Theorems about Composition

Charpentier, Michel; Chandy, K. Mani

doi:10.1007/10722010_12

Cited by 9 publications

(21 citation statements)

References 10 publications

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“…We have used existential and universal properties to derive examples of specifications and correctness proofs of distributed and concurrent systems [11,12,6,25]. Several of these examples make use of an operator called guarantees [8] which has been proved to be a special case of the transformer W E [14].…”

Section: Discussionmentioning

confidence: 99%

“…Note that these hypotheses make it possible for the composition operator to be either parallel composition ( ) or sequential composition (;) of programs, but does not allow us to describe systems where both operators are interleaved. Several predicate transformers have been defined and studied in [14,13]. Here, we show how they can be seen as special cases of our weakest and strongest transformers.…”

Section: Properties Such As (X•y ) Z or ((?•Y ) Z)t Make The Structumentioning

confidence: 94%

“…The same law of composition, such as concurrent composition of processes, can be coupled to different compatibility operators to allow shared variables or not, for instance. In order not to clutter up our notations, we do not use compatibility operators explicitly here (but we do in [14,13]). Instead, it is implicitly understood that systems that are referred to exist.…”

Section: Components Composition Systems and System Propertiesmentioning

confidence: 99%

“…We can for instance define a predicate transformer W E such that W E.X is the weakest existential property stronger than X (such a property always exists because disjunctions of existential properties are existential) [14]. Then, systems can be specified in terms of W E.X instead of X so that, when they are composed with other systems, the property X is preserved.…”

Section: Properties Such As (X•y ) Z or ((?•Y ) Z)t Make The Structumentioning

confidence: 99%

“…Things are different with the universal form of composition because it can be shown that, for some properties, there does not exist a weakest universal property that strengthen them [14]. Therefore, we cannot define a transformer W U in the same way as we defined W E. Still, any property X has a strongest universal property weaker than itself, denoted by SU.X.…”

Section: Proposition 4 For Any Property X There Exists a Strongest mentioning

confidence: 99%

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An Approach to Composition Motivated by wp

Charpentier

2002

Fundamental Approaches to Software Engineering

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Abstract. We consider the question of composition in system design, a fundamental issue in engineering. More precisely, we are interested in deducing system properties from components properties and vice-versa. This requires system and component specifications to be "compositional " in some sense. Depending on what systems are and how they are composed, this problem is satisfactorily solved (e.g., sequential composition of terminating programs) or remains a hot research topic (e.g., concurrent composition of reactive systems). In this paper, we aim at providing a logical framework in which composition issues can be reasoned about independently from the kind of systems and the laws of composition under consideration. We show that many composition related statements can be expressed in terms of predicate transformers in a way that presents interesting similarities with program semantics descriptions based on weakest precondition calculus. MotivationSystem designers, whether those systems are software, hardware, planes or buildings, are all faced with a common issue: How to compose systems from components and how to partition systems into components. Compositional design offers the hope of managing complexity by avoiding unnecessary details: Systems designers prove properties of systems given properties, but not detailed implementations, of components.As fundamental as it is, the question of composition is far from being solved in a fully satisfactory way. What does it mean for a formal framework to be "compositional "? Are there "good " and "bad " compositional frameworks? What characterizes "good " compositional specifications? Should system designers and components providers use the same kind of specifications? Are there fundamental laws of composition that are common to most areas of engineering? How are composition and reuse issues related? We believe these to be important questions one must (at least partially) answer before suitable solutions to the composition problem are found.In this paper, we aim at providing a basis that can be used to reason about composition. We seek a logical framework in which many of the questions mentioned above can be formulated and reasoned about. We try to keep the context of our approach as general as possible. Especially, we don't want to decide from

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Section: Discussionmentioning

confidence: 99%

Section: Properties Such As (X•y ) Z or ((?•Y ) Z)t Make The Structumentioning

confidence: 94%

Section: Components Composition Systems and System Propertiesmentioning

confidence: 99%

Section: Properties Such As (X•y ) Z or ((?•Y ) Z)t Make The Structumentioning

confidence: 99%

Section: Proposition 4 For Any Property X There Exists a Strongest mentioning

confidence: 99%

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An Approach to Composition Motivated by wp

Charpentier

2002

Fundamental Approaches to Software Engineering

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A UNITY-Based Framework Towards Component Based Systems

Prasetya¹,

Vos

Azurat³

et al. 2005

Lecture Notes in Computer Science

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The paper offers a UNITY-based framework to model distributed applications which are built with a component based approach. The framework enables components to be abstractly specified in terms of contracts. Temporal properties are expressed and proven in the UNITY style. Compositional reasoning about components' properties, including progress, is supported. The semantical model is simple and intuitive.

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On the Composition of Compositional Reasoning

Freiling

Santen

2006

Lecture Notes in Computer Science

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Theorems about Composition

Cited by 9 publications

References 10 publications

An Approach to Composition Motivated by wp

An Approach to Composition Motivated by wp

A UNITY-Based Framework Towards Component Based Systems

On the Composition of Compositional Reasoning

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