Lecture 2: Semantical Model

Transcription

1 Software Design, Modelling and Analysis in UML Lecture 2: Semantical Model Prof. Dr. Andreas Podelski, Dr. Bernd Westphal Albert-Ludwigs-Universität Freiburg, Germany main

2 ->enable_water(); Idle drinkready C50 OK waitok E1 have_c50> ->enable_soft(); C50 have_c100_or_e1> have_e1 have_c100 E1/itsChoicePanel->enableSoft(); W3 S3 T3 E1/itsChanger ->giveback_100() C50/itsChoicePanel C50 on DWATER/ Prepare_Water(); itscoinvalidator ->GEN(OK); DSOFT/ Prepare_Soft(); itscoinvalidator ->GEN(OK); DTEA/ Prepare_Tea(); itscoinvalidator ->GEN(OK); have_c150> ->enable_tea(); ->giveback_100() C50/ itschanger ->giveback_50() S2 T2 W2 FillingUp DWATER/ Prepare_Water(); itscoinvalidator ->GEN(OK); DSOFT/ Prepare_Soft(); itscoinvalidator ->GEN(OK); DTEA/ Prepare_Tea(); itscoinvalidator ->GEN(OK); Inactive FILLUP/itsCoinValidator ->update_choicepanel(); S1 T1 W1 WATER[Water_enabled] SOFT[Soft_enabled] TEA[Tea_enabled] DWATER/ Prepare_Water(); itscoinvalidator ->GEN(OK); DSOFT/ Prepare_Soft(); itscoinvalidator ->GEN(OK); DTEA/ Prepare_Tea(); itscoinvalidator ->GEN(OK); Water_selected Soft_selected Tea_selected Soft_out Tea_out /disable_all(); Water_out if (itscoinvalidator->is_in(have_c150)) itschanger->giveback_50(); itschanger->giveback_50(); /itsdrinkdispenser ->GEN(DTEA) Request_sent Course Map Entry Action: itschoicepanel Entry Action: itschoicepanel Entry Action: itschoicepanel /itsdrinkdispenser ->GEN(DWATER); itschanger->giveback_100(); else if (itscoinvalidator->is_in(have_c100)) VendingMachine ->enable_water(); E1/ itschanger /itsdrinkdispenser ->GEN(DSOFT); if (itscoinvalidator ->IS_IN(have_c150)) LSC: buy water AC: true AM: invariant I: strict 1 :CoinValidator +fallthrough():void +update_choicepanel() +C50() +E1() +OK() :ChoicePanel Water_enabled : int Soft_enabled : int Tea_enabled : int +disable_all():void +enable_water():void +enable_soft():void +enable_tea():void +WATER() +SOFT() +TEA() +ChoicePanel() 1 1 :DrinkDispenser +Prepare_Water():void +Prepare_Soft():void 1 +Prepare_Tea():void +DWATER() +DTEA() +DSOFT() +FILLUP() 1 1 :Changer 1 +giveback_100():void +giveback_50():void User CoinValidator ChoicePanel Dispenser C50 pwater water_in_stock OK dwater UML W N E CD,SM ϕ OCL CD,SD S Model S = (T, C,V,atr),SM M = (Σ D S,A S, SM ) expr S,SD B = (Q SD,q 0,A S, SD,F SD ) Sleplan Instances π = (σ 0,ε 0 ) (cons 0,Snd 0 ) u 0 (σ 1,ε 1 ) w π = ((σ i,cons i,snd i )) i N G = (N,E,f) OD Mathematics UML 2/20

3 Content Basic Object System Signature (basic) types, classes, typed attributes, attribute mapping. Basic Object System Structure objects / object identities, domains of basic and derived types. System State concrete and symbolic, dangling references, A Complete Example Scontent 3/20

4 Semantical Foundation 4/ main

5 Basic Object System Signature Definition. A (Basic) Object System Signature is a quadruple S = (T, C,V,atr) where T is a set of (basic) types, C is a finite set of classes, V is a finite set of typed attributes, i.e., eachv V has a type τ T, or C 0,1 orc, wherec C (writtenv : τ orv : C 0,1 orv : C ), atr : C 2 V maps each class to its set of attributes. Note: Inspired by OCL 2.0 standard OMG (2006), Annex A. 5/20

6 Basic Object System Signature Example S = (T, C,V,atr) where (basic) types T and classes C (both finite), typed attributesv,τ from T, orc 0,1 orc, for somec C, atr : C 2 V mapping classes to attributes. Example: S 0 = ({Int},{C,D},{x : Int,p : C 0,1,n : C },{C {p,n},d {x}}) 6/20

7 Basic Object System Signature Another Example S = (T, C,V,atr) where (basic) types T and classes C (both finite), typed attributesv,τ from T, orc 0,1 orc, for somec C, atr : C 2 V mapping classes to attributes. Example: 7/20

8 Basic Object System Structure Definition. A Basic Object System Structure of S = (T, C,V,atr) is a domain function D which assigns to each type a domain, i.e. τ T is mapped to D(τ), C C is mapped to an infinite set D(C) of (object) identities. Note: Object identities only have the =" operation. Sets of object identities for different classes are disjoint, i.e. C,D C : C D D(C) D(D) =. C andc 0,1 forc C are mapped to2 D(C). We use D(C) to denote C C D(C); analogously D(C ). Note: We identify objects and object identities, because both uniquely determine each other (cf. OCL 2.0 standard). 8/20

9 Basic Object System Structure Example Wanted: a structure for signature S 0 = ({Int},{C,D},{x : Int,p : C 0,1,n : C },{C {p,n},d {x}}) D needs to map: τ T to some D(τ), C C to some set of identities D(C) (infinite, disjoint for different classes), C andc 0,1 forc C : always mapped to D(C ) = D(C 0,1 ) = 2 D(C). D(Int) = Z D(C) = N + {C} = {1 C,2 C,3 C,...} D(D) = N + {D} = {1 D,2 D,3 D,...} D(C 0,1 ) = D(C ) = 2 D(C) D(D 0,1 ) = D(D ) = 2 D(D) 9/20

10 System State Definition. Let D be a structure of S = (T, C,V,atr). A system state of S wrt. D is a type-consistent mapping σ : D(C) (V (D(T ) D(C ))). That is, for eachu D(C),C C, ifu dom(σ) dom(σ(u)) = atr(c) σ(u)(v) D(τ) ifv : τ,τ T σ(u)(v) D(D ) ifv : D 0,1 orv : D withd C We callu D(C) alive inσ if and only ifu dom(σ). We useσ D S to denote the set of all system states of S wrt.d. 10/20

11 System State Example S 0 = ({Int},{C,D},{x : Int,p : C 0,1,n : C },{C {p,n},d {x}}) D(Int) = Z, D(C) = {1 C,2 C,3 C,...}, D(D) = {1 D,2 D,3 D,...} Wanted: σ : D(C) (V (D(T ) D(C ))) such that (i)dom(σ(u)) = atr(c), and (ii)σ(u)(v) D(τ) ifv : τ,τ T, (iii)σ(u)(v) D(C ) ifv : D withd C. 11/20

12 System State Example S 0 = ({Int},{C,D},{x : Int,p : C 0,1,n : C },{C {p,n},d {x}}) D(Int) = Z, D(C) = {1 C,2 C,3 C,...}, D(D) = {1 D,2 D,3 D,...} Wanted: σ : D(C) (V (D(T ) D(C ))) such that (i)dom(σ(u)) = atr(c), and (ii)σ(u)(v) D(τ) ifv : τ,τ T, (iii)σ(u)(v) D(C ) ifv : D withd C. Two options: Concrete, explicit identities: σ = {1 C {p,n {5 C }},5 C {p,n },1 D {x 23}}. Alternative: symbolic system state. σ = {c 1 {p,n {c 2 }},c 2 {p,n },d {x 23}} assumingc 1,c 2 D(C),d D(D),c 1 c 2. 12/20

13 System State: Spot the 10 (?) Mistakes S 0 = ({Int},{C,D},{x : Int,p : C 0,1,n : C },{C {p,n},d {x}}) D(Int) = Z, D(C) = {1 C,2 C,3 C,...}, D(D) = {1 D,2 D,3 D,...} Wanted: σ : D(C) (V (D(T ) D(C ))) such that (i)dom(σ(u)) = atr(c), and (ii)σ(u)(v) D(τ) ifv : τ,τ T, (iii)σ(u)(v) D(C ) ifv : D withd C. σ = {1 C {p,n {5 C }}, 5 C {p,n 1 C }, 1 D {x 2.3}}. σ = {1 C {p,n {5 C }}, 5 C {p 1 C,n }, 1 D {x 23}}. σ = {1 C {p,n {1 D }}, 5 C {p,n }, 1 D {x 22}}. σ = {1 C {p,n {5 C }}, 5 C {n }, 1 D {x 1,p {1 C }}}. σ = {1 C {p,n {5 C }}, 5 C {p,n {9 C }}} 13/20

14 Dangling References Definition. Letσ Σ D S be a system state. We say attributev V 0,1,, i.e. v : C 0,1 or v : C, in object u dom(σ) has a dangling reference if and only if the attribute s value comprises an object which is not alive inσ, i.e. if σ(u)(v) dom(σ). We callσ closed if and only if no attribute has a dangling reference in any object alive inσ. Example: σ = {1 C {p,n {5 C }}} 14/20

15 A Complete Example: Vending Machine Structure 15/20

16 You Are Here. 16/ main

17 Course Map UML CD,SM ϕ OCL CD,SD Model S = (T, C,V,atr),SM M = (Σ D S,A S, SM ) expr S,SD B = (Q SD,q 0,A S, SD,F SD ) Instances π = (σ 0,ε 0 ) (cons 0,Snd 0 ) u 0 (σ 1,ε 1 ) w π = ((σ i,cons i,snd i )) i N G = (N,E,f) Mathematics main OD UML 17/20

18 Tell Them What You ve Told Them... We can directly use object system signatures to model the structure of systems. We don t need diagrams, they will be more pleasent to read. We introduce basic types and classes, basic type and derived type attributes, and assign to each class a set of attributes. Object system structures provide domains for basic and derived types. An object system signature S and an object system structure D uniquely define the setσ D S of system states. Outlook: Sttwytt Object system signatures will be used to capture the abstract syntax of class diagrams. OCL expressions will be evaluated on system states. State machines will define sequences of system configurations (consisting of a system state and an ether). 18/20

19 References 19/ main

20 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/ main 20/20