In praise of algebra

Hoare, Tony; Staden, Stephan van

doi:10.1007/s00165-012-0249-0

Cited by 26 publications

(15 citation statements)

References 16 publications

(8 reference statements)

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“…In [10], Hoare and Staden highlight, among other advantages, the incrementality of the algebraic method. When a new programming language concept or design pattern is added, new axioms can be introduced, keeping intact at least some axioms and theorems of the existing theory of the language.…”

Section: Introductionmentioning

confidence: 99%

Laws of Programming for References

Lucero

Naumann

Sampaio

2013

Programming Languages and Systems

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Abstract. We propose a set of algebraic laws for reasoning with sequential imperative programs that use object references like in Java. The theory is based on previous work by adding laws to cope with object references. The incrementality of the algebraic method is fundamental; with a few exceptions, existing laws for copy semantics are entirely reused, as they are not affected by the proposed laws for reference semantics. As an evidence of relative completeness, we show that any program can be transformed, through the use of our laws, to a normal form which simulates it using an explicit heap with copy semantics.

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Section: Introductionmentioning

confidence: 99%

Laws of Programming for References

Lucero

Naumann

Sampaio

2013

Programming Languages and Systems

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“…The total correctness of the derived GCL's operational semantics was also discussed in [HJS97]. 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].…”

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

Section: Languages and Lawsmentioning

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 praise of algebra

Cited by 26 publications

References 16 publications

Laws of Programming for References

Laws of Programming for References

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

Constructing the Views Framework

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