Algebra Unifies Operational Calculi

Staden, Stephan van; Hoare, Tony

doi:10.1007/978-3-642-35705-3_4

Cited by 7 publications

(8 citation statements)

References 10 publications

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“…In summary, the languages with interleaving satisfy all the laws of programming mentioned in [6,7,8].…”

Section: Languages and Lawsmentioning

confidence: 91%

“…The laws yield abstract versions of several familiar calculi of programming, as discussed in [4,6,7,8]. Later sections of the paper will instantiate selected rules of the abstract calculi to obtain concrete calculi.…”

Section: Abstract Calculimentioning

confidence: 99%

“…By making the abstract calculi explicit, one can often see immediately why a concrete rule is a theorem. Although it is not the primary goal of this paper, the connection between the abstract and concrete calculi can help to understand the relationship between the results in [4,6,7,8] and their counterparts in more conventional work.…”

Section: Abstract Calculimentioning

confidence: 99%

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Constructing the Views Framework

Staden

2015

Lecture Notes in Computer Science

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Abstract. The views framework of Dinsdale-Young and others unifies several compositional techniques for reasoning about concurrent programs. This paper uses simple mathematics to construct the views framework incrementally from first principles. The result is a model for the views framework, which can also be understood as an independent theory of concurrent programs. Along the lines of "sequential programs are binary relations", the theory adopts the maxim "concurrent programs are formal languages". Consequently, programs obey familiar algebraic laws that can simplify reasoning; there is no need to postulate operational rules; the views program logic can be constructed in a stepwise fashion from more basic logics; program logic and operational thinking become largely decoupled; proving partial correctness becomes straightforward and it holds irrespectively of the specific choice of programming language constructs, operational rules, and the atomic actions that are implemented in a computer. All theorems have been formally checked with Isabelle/HOL. A proof script is available online.

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“…In summary, the languages with interleaving satisfy all the laws of programming mentioned in [6,7,8].…”

Section: Languages and Lawsmentioning

confidence: 91%

Section: Abstract Calculimentioning

confidence: 99%

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Constructing the Views Framework

Staden

2015

Lecture Notes in Computer Science

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“…Recently, Hoare proposed a challenging research topic of the semantic linking between algebra, denotations, transitions and deductions [Hoa11,HvS12]. Various familiar operational calculi have been derived from the algebraic semantics [vSH13]. Compared with the above explorations, this paper studied the linking theory between the denotational semantics and algebraic semantics for SystemC.…”

Section: Related Workmentioning

confidence: 99%

Denotational semantics and its algebraic derivation for an event-driven system-level language

Zhu

Qin

et al. 2015

Form. Asp. Comput.

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Abstract. As a system-level modelling language, SystemC possesses several novel features such as delayed notifications, notification cancelling, notification overriding and delta-cycle. It is challenging to formalise SystemC. In this paper, we study the denotational semantics for SystemC using Unifying Theories of Programming (abbreviated as UTP) [HH98]. Two trace variables are introduced, one to record the state behaviours and another to record the event behaviours. The timed model is formalised in a three-dimensional structure. A set of algebraic laws is explored, which can be proved via the presented denotational semantics.In this paper, we also consider the inverse work; i.e., generating the denotational semantics from algebraic semantics for SystemC. A complete set of parallel expansion laws is explored, where the location status of an instantaneous action is studied. We introduce the concept of head normal form for each program and every program is expressed in the form of guarded choice with location status. Based on this, the derivation strategy for deriving denotational semantics from algebraic semantics is provided.

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“…For example, the weakest precondition calculus of Dijkstra and the refinement calculus of Back/Morgan are treated in [25]. The unification of several operational calculi, including the small-step calculus of Plotkin, appear in [26]. Finally, the rely-guarantee calculus of Jones is presented in [27] in the context of a graphical model of the laws.…”

Section: Related Workmentioning

confidence: 99%

The laws of programming unify process calculi

Hoare

Staden

2014

Science of Computer Programming

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We survey the well-known algebraic laws of sequential programming, and propose some less familiar laws for concurrent programming. On the basis of these laws, we derive the rules of a number of classical programming and process calculi, for example, those due to Hoare, Milner, and Kahn. The algebraic laws are simpler than each of the calculi derived from it, and they are stronger than all the calculi put together. Conversely, most of the laws are derivable from one or more of the calculi. This suggests that the laws are useful as a presentation of program semantics, and correspond to a widely held common understanding of the meaning of programs. For further evidence, Appendix A describes a realistic and generic model of program behaviour, which has been proved to satisfy the laws.

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Algebra Unifies Operational Calculi

Cited by 7 publications

References 10 publications

Constructing the Views Framework

Constructing the Views Framework

Denotational semantics and its algebraic derivation for an event-driven system-level language

The laws of programming unify process calculi

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