Algebras for Program Correctness in Isabelle/HOL

Armstrong, Alasdair; Gomes, Victor B. F.; Struth, Georg

doi:10.1007/978-3-319-06251-8_4

Cited by 8 publications

(7 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proof of (87) then follows from (86) using Corollary 16 for synchronisation operator weak conjunction ( ). 2 If we assume that commands only consist of atomic steps (which are closed under the operators), then we have that an iterated atomic step distributes over a sequence of commands, a ω ⊗ (c ; d) = (a ω ⊗ c) ; (a ω ⊗ d). With this assumption, it follows that guarantees also distribute over a sequence of commands.…”

Section: The Guarantee Commandmentioning

confidence: 99%

“…The key axiom in the interpretation of parallel is, again, in the behaviour of two program steps. 2 We define two program steps on event e to merge into a single "synchronised" event, e. The set of events is extended with new events e for every event e, and introduce a step (e), where (e) for all e ∈ Event.…”

Section: Communication In Cspmentioning

confidence: 99%

“…where is the top of the refinement lattice and represents the everywhere infeasible command (sometimes referred to as "magic"). For example, the above laws hold with ⊗ instantiated with , so that (3) corresponds to (2). The other laws codify that two null commands synchronise to give null (4) and that a null command cannot synchronise with a command that performs at least one atomic step -their combination is infeasible (5).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency

et al. 2019

View full text Add to dashboard Cite

This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave) when composed in parallel. The algebra of rely/guarantee concurrency then becomes an instantiation of the more abstract algebra. Many of the core properties needed for rely/guarantee reasoning can be shown to hold in the abstract algebra where their proofs are simpler and hence allow a higher degree of automation. The algebra has been encoded in Isabelle/HOL to provide a basis for tool support for program verification.In rely/guarantee concurrency, programs are specified to guarantee certain behaviours until assumptions about the behaviour of their environment are violated. When assumptions are violated, program behaviour is unconstrained (aborting), and guarantees need no longer hold. To support these guarantees a second synchronous operator, weak conjunction, was introduced: both processes in a weak conjunction must agree to take each atomic step, unless one aborts in which case the whole aborts. In developing the laws for parallel and weak conjunction we found many properties were shared by the operators and that the proofs of many laws were essentially the same. This insight led to the idea of generalising synchronisation to an abstract operator with only the axioms that are shared by the parallel and weak conjunction operator, so that those two operators can be viewed as instantiations of the abstract synchronisation operator. The main differences between parallel and weak conjunction are how they combine individual atomic steps; that is left open in the axioms for the abstract operator.Milner's process algebra SCCS also includes a synchronous parallel operator and (again) the main difference between it and Aczel's synchronous parallel operator is how it combines individual atomic steps. Milner's parallel can be seen as another instance of the abstract synchronisation operator. Moreover, the realisation that the synchronisation mechanisms of standard process algebras, such as CSP and CCS/SCCS, can be interpreted in our abstract algebra gives evidence of its unifying power.Correspondence and offprint requests to: Ian J. Hayes,

show abstract

Section: The Guarantee Commandmentioning

confidence: 99%

Section: Communication In Cspmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Our approach benefits from Isabelle's support for engineering algebraic hierarchies and their models, and its emphasis on proof automation through the integration of automated theorem proving and counterexample search technology, which can deal with algebraic proofs efficiently. This and our own libraries for variants of Kleene algebras, including Kleene algebras with tests, action algebras, quantales, demonic refinement algebras, modal Kleene algebras, CKA and Tarski's relation algebras and their most important models [5,34,4,3] make the approach simple and modular. In addition, Isabelle provides large libraries for data structures and their properties.…”

Section: Cka-based Concurrency Verification Toolsmentioning

confidence: 99%

Developments in concurrent Kleene algebra

Hoare

Staden

Möller

et al. 2016

Journal of Logical and Algebraic Methods in Programming

Self Cite

View full text Add to dashboard Cite

This report summarises the background and recent progress in the research of its co-authors. It is aimed at the construction of links between algebraic presentations of the principles of programming and the exploitation of concurrency in modern programming practice. The signature and laws of a Concurrent Kleene Algebra (CKA) largely overlap with those of a Regular Algebra, with the addition of concurrent composition and a few simple laws for it. They are re-interpreted here in application to computer programs. The inclusion relation for regular expressions is re-interpreted as a refinement ordering, which supports a stepwise contractual approach to software system design and to program debugging.The laws are supported by a hierarchy of models, applicable and adaptable to a range of different purposes and to a range of different programming languages. The algebra is presented in three tiers. The bottom tier defines traces of program execution, represented as sets of events that have occurred in a particular run of a program; the middle tier defines a program as the set of traces of all its possible behaviours. The top tier introduces additional incomputable operators, which are useful for describing the desired or undesired properties of computer program behaviour. The final sections outline directions in which further research is needed.

show abstract

“…Kleene algebras have been used in applications including compiler optimisation, program construction, transformation and termination analysis, and static analysis. Formalisations and tools are available in interactive theorem provers such as Coq [26] and Isabelle [2,3,1]. A first step towards an algebraic description of rely-guarantee based reasoning has recently been undertaken [16].…”

Section: Introductionmentioning

confidence: 99%

Algebraic Principles for Rely-Guarantee Style Concurrency Verification Tools

Armstrong

Gomes

Struth

2014

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. We provide simple equational principles for deriving relyguarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution traces. We have implemented the approach in Isabelle/HOL as a lightweight concurrency verification tool that supports reasoning about the control and data flow of concurrent programs with shared variables at different levels of abstraction. This is illustrated on two simple verification examples.

show abstract

Algebras for Program Correctness in Isabelle/HOL

Cited by 8 publications

References 19 publications

A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency

A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency

Developments in concurrent Kleene algebra

Algebraic Principles for Rely-Guarantee Style Concurrency Verification Tools

Contact Info

Product

Resources

About