Mobile Processes and Termination

Demangeon, Romain; Hirschkoff, Daniel; Sangiorgi, Davide

doi:10.1007/978-3-642-04164-8_13

Cited by 9 publications

(13 citation statements)

References 15 publications

(22 reference statements)

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“…Termination (more commonly known as strong normalization in the functional setting) is indeed a most desirable liveness property; in session-based concurrency, it may substantially improve the correctness guarantees provided by subject reduction and progress. Ensuring termination in concurrent calculi, however, is known to be hard: in (variants of) the π-calculus, proofs require heavy constraints on the language and/or its types, often relying on ad-hoc machineries (see [8] for a survey).…”

Section: Introductionmentioning

confidence: 99%

Linear Logical Relations for Session-Based Concurrency

Pérez

Caires

Pfenning

et al. 2012

Programming Languages and Systems

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Abstract. In prior work we proposed an interpretation of intuitionistic linear logic propositions as session types for concurrent processes. The type system obtained from the interpretation ensures fundamental properties of session-based typed disciplines-most notably, type preservation, session fidelity, and global progress. In this paper, we complement and strengthen these results by developing a theory of logical relations. Our development is based on, and is remarkably similar to, that for functional languages, extended to an (intuitionistic) linear type structure. A main result is that well-typed processes always terminate (strong normalization). We also introduce a notion of observational equivalence for sessiontyped processes. As applications, we prove that all proof conversions induced by the logic interpretation actually express observational equivalences, and explain how type isomorphisms resulting from linear logic equivalences are realized by coercions between interface types of session-based concurrent systems.

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Section: Introductionmentioning

confidence: 99%

Linear Logical Relations for Session-Based Concurrency

Pérez

Caires

Pfenning

et al. 2012

Programming Languages and Systems

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“…Specifically, we show how to obtain adequate representations of least and greatest fixed points in Polyπ through the encoding of initial and final (co)algebras in the λ-calculus. We also straightforwardly derive a strong normalisation result for the higher-order session calculus, which otherwise involves non-trivial proof techniques [5,7,12,13,36]. Future work includes extensions to the classical linear logic-based framework, including multiparty session types [10,11].…”

Section: Related Work and Concluding Remarksmentioning

confidence: 99%

On Polymorphic Sessions and Functions

Toninho

Yoshida

2018

Programming Languages and Systems

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This work exploits the logical foundation of session types to determine what kind of type discipline for the π-calculus can exactly capture, and is captured by, λ-calculus behaviours. Leveraging the proof theoretic content of the soundness and completeness of sequent calculus and natural deduction presentations of linear logic, we develop the first mutually inverse and fully abstract processes-as-functions and functionsas-processes encodings between a polymorphic session π-calculus and a linear formulation of System F. We are then able to derive results of the session calculus from the theory of the λ-calculus: (1) we obtain a characterisation of inductive and coinductive session types via their algebraic representations in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation.

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“…We discuss below the first kind of methods, and return to semanticsbased approaches towards the end of this section. Level-based methods for the termination of processes arXiv:1107.5722v3 [cs.LO] 26 Aug 2011 originate in [5], and have been further analysed and developed in [3]. They exploit a stratification of names, obtained by associating a level (given by a natural number) to each name.…”

Section: Introductionmentioning

confidence: 99%

“…Example 16 (From[3]) The λ -term M 1de f = f (λ x. ( f u (u v)) can be typed in the simply typed λcalculus, in a typing context containing the hypotheses f : (σ −→ τ) −→ τ −→ τ, v : σ , u : σ −→ τ. Computing [[M 1 ]] p yields the process:…”

mentioning

confidence: 99%

Termination in a Pi-calculus with Subtyping

Cristescu

Hirschkoff

2011

Electron. Proc. Theor. Comput. Sci.

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We present a type system to guarantee termination of π-calculus processes that exploits input/output capabilities and subtyping, as originally introduced by Pierce and Sangiorgi, in order to analyse the usage of channels.We show that our system improves over previously existing proposals by accepting more processes as terminating. This increased expressiveness allows us to capture sensible programming idioms. We demonstrate how our system can be extended to handle the encoding of the simply typed λ -calculus, and discuss questions related to type inference.

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Mobile Processes and Termination

Cited by 9 publications

References 15 publications

Linear Logical Relations for Session-Based Concurrency

Linear Logical Relations for Session-Based Concurrency

On Polymorphic Sessions and Functions

Termination in a Pi-calculus with Subtyping

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