The Object Contraint Language by Example

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1 Formal Specification of Software The Object Contraint Language by Example Bernhard Beckert UNIVERSITÄT KOBLENZ-LANDAU B. Beckert: Formal Specification of Software p.1

2 The Classifier Context inv ( c :)? typename expressionname? : OclExpression ( c :)? typename inv expressionname 1? : OclExpression inv expressionname n? : OclExpression n B. Beckert: Formal Specification of Software p.2

3 The Operator Context ( c :)? typename ::opname(p 1 : type 1 ;... ;p k : type k ):rtype {pre,post } expressionname? : OclExpression B. Beckert: Formal Specification of Software p.3

4 Ò Ñ ËØÖ Ò ¹Ñ Ð ËØÖ Ò Ù Ñ ØØ ÔØ ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Ø ØÙ ËØ ØÙ ØÓØ ÐÒÙÑ Ö ÁÒØ Constraints with Attributes È Ô Ö È Ö ÓÒ Ö Ö Ö Ú Û ÙÑÔ ÁÒØ Ú ÐÙ Ø µ ÒÙÑ Ö Ø ÓÒ ËØ ØÙ Paper inv number 1 Ö Ø B. Beckert: Formal Specification of Software p.4

5 Equivalent notational variations Paper inv self.number 1 B. Beckert: Formal Specification of Software p.5

6 Equivalent notational variations Paper inv self.number 1 c:paper inv c.number 1 B. Beckert: Formal Specification of Software p.5

7 Equivalent notational variations Paper inv self.number 1 c:paper inv c.number 1 c:paper inv startcount : c.number 1 B. Beckert: Formal Specification of Software p.5

8 Equivalent notational variations Paper inv self.number 1 c:paper inv c.number 1 c:paper inv startcount : c.number 1 Paper inv startcount : number 1 B. Beckert: Formal Specification of Software p.5

9 Ò Ñ ËØÖ Ò ¹Ñ Ð ËØÖ Ò Ù Ñ ØØ ÔØ ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Ø ØÙ ËØ ØÙ ØÓØ ÐÒÙÑ Ö ÁÒØ Operator Constraint È Ô Ö È Ö ÓÒ Ö Ö Ö Ú Û ÙÑÔ ÁÒØ Ú ÐÙ Ø µ ÒÙÑ Ö Ø ÓÒ ËØ ØÙ Ö Ø pre post c:paper::evaluate() c.status = submitted c.status = accept or c.status = reject B. Beckert: Formal Specification of Software p.6

10 Types Model types The classes form the diagram of an OCL constraint B. Beckert: Formal Specification of Software p.7

11 Types Model types The classes form the diagram of an OCL constraint Basic types Integer, Real, Boolean and String B. Beckert: Formal Specification of Software p.7

12 Types Model types The classes form the diagram of an OCL constraint Basic types Integer, Real, Boolean and String Enumeration types The user defined enumeration types B. Beckert: Formal Specification of Software p.7

13 Types Model types The classes form the diagram of an OCL constraint Basic types Integer, Real, Boolean and String Enumeration types The user defined enumeration types Collection types Set, Bag, Sequence B. Beckert: Formal Specification of Software p.7

14 Types Model types The classes form the diagram of an OCL constraint Basic types Integer, Real, Boolean and String Enumeration types The user defined enumeration types Collection types Set, Bag, Sequence Special types e.g. Ocl Any, OclType B. Beckert: Formal Specification of Software p.7

15 Subtyping T 1, T 2 model types: T 1 < T 2 holds exactly if T 1 is a subclass of T 2 B. Beckert: Formal Specification of Software p.8

16 Subtyping T 1, T 2 model types: T 1 < T 2 holds exactly if T 1 is a subclass of T 2 Integer < Real B. Beckert: Formal Specification of Software p.8

17 Subtyping T 1, T 2 model types: T 1 < T 2 holds exactly if T 1 is a subclass of T 2 Integer < Real For all type expressions T, not denoting a collection type: Set(T) < Collection(T) Bag(T) < Collection(T) Sequence(T) < Collection(T) B. Beckert: Formal Specification of Software p.8

18 Subtyping T 1, T 2 model types: T 1 < T 2 holds exactly if T 1 is a subclass of T 2 Integer < Real For all type expressions T, not denoting a collection type: Set(T) < Collection(T) Bag(T) < Collection(T) Sequence(T) < Collection(T) If T is a model, basic, or enumeration type: T < OCLAny B. Beckert: Formal Specification of Software p.8

19 Subtyping T 1, T 2 model types: T 1 < T 2 holds exactly if T 1 is a subclass of T 2 Integer < Real For all type expressions T, not denoting a collection type: Set(T) < Collection(T) Bag(T) < Collection(T) Sequence(T) < Collection(T) If T is a model, basic, or enumeration type: T < OCLAny If T 1 < T 2 and C is any of the type constructors Collection, Set, Bag, Sequence: C(T 1 ) < C(T 2 ). B. Beckert: Formal Specification of Software p.8

20 Ò Ñ ËØÖ Ò ¹Ñ Ð ËØÖ Ò Ù Ñ ØØ ÔØ ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Ø ØÙ ËØ ØÙ ØÓØ ÐÒÙÑ Ö ÁÒØ Typing Examples È Ô Ö È Ö ÓÒ Ö Ö Ö Ú Û ÙÑÔ ÁÒØ Ú ÐÙ Ø µ constraint p:person ÒÙÑ Ö Ø ÓÒ ËØ ØÙ Ö Ø p.name, p. have type String. constraint c:paper c.number has type Integer, c.status has type Status, c.authors has type Set(Person) B. Beckert: Formal Specification of Software p.9

21 Ò Ñ ËØÖ Ò ¹Ñ Ð ËØÖ Ò ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Constraints with Associations È Ö ÓÒ È Ô Ö ½ Ö Ö Ö Ú Û inv c:paper c.author <> c.referee B. Beckert: Formal Specification of Software p.10

22 Ò Ñ ËØÖ Ò ¹Ñ Ð ËØÖ Ò ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Constraints with Associations È Ö ÓÒ È Ô Ö Ö Ö Ö Ú Û inv c:paper c.authors > intersection(c.referee) > isempty B. Beckert: Formal Specification of Software p.11

23 Ò Ñ ËØÖ Ò ¹Ñ Ð ËØÖ Ò ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Constraints and Navigation È Ö ÓÒ È Ô Ö Ö Ú Û Ö Ú Û Ô Ô Ö Ö Ö Ö ½ ½ Ë ÓÒ c:paper Ö ÓÒ inv not(c.authors > includes(c.session.chair)) Ø ØÐ ËØÖ Ò inv p:person p.reviewed_papers.session.chair > includes(p) B. Beckert: Formal Specification of Software p.12

24 Ò Ñ ËØÖ Ò ¹Ñ Ð ËØÖ Ò ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ allinstances È Ö ÓÒ È Ô Ö Ö Ö Ö Ú Û Person inv Person.allInstances > forall(p p. .size 3) Paper inv Paper.allInstances > forall(p1, p2 p1 <> p2 implies p1.number <> p2.number) B. Beckert: Formal Specification of Software p.13

25 Ò Ñ ËØÖ Ò ¹Ñ Ð ËØÖ Ò ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Avoiding allinstances È Ö ÓÒ È Ô Ö Ö Ö Ö Ú Û Person inv Person.allInstances > forall(p p. .size 3) Can be equivalently replaced by: p:person inv p. .size 3 B. Beckert: Formal Specification of Software p.14

26 Ò Ñ ËØÖ Ò ¹Ñ Ð ËØÖ Ò ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Avoiding allinstances È Ö ÓÒ È Ô Ö Ö Ö Ö Ú Û Paper inv Paper.allInstances > forall(p1, p2 p1 <> p2 implies p1.number <> p2.number) Can be equivalently replaced by: p1,p2:papers inv p1 <> p2 implies p1.number <> p2.number) B. Beckert: Formal Specification of Software p.15

27 Ò Ñ ËØÖ Ò ¹Ñ Ð ËØÖ Ò ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Avoiding allinstances È Ö ÓÒ È Ô Ö Ö Ö Ö Ú Û Ù Ñ ØØ Ô Ô Ö ÓÒ Ö Ò Conference inv self.submitted_papers > forall(p1, p2 p1 <> p2 implies p1.number <> p2.number) Ò Ñ ËØÖ Ò B. Beckert: Formal Specification of Software p.16

28 ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Ô ÁÒØ ØÓØ ÐÒÙÑ Ö ÁÒØ Introducing the iterate Operation È Ô Ö p:papers ÙÑÔ ÁÒØ inv Papers.allInstances > iterate(x:paper ; y:int = 0 y+x.pages) = Papers.sumpages B. Beckert: Formal Specification of Software p.17

29 Syntax of the iterate construct iterator variable term of sort T, initial term range formula t -> iterate(x : S; y : T = t 0 u) accumulator variable term of sort T, step term B. Beckert: Formal Specification of Software p.18

30 iterate: Example 1 Adding a new operation occurences to the built-in OCL type String string.occurences(string2:string):set(integer) The set of positions in string where an occurence of string2 as a substring starts. Strings start with position 0. B. Beckert: Formal Specification of Software p.19

31 iterate: Example 1 Adding a new operation occurences to the built-in OCL type String string.occurences(string2:string):set(integer) The set of positions in string where an occurence of string2 as a substring starts. Strings start with position 0. pre : string2.size =< string.size post : result = { 0.. (string.size - string2.size) } > iterate(x; y:set(integer)=set{} if string.substring(x,x+string2.size) = string2 then y > including(x) else y) B. Beckert: Formal Specification of Software p.19

32 iterate: Example 2 Adding a new operation substringocc to the built-in OCL type String string.substringocc(string2:string):boolean True if string2 occurs at least once as a substring in string. B. Beckert: Formal Specification of Software p.20

33 iterate: Example 2 Adding a new operation substringocc to the built-in OCL type String string.substringocc(string2:string):boolean True if string2 occurs at least once as a substring in string. post : result = (string2.size =< string.size) and not (string.occurences(string2) > isempty) B. Beckert: Formal Specification of Software p.20

34 Quantifiers t > iterate(x; y : Boolean = true y and a) t is an expression of type Set(T) x is a variable of type T a is an expression of type Boolean B. Beckert: Formal Specification of Software p.21

35 Quantifiers t > iterate(x; y : Boolean = true y and a) t is an expression of type Set(T) x is a variable of type T a is an expression of type Boolean Can be equivalently expressed by t >forall(x a) B. Beckert: Formal Specification of Software p.21

36 Quantifiers t > iterate(x; y : Boolean = true y and a) t is an expression of type Set(T) x is a variable of type T a is an expression of type Boolean Can be equivalently expressed by t >forall(x a) Likewise t > iterate(x; y : Boolean = false y or a) B. Beckert: Formal Specification of Software p.21

37 Quantifiers t > iterate(x; y : Boolean = true y and a) t is an expression of type Set(T) x is a variable of type T a is an expression of type Boolean Can be equivalently expressed by t >forall(x a) Likewise t > iterate(x; y : Boolean = false y or a) Can be expressed by t > exists(x a) B. Beckert: Formal Specification of Software p.21

38 Collecting Elements Paper author:person number:int submitted papers Conference name:string totalnumber:integer Boolean:isAuthor(name:String) pre c:conference::isauthor(name:string) true post result = c.sp > collect(p p.author.name) > includes(name) B. Beckert: Formal Specification of Software p.22

39 Reducing collect to iterate set > collect(x expr ) : Bag(T) = set > iterate(x; acc : Bag(T) = Bag{} acc > including(expr) ) Evaluation of c.sp > collect(p p.authors.name) involves implicit flattening. B. Beckert: Formal Specification of Software p.23

40 Selecting Elements Paper authors[*]:person number:int pages:int countshortpapers():integer pre Paper::countShortPapers():Integer true post result = Paper.allInstances > select(p p.pages < 10) > size B. Beckert: Formal Specification of Software p.24

41 Reducing select to iterate s > select(x expr ) : Set(T) = s > iterate(x; acc : Set(T) = Set{} if expr then acc > including(x) else acc) where s is of type Set(T) expr is an OCL expression of type Boolean B. Beckert: Formal Specification of Software p.25

42 ÙØ ÓÖ È Ö ÓÒ ÒÙÑ Ö ÁÒØ Ò Ñ ËØÖ Ò ØÓØ ÐÒÙÑ Ö ÁÒØ Ö Refering to Previous Values ÓÒ Ö Ò È Ô Ö Ù Ñ ØØ Ô Ô Ö È Ô Ö µ pre c:conference::addpaper() true post totalnumber = totalnumber@pre + 1 B. Beckert: Formal Specification of Software p.26

43 Multiple Occurences Ò ½ ÚÓ Ñ µ ÑÔÐÓÝÑ ÒØ Ù ØÓÑ Ö È ÓÔÐ ½ Ø ÒØ c.pa.phone the new phone number of the current p.a. the new phone number of the previous p.a. the old phone number of the current p.a. the old phone number of the previous p.a. B. Beckert: Formal Specification of Software p.27 ÁÒØ Ö Ô ÓÒ Ô

What is OCL? OCL/Context

What is OCL? OCL/Context What is? Software Engineering Lecture 5: Prof. Dr. Peter Thiemann Universität Freiburg SS 20 = object constraint language standard query language of UML 2 specify expressions and constraints in object-oriented