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Bisimulations for Delimited-Control Operators

Dariusz Biernacki ; Sergueï Lenglet ; Piotr Polesiuk.

We present a comprehensive study of the behavioral theory of an untyped $\lambda$-calculus extended with the delimited-control operators shift and reset. To that end, we define a contextual equivalence for this calculus, that we then aim to characterize with coinductively defined relations, called&nbsp;[&hellip;]

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Logical relations for coherence of effect subtyping

Dariusz Biernacki ; Piotr Polesiuk.

A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the typing derivation for a given typing judgment. In this article&nbsp;[&hellip;]

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Environmental Bisimulations for Delimited-Control Operators with Dynamic Prompt Generation

Andrés Aristizábal ; Dariusz Biernacki ; Sergueï Lenglet ; Piotr Polesiuk.

We present sound and complete environmental bisimilarities for a variant of Dybvig et al.'s calculus of multi-prompted delimited-control operators with dynamic prompt generation. The reasoning principles that we obtain generalize and advance the existing techniques for establishing program&nbsp;[&hellip;]

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Proving Soundness of Extensional Normal-Form Bisimilarities

Dariusz Biernacki ; Serguei Lenglet ; Piotr Polesiuk.

Normal-form bisimilarity is a simple, easy-to-use behavioral equivalence that relates terms in $\lambda$-calculi by decomposing their normal forms into bisimilar subterms. Moreover, it typically allows for powerful up-to techniques, such as bisimulation up to context, which simplify bisimulation&nbsp;[&hellip;]

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