the same attributes and behavioural features as C , and n � � signal � � n � signal � � � A C A C 0 , 1 E 0 , 1 E (ii) D objects (identities) can replace C objects. • • E/ E/ Two approaches to semantics: � � signal � � � � signal � � D SM D : s 1 s 2 D SM D : s 1 s 2 F F • Domain-inclusion Semantics (more theoretical ) u 1 : A u 1 : A u 1 : A u 1 : A u 1 : A st = s 1 st = s 2 st = s 1 st = s 2 st = s 2 stable = 0 stable = 1 stable = 0 stable = 1 stable = 1 n n n n n u 2 : D u 2 : D u 2 : D u 2 : D u 2 : D st = s 1 st = s 1 st = s 1 ( ∅ , { ( u 3 : F,u 2 ) } ) (? , ?) st = s 1 ( ∅ , { ( u 3 : F,u 2 ) } ) ( { F } , ∅ ) st = s 2 • Uplink Semantics (more technical ) − − − − − − − − − − → stable = 1 − − − → − − − − − − − − − − → stable = 1 − − − − − → stable = 1 stable = 1 stable = 1 u 1 ? u 1 u 2 u 3 : F u 3 : F – 22 – 2017-02-07 – Sinhessence – – 22 – 2017-02-07 – Sinhessence – – 22 – 2017-02-07 – Sinhessence – ε = ǫ ε = ( u 2 , u 3 : F ) ε = ǫ ε = ( u 2 , u 3 : F ) ε = ǫ 9 /41 10 /41 10 /41
s Student 0 , 1 att : Int Recall: Subtyping Subtyping: Example Teacher t 0 , 1 (ii) Dispatch GenStWorker There is a classical description of what one expects from sub-types , which is closely related to workload : Int Genius Polite Clown ( cons , Snd ) ( � , � ) ( � � , � � ) � � � � � � � � inheritance in object-oriented approaches: u SM Teacher • • if s 1 /t ! Silence s 1 The principle of type substitutability : s : Student SM Student • u � dom( � ) � D ( C ) � � u E � D ( E ) : u E � ready ( � , u ) GoodAns / [ s. att > 0] /s ! Q : Teacher Q/ Liskov Substitution Principle (LSP) Liskov (1988); Liskov and Wing (1994). att = 3 t /t ! GoodAns s 2 s 2 • u is stable and in state machine state s , i.e. � ( u )( stable ) = 1 and � ( u )( st ) = s , /t ! WrongAns “If for each object o S of type S • • a transition is enabled , i.e. s 1 WrongAns / there is an object o T of type T s SM Genius � ( s, F, expr , act , s � ) �� ( SM C ) : F = E � I � expr � (˜ : Teacher : Genius � , u ) = 1 Q/ t such that for all programs P defined in terms of T /t ! GoodAns s 2 where ˜ � = � [ u. params E 7 � u E ] . the behavior of P is unchanged when o S is substituted for o T • /t ! Silence s 1 and then S is a subtype of T .” s SM Polite : Teacher : Polite Q/ • ( � � , � � ) results from applying t act to ( � , � ) and removing u E from the ether, i.e. t /t ! GoodAns s 2 In other words: Fischer and Wehrheim (2000) ( � �� , � � ) � t act [ u ](˜ � , � � u E ) , • � � = ( � �� [ u. st 7 � s � , u. stable 7 � b, u. params E 7 � � ]) | D ( C ) \{ u E } s 1 “An instance of the sub-type shall be usable s SM Clown : Teacher : Clown Q/ whenever an instance of the supertype was expected, t /t ! StupidJoke where b depends (see (i)) s 2 without a client being able to tell the difference .” – 12 – 2016-12-13 – Sstmrtc – • Consumption of u E and the side effects of the action are observed, i.e. • – 22 – 2017-02-07 – Sinhessence – – 22 – 2017-02-07 – Sinhessence – – 22 – 2017-02-07 – Sinhessence – • SM GenStWorker cons = { u E } , Snd = Obs t act [ u ](˜ � , � � u E ) . s 1 • s : Teacher : GenStWorker s 3 Q/ t /t ! GoodAns Task / s 2 21 /32 11 /41 12 /41 13 /41 Meta-Modelling: Why and What Meta-Modelling: Example • Meta-Modelling is one major prerequisite for understanding For example, let’s consider a class. • the standard documents OMG (2011a,b), and • A class has ( among others ) • the MDA ideas of the OMG. • a name , • any number of attributes , • The idea is somewhat simple : Meta-Modelling: Idea • any number of behavioural features . • if a modelling language is about modelling things , Each of the latter two has • and if UML models are things , • a name and • then why not describe (or: model ) the set of all UML models using a modelling language ? • a visibility . Behavioural features in addition have • a boolean attribute isQuery , • any number of parameters, • a return type. Can we model this (in UML, for a start)? – 22 – 2017-02-07 – Smm – – 22 – 2017-02-07 – Smm – – 22 – 2017-02-07 – main – 14 /41 15 /41 16 /41
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