Architecture Modeling - SPES 2020

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Architecture Modeling For our application as specifications, the logical formulas in question will denote sets of traces of valuations of connections, resp., ports. Then we can define satisfaction of contracts by components (and systems). Definition 6.3.3 (Satisfaction) A component M satisfies a formula G, written M |= G, if and only if [[M]] ⊆ [[G]]. Similarly, it satisfies a contract C, written M |= C, if and only if [[M]] ⊆ [[C]]. Thus, we have 6.3.2 Contracts: Properties M |= (As,Aw,G) ⇔ [[M]] ∩ [[As]] ∩ [[Aw]] ⊆ [[G]] . To be able to base the design process on contracts, we need operations on contracts and related properties. The most basic relation between contracts is that of entailment, which is called refinement here. Definition 6.3.4 (Refinement) A contract C ′ = (A ′ s,A ′ w,G ′ ) refines a contract C = (As,Aw,G), written C ′ ⇒ C, if [[C ′ ]] ⊆ [[C]] and[[As]] ⊆ [[A ′ s]] , i. e. if it is (in total) more restrictive and its strong assumption is less restrictive. Equivalently, C ′ ⇒ C if form(C ′ ) ⇒ form(C) and As ⇒ A ′ s in the usual logical meaning of implication. Thus, a component satisfying a refinement of a contract C satisfies also C. The second part of the condition for refinement states that the strong assumption may only get weaker in refinements. As a consequence, the strong assumption of a contract will always remain sufficient to establish the strong assumption made by a component satisfying a refinement. In practice, refinement usually removes nondeterminism from the guarantee, thus strengthening it, and/or permits more environment behaviour, weakening the assumption(s). This relation is called dominance. Definition 6.3.5 (Dominance) A contract C ′ = (A ′ s,A ′ w,G ′ ) dominates a contract C = (As,Aw,G), written C ′ C, if A ′ s ⇐ As, A ′ w ⇐ Aw and G ′ ⇒ G. It is easy to see that dominance implies refinement but not vice versa. In practice, dominance is easier to establish (i. e., less complex to check) and often sufficient for refinement proofs to go through. In the design process, often more general relations than refinement are called for because A specification should be implementable. We capture this intuition by the notion of (strong) consistency. Definition 6.3.6 (Consistency) Let the interface I of a component in HRC be given. 1. A contract C (resp., a set of contracts C ) over I is weakly consistent if [[C]] is nonempty (resp., C∈C [[C]] is nonempty). 2. A contract C (resp., set of contracts C ) over I is strongly consistent if the receptive kernel of [[C]] (resp., C∈C [[C]]) w.r.t. the inports in I is nonempty. Weak consistency is consistency in the logical sense, a necessary condition for every meaningful specification. Strong consistency takes the direction of ports into account, guaranteeing the existence of an implementation on the semantic level. It is more difficult to check than weak consistency. Whether the direction of ports is taken into account in a contract can be defined on the logical level. 146/ 156
Architecture Modeling Definition 6.3.7 (Directed Contract) Let the interface I of a component be given. A contract C = (As,Aw,G) over I is directed w.r.t. I if As and Aw are receptive on the outports in I and G is receptive on the inports in I. Directed contracts may be viewed as the most natural form of utilizing the contract format for specifications. This is supported by the observation that directed contracts are strongly consistent. Lemma 6.3.8 (Directedness and Consistency) Let the interface I of a component and a contract C = (As,Aw,G) be given. 1. If the guarantee of C is receptive on the inports in I, then C is strongly consistent. 2. A directed contract is strongly consistent. Proof: Ad 1: Since [[C]] ⊇ [[G]] and the receptive kernel of G w.r.t. the inports is nonempty, also the receptive kernel of C is nonempty. Ad 2: Follows immediately from 1. An important operation to be performed on contracts is conjunction. This might be useful to combine specifying contracts of one component, or to derive a contract valid for a composition from part contracts. Though one can always find a contract equivalent to the conjunction of a set of contracts, properties like directedness are not automatically retained. We provide different schemata for performing the conjunction. Lemma 6.3.9 (Contract Conjunction) Let (tt,B,G) and (tt,F,H) be contracts. Then are equivalent to (tt,B,G) ∧ (ff ,F,H). 6.4 Formalization of Typical Design Steps (tt,BG + FH , GH) (6.1) (tt,BF + BG + FH , GH) (6.2) (tt,B + F , BH + FG + GH) (6.3) The parallel composition of components has a logical counterpart on the level of contracts. Lemma 6.4.1 (Logical Composition) Let a hierarchically defined component M with port set P, parts Mi, i = 1,...,n, and connecting substitutions (ρ1,...,ρn,ρ be given. Let the parts be specified by sets of contracts Ci, j, i = 1,...,n, j = 1,...ni. Then n ni n Mi |= Ci, j ⇒ M |= i=1 j=1 i=1 ni j=1 Ci, j ρi ρ ↓P . The lemma follows from Definition 6.2.6. It immediately provides the criterion for virtual integration testing. 147/ 156
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Architecture Modeling ∗ Andreas B
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Contents 1 Introduction 1 2 Quick-T
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1 Introduction This document propos
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Architecture Modeling allowing to m
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3 The Architecture Meta-Model In Se
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Abstraction-Levels (detail increase
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3.2.2 Functional Perspective Archit
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Architecture Modeling The semantics
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