Lecture 03: Object Constraint Language

(1)

–main–

Software Design, Modelling and Analysis in UML

Lecture 03: Object Constraint Language

2014-10-29

Prof. Dr. Andreas Podelski, Dr. Bernd Westphal

Albert-Ludwigs-Universit¨at Freiburg, Germany

(2)

Contents & Goals

03–2014-10-29–Sprelim–

Last Lecture:

• Basic Object System Signature S and Structure D, System State σ ∈ Σ^D_S

This Lecture:

• Educational Objectives: Capabilities for these tasks/questions:

• Please explain this OCL constraint.

• Please formalise this constraint in OCL.

• Does this OCL constraint hold in this system state?

• Give a system state satisfying this constraint?

• Please un-abbreviate all abbreviations in this OCL expression.

• In what sense is OCL a three-valued logic? For what purpose?

• How are D(C) and T_C related?

• Content:

• OCL Syntax

• OCL Semantics (over system states)

(3)

Recall. . .

–main–

(4)

03–2014-10-29–Srunningexa–

A Complete Example: Vending Machine

–2–2015-10-22–Ssemdom–

15_/34

context DD inv : wen implies win > 0

(5)

(Core) OCL Syntax OMG (2006)

–main–

(6)

OCL Syntax 1/4: Expressions

03–2014-10-29–Soclsyn–

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 )

| isEmpty( expr

1

) : Set ( τ ) → Bool

| 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

)

Where, given S = (T,C, V,atr),

• W ⊇ {self _C : τ_C | C ∈ C}

is a set of typed logical variables, w has type τ(w)

• τ is any type from T ∪ T_B ∪ TC

∪ {Set(τ₀) | τ₀ ∈ T ∪ T_B ∪ TC}

• T_B is a set of (OCL) basic types, in the following we use T_B = {Bool,Int,String}

• TC = {τC | C ∈ C} is the set of object types,

• Set(τ₀) denotes the set-of-τ₀ type for τ₀ ∈ T_B ∪ TC

(sufficient because of

“flattening” (cf. standard))

• v : T(v) ∈ atr(C), T(v) ∈ T ,

• r₁ : D_0,1 ∈ atr(C),

• r₂ : D_∗ ∈ atr(C),

• C, D ∈ C.

(7)

Expression Examples

–Soclsyn–

expr ::=

w : τ(w)

| expr₁=^τexpr₂ : τ × τ → Bool

| oclIsUndefined^τ(expr1) : τ → Bool

| {expr1,. . . ,exprn} : τ × · · · × τ → Set(τ)

| isEmpty(expr1) : Set(τ) → Bool

| size(expr1) : Set(τ) → Int

| allInstances^C : Set(τ^C)

| v(expr1) : τC → τ(v)

| r¹(expr1) : τC → τD

| r2(expr1) : τC → Set(τ^D)

S₀ = ({Int},{C, D},{x : Int, p : C₀_,₁, n : C_∗},{C 7→ {p, n}, D 7→ {x}})

(8)

Expression Examples

03–2014-10-29–Soclsyn–

expr ::=

w : τ(w)

| expr₁=^τexpr₂ : τ × τ → Bool

| oclIsUndefined^τ(expr1) : τ → Bool

| {expr1,. . . ,exprn} : τ × · · · × τ → Set(τ)

| isEmpty(expr1) : Set(τ) → Bool

| size(expr1) : Set(τ) → Int

| allInstances^C : Set(τ^C)

| v(expr1) : τC → τ(v)

| r¹(expr1) : τC → τD

| r2(expr1) : τC → Set(τ^D)

S₀ = ({Int},{C, D},{x : Int, p : C₀_,₁, n : C_∗},{C 7→ {p, n}, D 7→ {x}})

context DD inv : wen implies win > 0

(9)

Notational Conventions for Expressions

–Soclsyn–

• 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

) if τ

1

is an object type, i.e. if τ

1

∈ T

C

.

• expr

1

-> ω (expr

2

, . . . , expr

n

) if τ

1

is a collection type

(here: only sets), i.e. if τ

1

= Set ( τ

0

) for some τ

0

∈ T

B

∪ T

C

.

(10)

Notational Conventions for Expressions

03–2014-10-29–Soclsyn–

• 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

) if τ

1

is an object type, i.e. if τ

1

∈ T

C

.

• expr

1

-> ω (expr

2

, . . . , expr

n

) if τ

1

is a collection type

(here: only sets), i.e. if τ

1

= Set ( τ

0

) for some τ

0

∈ T

B

∪ T

C

.

• Examples:

(self : τ_C ∈ W; v, w : Int ∈ V ; r₁ : D_0,1, r₂ : D_∗ ∈ V )

• self . v

• self . r

1

. w

• self . r

2

-> isEmpty

(11)

OCL Syntax 2/4: Constants & Arithmetics

–Soclsyn–

For example : expr ::= . . .

| true , false : Bool

| expr

1

{and , or , implies} expr

2

: Bool × Bool → Bool

| not expr

1

: Bool → Bool

| 0 , −1 , 1 , −2 , 2 , . . . : Int

| OclUndefined

^τ

: τ

| expr

1

{+ , − , . . . } expr

2

: Int × Int → Int

| expr

1

{ <, ≤ , . . . } expr

2

: Int × Int → Bool

Generalised notation:

expr ::= ω (expr

1

, . . . , expr

n

) : τ

1

× · · · × τ

n

→ τ

(12)

Constants & Arithmetics Examples

03–2014-10-29–Soclsyn–

expr ::= . . .

| true,false : Bool

| expr1 {and,or,implies} expr2 : Bool × Bool → Bool

| not expr₁ : Bool → Bool

| 0,−1,1,−2,2, . . . : Int

| OclUndefinedτ : τ

| expr₁ {+,−, . . .} expr₂ : Int × Int → Int

| expr1 {<,≤, . . .} expr2 : Int × Int → Bool

S₀ = ({Int},{C, D},{x : Int, p : C_0,1, n : C_∗},{C 7→ {p, n}, D 7→ {x}})

context DD inv : wen implies win > 0

(13)

OCL Syntax 3/4: Iterate

–Soclsyn–

expr ::= · · · | expr

1

-> iterate( w

1

: τ

1

; w

2

: τ

2

= expr

2

| expr

3

)

or, with a little renaming,

expr ::= · · · | expr

1

-> iterate(iter : τ

1

; result : τ

2

= expr

2

| expr

3

)

where

• expr1 is of a collection type (here: a set Set(τ₀) for some τ₀),

• iter ∈ W is called iterator, gets type τ₁

(if τ₁ is omitted, τ₀ is assumed as type of iter)

• result ∈ W is called result variable, gets type τ₂,

• expr₂ in an expression of type τ₂ giving the initial value for result,

(14)

Iterate: Intuitive Semantics (Formally: later)

03–2014-10-29–Soclsyn–

expr ::= expr₁->iterate(iter : τ₁;

result : τ₂ = expr₂ | expr₃)

Set(τ₀) hlp = expr₁; τ₁ iter;

τ₂ result = expr₂;

while (!hlp.empty()) do iter = hlp.pop();

result = expr₃; od

Note: In our (simplified) setting, we always have expr₁ : Set(τ₁) and τ₀ = τ₁. In the type hierarchy of full OCL with inheritance and oclAny,

they may be different and still type consistent.

(15)

Abbreviations on Top of Iterate

–Soclsyn–

expr ::= expr₁->iterate(w₁ : τ₁; w₂ : τ₂ = expr₂ | expr₃)

•

^expr₁_->forAll(w₁ : τ₁ | expr₃)

(16)

Abbreviations on Top of Iterate

03–2014-10-29–Soclsyn–

expr ::= expr₁->iterate(w₁ : τ₁; w₂ : τ₂ = expr₂ | expr₃)

•

^expr₁_->forAll(w₁ : τ₁ | expr₃)

is an abbreviation for

expr₁->iterate(w₁: τ₁; w₂ : Bool = true | w₂ and expr₃).

• expr₁->Exists(w : τ₁ | expr₃)

To ensure confusion, we may again omit all kinds of things, cf. OMG (2006).

(17)

OCL Syntax 4/4: Context

–Soclsyn–

context ::= context w₁ : τ₁, . . ., w_n : τ_n inv : expr where w_i ∈ W and τ_i ∈ TC for all 1 ≤ i ≤ n, n ≥ 0.

context w₁ : C₁, . . . , w_n : C_n inv : expr

allInstancesC₁ -> forAll(w₁ : τ_C₁ | . . .

allInstancesCn -> forAll(w_n : τ_C_n | expr

) . . .

(18)

Context: More Notational Conventions

03–2014-10-29–Soclsyn–

• For

context self : τ

C

inv : expr we may alternatively write (“abbreviate as”)

context τ

C

inv : expr

• Within the latter abbreviation, we may omit the “self ” in expr , i.e. for self .v and self .r

we may alternatively write (“abbreviate as”)

v and r

(19)

Example

–Soclsyn–

context DD inv : wen implies win > 0

(20)

Example

03–2014-10-29–Soclsyn–

S = ({Bool, Nat},{VM,CP,DD},

{cp : CP_∗,dd : DD_0,1,wen : Bool,win : Nat},

{VM 7→ {cp,dd},CP 7→ {wen},DD 7→ {win, wen})

(21)

“Not Interesting”

–Soclsyn–

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)

References

03–2014-10-29–main–

(23)

References

–main–

OMG (2006). Object Constraint Language, version 2.0. Technical Report formal/06-05-01.

OMG (2011a). Unified modeling language: Infrastructure, version 2.4.1. Technical Report formal/2011-08-05.

OMG (2011b). Unified modeling language: Superstructure, version 2.4.1. Technical Report formal/2011-08-06.

Warmer, J. and Kleppe, A. (1999). The Object Constraint Language. Addison-Wesley.