Lecture 03: Object Constraint Language

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1 Software Design, Modelling and Analysis in UML Lecture 03: Object Constraint Language Prof. Dr. Andreas Podelski, Dr. Bernd Westphal Albert-Ludwigs-Universität Freiburg, Germany main

2 Content The Object Constraint Language (OCL): Syntax Running Example Overview Expressions Notational Conventions (. (OCL-Dot) and -> (OCL-Arrow)) Constants & Arithmetics Iterate Context More Notational Conventions The Running Example Revisited Not Interesting Scontent 2/24

3 (Core) OCL Syntax OMG (2006) 3/ main

4 Overview expr ::= w : τ(w) expr 1 = τ expr 2 : τ τ Bool oclisundefined τ (expr 1 ) : τ Bool {expr 1,...,expr n } : τ τ Set(τ) size(expr 1 ) : Set(τ) Int allinstances C : Set(τ C ) v(expr 1 ) : τ C τ(v) r 1 (expr 1 ) : τ C τ D r 2 (expr 1 ) : τ C Set(τ D ) true, false : Bool notexpr 1 : Bool Bool expr 1 {and,or,implies}expr 2 : Bool Bool Bool... OclUndefined τ : τ expr 1 ->iterate(w 1 :T 1 ;w 2 :T 2 =expr 2 expr 3 ) : Set(τ 0 ) τ T2 context ::= contextw 1 :T 1,...,w n :T n inv :expr : Bool 4/24

5 Recall: Vending Machine Structure S = ({Bool,Int},{VM,CP,DD}, {cp : CP,dd : DD 0,1,wen : Bool,wis : Nat}, {VM {cp,dd},cp {wen,dd},dd {wis}) Claim: this is a proper OCL constraint over S : context CP inv : wen implies dd.wis > 0 5/24

6 Plan expr ::= w : τ(w) expr 1 = τ expr 2 : τ τ Bool oclisundefined τ (expr 1 ) : τ Bool {expr 1,...,expr n } : τ τ Set(τ) size(expr 1 ) : Set(τ) Int allinstances C : Set(τ C ) v(expr 1 ) : τ C τ(v) r 1 (expr 1 ) : τ C τ D r 2 (expr 1 ) : τ C Set(τ D ) true, false : Bool notexpr 1 : Bool Bool expr 1 {and,or,implies}expr 2 : Bool Bool Bool... OclUndefined τ : τ expr 1 ->iterate(w 1 :T 1 ;w 2 :T 2 =expr 2 expr 3 ) : Set(τ 0 ) τ T2 context ::= contextw 1 :T 1,...,w n :T n inv :expr : Bool 6/24

7 OCL Syntax 1/4: Expressions expr ::= w : τ(w) Where, given S = (T, C,V,atr), w W {self C : τ C C C} is a set of typed logical variables, w has typeτ(w) expr 1 = τ expr 2 : τ τ Bool oclisundefined τ (expr 1 ) : τ Bool {expr 1,...,expr n } : τ τ Set(τ) isempty(expr 1 ) : Set(τ) Bool size(expr 1 ) : Set(τ) Int allinstances C : Set(τ C ) τ is any type from T T B T C {Set(τ 0 ) τ 0 T T B T C } T B is a set of (OCL) basic types, in the following we use T B = {Bool,Int,String} T C = {τ C C C} is the set of object types, Set(τ 0 ) denotes the set-of-τ 0 type forτ 0 T B T C (sufficient because of flattening (cf. standard)). v(expr 1 ) : τ C τ where v : τ atr(c), τ T, r 1 (expr 1 ) : τ C τ D where r 1 : D 0,1 atr(c),c,d C, r 2 (expr 1 ) : τ C Set(τ D ) where r 2 : D atr(c),c,d C. 7/24

8 Expression Examples expr ::= w : τ(w) size(expr 1 ) : Set(τ) Int expr 1 = τ expr 2 : τ τ Bool oclisundefined τ (expr 1 ) : τ Bool {expr 1,...,expr n } : τ τ Set(τ) isempty(expr 1 ) : Set(τ) Bool allinstances C : Set(τ C ) v(expr 1 ) : τ C τ(v) r 1 (expr 1 ) : τ C τ D r 2 (expr 1 ) : τ C Set(τ D ) S 0 = ({Int},{C,D},{x : Int,p : C 0,1,n : C },{C {p,n},d {x}}) 8/24

9 Expression Examples expr ::= w : τ(w) size(expr 1 ) : Set(τ) Int expr 1 = τ expr 2 : τ τ Bool oclisundefined τ (expr 1 ) : τ Bool {expr 1,...,expr n } : τ τ Set(τ) isempty(expr 1 ) : Set(τ) Bool allinstances C : Set(τ C ) v(expr 1 ) : τ C τ(v) r 1 (expr 1 ) : τ C τ D r 2 (expr 1 ) : τ C Set(τ D ) S 0 = ({Int},{C,D},{x : Int,p : C 0,1,n : C },{C {p,n},d {x}}) context CP inv : wen implies dd.wis > 0 8/24

10 Notational Conventions for Expressions Each expression ω(expr 1,expr 2,...,expr n ) : τ 1 τ n τ may alternatively be written ( abbreviated as ) expr 1. ω(expr 2,...,expr n ) ifτ 1 is an object type, i.e. ifτ 1 T C. expr 1 -> ω(expr 2,...,expr n ) ifτ 1 is a collection type (here: only sets), i.e. ifτ 1 = Set(τ 0 ) for someτ 0 T B T C. Examples: ({Int},{C,D},{x : Int,p : C 0,1,n : C },{C {p,n},d {x}}) self C.p self C.p.n self C.p.n->isEmpty context CP inv : wen implies dd.wis > 0 (atr(cp) = {wen : Bool,dd : DD 0,1 }) 9/24

11 OCL Syntax 2/4: Constants & Arithmetics For example: expr ::=... true, false : Bool expr 1 {and,or,implies}expr 2 : Bool Bool Bool notexpr 1 : Bool Bool 0, 1,1, 2,2,... : Int expr 1 {+,,...}expr 2 : Int Int Int expr 1 {<,,...}expr 2 : Int Int Bool OclUndefined τ : τ Generalised notation: expr ::= ω(expr 1,...,expr n ) : τ 1 τ n τ withω {+,,...} 10/24

12 Constants & Arithmetics Examples expr ::=... true, false : Bool expr 1 {and,or,implies}expr 2 : Bool Bool Bool notexpr 1 : Bool Bool 0, 1,1, 2,2,... : Int expr 1 {+,,...}expr 2 : Int Int Int expr 1 {<,,...}expr 2 : Int Int Bool OclUndefined τ : τ S 0 = ({Int},{C,D},{x : Int,p : C 0,1,n : C },{C {p,n},d {x}}) context CP inv : wen implies dd.wis > 0 11/24

13 OCL Syntax 3/4: Iterate expr ::= expr 1 ->iterate(w 1 :T 1 ;w 2 :T 2 =expr 2 expr 3 ) or, with a little renaming, expr ::= expr 1 ->iterate(iter :T 1 ;result :T 2 =expr 2 expr 3 ) where expr 1 is of a collection type (here: a setset(τ 0 ) for someτ 0 ), iter W is called iterator, of the type denoted byt 1 (ift 1 is omitted,τ 0 is assumed as type ofiter) result W is called result variable, gets typeτ 2 denoted byt 2, expr 2 in an expression of typeτ 2 giving the initial value forresult, (OclUndefined τ2, if omitted) expr 3 is an expression of typeτ 2, in particulariter andresult may appear inexpr 3. 12/24

14 Iterate Example S = ({Bool,Int},{VM,CP,DD}, {cp : CP,dd : DD 0,1,wen : Bool,wis : Nat}, {VM {cp,dd},cp {wen,dd},dd {wis}) expr ::= expr 1 ->iterate(w 1 :T 1 ;w 2 :T 2 =expr 2 expr 3 ) 13/24

15 Abbreviations on Top of Iterate expr ::= expr 1 ->iterate(w 1 :T 1 ;w 2 :T 2 =expr 2 expr 3 ) expr 1 ->forall(w 1 : τ 1 expr 3 ) is an abbreviation for expr 1 ->iterate(w 1 :T 1 ;w 2 :Bool =true w 2 and expr 3 ). expr 1 ->Exists(w : τ 1 expr 3 ) is an abbreviation for To ensure confusion, we may again omit all kinds of things, cf. OMG (2006). 14/24

16 Recall: Overview expr ::= w : τ(w) expr 1 = τ expr 2 : τ τ Bool oclisundefined τ (expr 1 ) : τ Bool {expr 1,...,expr n } : τ τ Set(τ) size(expr 1 ) : Set(τ) Int allinstances C : Set(τ C ) v(expr 1 ) : τ C τ(v) r 1 (expr 1 ) : τ C τ D r 2 (expr 1 ) : τ C Set(τ D ) true, false : Bool notexpr 1 : Bool Bool expr 1 {and,or,implies}expr 2 : Bool Bool Bool... OclUndefined τ : τ expr 1 ->iterate(w 1 :T 1 ;w 2 :T 2 =expr 2 expr 3 ) : Set(τ 0 ) τ T2 context ::= contextw 1 :T 1,...,w n :T n inv :expr : Bool 15/24

17 More Iterate Examples S = ({Bool,Int},{VM,CP,DD}, {cp : CP,dd : DD 0,1,wen : Bool,wis : Nat}, {VM {cp,dd},cp {wen,dd},dd {wis}) expr ::= expr 1 ->iterate(w 1 :T 1 ;w 2 :T 2 =expr 2 expr 3 ) 16/24

18 OCL Syntax 4/4: Context Syntax: (Assuming signature S = (T, C,V,atr).) context ::= contextw 1 :T 1,...,w n :T n inv :expr wheret i C andw i : τ Ti W for all1 i n,n 0. Semantics: contextw 1 : C 1,...,w n : C n inv :expr is (just) an abbreviation for allinstances C1 ->forall(w 1 : τ C1... allinstances Cn ->forall(w n : τ Cn expr )... ) 17/24

19 Context: More Notational Conventions For context self : T inv :expr we may alternatively write ( abbreviate as ) context T inv :expr Within the latter abbreviation, we may omit the self in expressionexpr, i.e. for context T inv :self.v (which is an abbreviation for context T inv :v(self) ) we may alternatively write ( abbreviate as ) context T inv :v 18/24

20 The Running Example context CP inv : wen implies dd.wis > 0 19/24

21 Recall: Overview expr ::= w : τ(w) expr 1 = τ expr 2 : τ τ Bool oclisundefined τ (expr 1 ) : τ Bool {expr 1,...,expr n } : τ τ Set(τ) size(expr 1 ) : Set(τ) Int allinstances C : Set(τ C ) v(expr 1 ) : τ C τ(v) r 1 (expr 1 ) : τ C τ D r 2 (expr 1 ) : τ C Set(τ D ) true, false : Bool notexpr 1 : Bool Bool expr 1 {and,or,implies}expr 2 : Bool Bool Bool... OclUndefined τ : τ expr 1 ->iterate(w 1 :T 1 ;w 2 :T 2 =expr 2 expr 3 ) : Set(τ 0 ) τ T2 context ::= contextw 1 :T 1,...,w n :T n inv :expr : Bool 20/24

22 Not Interesting Among others: Enumeration types Type hierarchy Complete list of arithmetical operators The two other collection types Bag and Sequence Casting Runtime type information Pre/post conditions (maybe later, when we officially know what an operation is)... 22/24

23 References 23/ main

24 References OMG (2006). Object Constraint Language, version 2.0. Technical Report formal/ OMG (2011a). Unified modeling language: Infrastructure, version Technical Report formal/ OMG (2011b). Unified modeling language: Superstructure, version Technical Report formal/ Warmer, J. and Kleppe, A. (1999). The Object Constraint Language. Addison-Wesley main 24/24

Software Design, Modelling and Analysis in UML

Software Design, Modelling and Analysis in UML Lecture 03: Object Constraint Language (OCL) 2013-10-28 03 2013-10-28 main Prof. Dr. Andreas Podelski, Dr. Bernd Westphal Albert-Ludwigs-Universität Freiburg,