Delimited control and computational effects

Downen, Paul; Ariola, Zena M.

doi:10.1017/s0956796813000312

Cited by 5 publications

(2 citation statements)

References 37 publications

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“…Furthermore, in practice functional languages with delimited control allow for the use of multiple different prompts [12] for different purposes, like the ability to create exception handlers that catch only certain kinds of exceptions. The λµ-calculus has already [11] shed some light on this language feature, and the analysis of delimited control in the Λµ-calculus may provide more insight into a formulation that is practical yet easy to reason about with strong observational guarantees similar to shift and reset.…”

Section: Resultsmentioning

confidence: 99%

Compositional semantics for composable continuations

Downen

Ariola

2014

Proceedings of the 19th ACM SIGPLAN International Conference on Functional Programming

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Parigot's λµ-calculus, a system for computational reasoning about classical proofs, serves as a foundation for control operations embodied by operators like Scheme's callcc. We demonstrate that the call-by-value theory of the λµ-calculus contains a latent theory of delimited control, and that a known variant of λµ which unshackles the syntax yields a calculus of composable continuations from the existing constructs and rules for classical control. To relate to the various formulations of control effects, and to continuationpassing style, we use a form of compositional program transformations which preserves the underlying structure of equational theories, contexts, and substitution. Finally, we generalize the callby-name and call-by-value theories of the λµ-calculus by giving a single parametric theory that encompasses both, allowing us to generate a call-by-need instance that defines a calculus of classical and delimited control with lazy evaluation and sharing.

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Section: Resultsmentioning

confidence: 99%

Compositional semantics for composable continuations

Downen

Ariola

2014

Proceedings of the 19th ACM SIGPLAN International Conference on Functional Programming

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“…The calculus of delimited control studied in this work is the call-by-value λ-calculus extended with natural numbers, recursion, and the control operators shift 0 (S 0 ) and reset 0 ( • )-a variant of shift and reset [15]. These operators have recently enjoyed an upsurge of interest due to their considerable expressive power and connections with the λµ-calculi [25,26,24,17,16,29]. Both the calculus and the coercion semantics we consider in the rest of the article are based on the type system and the CPS translation introduced by Materzok and the first author [25].…”

Section: Coherence Of a Cps Translation Of Control-effect Subtypingmentioning

confidence: 99%

Logical relations for coherence of effect subtyping

Biernacki¹,

Polesiuk²

2018

Logical Methods in Computer Science ; Volume 14

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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 we present heterogeneous, biorthogonal, stepindexed logical relations for establishing the coherence of coercion semantics of programming languages with subtyping. To illustrate the effectiveness of the proof method, we develop a proof of coherence of a type-directed, selective CPS translation from a typed call-by-value lambda calculus with delimited continuations and control-effect subtyping. The article is accompanied by a Coq formalization that relies on a novel shallow embedding of a logic for reasoning about step-indexing.

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A typed lambda-calculus with first-class configurations

Abe

Kimura

2022

Journal of Logic and Computation

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Filinski and Griffin have independently succeeded in extending the formulae-as-types notion to deal with continuations. Whereas Griffin adopted control operators primitively, Filinski adopted the duality of functions to construct a symmetric lambda-calculus in which continuations are first-class objects. In this paper, we construct a typed lambda-calculus with first-class configurations consisting of expressions and continuations of the same types. Our calculus corresponds to a natural deduction based on Rumfitt’s bilateralism. Function types are represented as the implication and but-not connectives in intuitionistic and paraconsistent logics, respectively. Our calculus is not only logically consistent, but also computationally consistent. Our calculus with call-by-value and call-by-name strategies correspond to Wadler’s call-by-value and call-by-name dual calculi, respectively. Furthermore, we propose a notion of relaxed configurations, which loosely take expressions and continuations of different types. We confirm that the relaxedness defines control operators for delimited continuations.

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Delimited control and computational effects

Cited by 5 publications

References 37 publications

Compositional semantics for composable continuations

Compositional semantics for composable continuations

Logical relations for coherence of effect subtyping

A typed lambda-calculus with first-class configurations

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