Environmental Bisimulations for Delimited-Control Operators

Biernacki, Dariusz; Lenglet, Sergueï

doi:10.1007/978-3-319-03542-0_24

Cited by 8 publications

(6 citation statements)

References 26 publications

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“…An older work [15] gives definitions of environmental bisimulations that are now completely obsolete. We revisit results originally published in a previous article [3], where the focus is more on a multi-prompted calculus.…”

Section: Environmental Bisimilaritymentioning

confidence: 99%

“…In this article, we present a comprehensive study of the behavioral theory of a λ-calculus extended with the operators shift and reset, called λ S . In previous works, we defined applicative [13], normal-form [14,17], and environmental [15,3] bisimilarities for this calculus. Here we present these results in a systematic and uniform way, with examples allowing for comparisons between the different styles of bisimulation.…”

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confidence: 99%

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Applicative Bisimulations for Delimited-Control Operators

Biernacki¹,

Lenglet²

2012

Foundations of Software Science and Computational Structures

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Abstract. We develop a behavioral theory for the untyped call-by-value λ-calculus extended with the delimited-control operators shift and reset. For this calculus, we discuss the possible observable behaviors and we define an applicative bisimilarity that characterizes contextual equivalence. We then compare the applicative bisimilarity and the CPS equivalence, a relation on terms often used in studies of control operators. In the process, we illustrate how bisimilarity can be used to prove equivalence of terms with delimited-control effects.

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Section: Environmental Bisimilaritymentioning

confidence: 99%

mentioning

confidence: 99%

Applicative Bisimulations for Delimited-Control Operators

Biernacki¹,

Lenglet²

2012

Foundations of Software Science and Computational Structures

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“…They work on closed terms, computing the arguments that contexts can provide to terms using an environment similar to our component γ. They have also been extended to languages with call/cc [34] and delimited control operators [5,6].…”

Section: Related Workmentioning

confidence: 99%

Complete trace models of state and control

Jaber

Murawski

2021

Lecture Notes in Computer Science

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We consider a hierarchy of four typed call-by-value languages with either higher-order or ground-type references and with either $$\mathrm {call/cc}$$ call / cc or no control operator.Our first result is a fully abstract trace model for the most expressive setting, featuring both higher-order references and $$\mathrm {call/cc}$$ call / cc , constructed in the spirit of operational game semantics. Next we examine the impact of suppressing higher-order references and callcc in contexts and provide an operational explanation for the game-semantic conditions known as visibility and bracketing respectively. This allows us to refine the original model to provide fully abstract trace models of interaction with contexts that need not use higher-order references or $$\mathrm {call/cc}$$ call / cc . Along the way, we discuss the relationship between error- and termination-based contextual testing in each case, and relate the two to trace and complete trace equivalence respectively.Overall, the paper provides a systematic development of operational game semantics for all four cases, which represent the state-based face of the so-called semantic cube.

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“…The elements of the environment can be used to construct terms to be supplied as inputs during the bisimulation game. The notion has been applied to a variety of languages, including pure λ-calculi [35,39], extensions of λ-calculi [3,18,19,38], or languages for concurrency or distribution [26,27,36]. In environmental bisimulations the proof of congruence goes by induction over contexts, as in proofs for first-order languages.…”

Section: Introductionmentioning

confidence: 99%

Environmental Bisimulations for Probabilistic Higher-order Languages

Sangiorgi

Vignudelli

2019

ACM Trans. Program. Lang. Syst.

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Environmental bisimulations for probabilistic higher-order languages are studied. In contrast with applicative bisimulations, environmental bisimulations are known to be more robust and do not require sophisticated techniques such as Howe's in the proofs of congruence.As representative calculi, call-by-name and call-by-value λcalculus, and a (call-by-value) λ-calculus extended with references (i.e., a store) are considered. In each case full abstraction results are derived for probabilistic environmental similarity and bisimilarity with respect to contextual preorder and contextual equivalence, respectively. Some possible enhancements of the (bi)simulations, as 'up-to techniques', are also presented.Probabilities force a number of modifications to the definition of environmental bisimulations in non-probabilistic languages. Some of these modifications are specific to probabilities, others may be seen as general refinements of environmental bisimulations, applicable also to non-probabilistic languages. Several examples are presented, to illustrate the modifications and the differences.

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Environmental Bisimulations for Delimited-Control Operators

Cited by 8 publications

References 26 publications

Applicative Bisimulations for Delimited-Control Operators

Applicative Bisimulations for Delimited-Control Operators

Complete trace models of state and control

Environmental Bisimulations for Probabilistic Higher-order Languages

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