Higher-order psi-calculi

Parrow, Joachim; Borgström, Johannes; Raabjerg, Palle; Pohjola, Johannes Åman

doi:10.1017/s0960129513000170

Cited by 14 publications

(23 citation statements)

References 18 publications

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“…While pen-and-paper proofs would have to be carefully reexamined, formal proofs can be checked mostly automatically, sometimes in minutes [7]. The psi-calculi formalisation described here has already been used as a basis for the implementation of various extensions of psi-calculi in Isabelle, notably broadcast psi-calculi [17], higher-order psi-calculi [43], and sorted psi-calculi [16].…”

Section: Resultsmentioning

confidence: 99%

Psi-Calculi in Isabelle

2015

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This paper presents a mechanisation of psi-calculi, a parametric framework for modelling various dialects of process calculi including (but not limited to) the pi-calculus, the applied pi-calculus, and the spi calculus. psi-calculi are significantly more expressive, yet their semantics is as simple in structure as the semantics of the original pi-calculus. Proofs of meta-theoretic properties for psi-calculi are more involved, however, not least because psi-calculi (unlike simpler calculi) utilise binders that bind multiple names at once. The mechanisation is carried out in the Nominal Isabelle framework, an interactive proof assistant designed to facilitate formal reasoning about calculi with binders. Our main contributions are twofold. First, we have developed techniques that allow efficient reasoning about calculi that bind multiple names in Nominal Isabelle. Second, we have adopted these techniques to mechanise substantial results from the meta-theory of psi-calculi, including congruence properties of bisimilarity and the laws of structural congruence. To our knowledge, this is the most extensive formalisation of process calculi mechanised in a proof assistant to date.

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Section: Resultsmentioning

confidence: 99%

Psi-Calculi in Isabelle

2015

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“…We aim to extend the use of sorts and generalized pattern matching to other variants of psi-calculi, including higher-order psi calculi [PBRÅP13] and reliable broadcast psicalculi [ÅPBP + 13]. Although assertions and conditions are unsorted, we intend to investigate adding sorts and pattern-matching to psi-calculi with non-trivial assertions [BJPV11].…”

Section: Conclusion and Further Workmentioning

confidence: 99%

A Sorted Semantic Framework for Applied Process Calculi

Borgström¹,

Gutkovas²,

Parrow³

et al. 2016

Logical Methods in Computer Science

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Abstract. Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies. Several such formalisms, e.g. the applied pi calculus, are extensions of the the pi-calculus; a growing number is geared towards particular applications or computational paradigms.Our goal is a unified framework to represent different process calculi and notions of computation. To this end, we extend our previous work on psi-calculi with novel abstract patterns and pattern matching, and add sorts to the data term language, giving sufficient criteria for subject reduction to hold. Our framework can directly represent several existing process calculi; the resulting transition systems are isomorphic to the originals up to strong bisimulation. We also demonstrate different notions of computation on data terms, including cryptographic primitives and a lambda-calculus with erratic choice. Finally, we prove standard congruence and structural properties of bisimulation; the proof has been machine-checked using Nominal Isabelle in the case of a single name sort.

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“…For this, a reformulation of the operational semantics in the late style, where input objects are not instantiated until communication takes place, is necessary. We also aim to extend the use of sorts and generalized pattern matching to other variants of psi-calculi, including higher-order psi calculi [21] and reliable broadcast psi-calculi [22]. As mentioned in Sect.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

A Sorted Semantic Framework for Applied Process Calculi (Extended Abstract)

Borgström¹,

Gutkovas²,

Parrow³

et al. 2014

Trustworthy Global Computing

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Abstract. Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies. Several such formalisms, e.g. the applied pi calculus, are extensions of the the pi-calculus; a growing number is geared towards particular applications or computational paradigms.Our goal is a unified framework to represent different process calculi and notions of computation. To this end, we extend our previous work on psi-calculi with novel abstract patterns and pattern matching, and add sorts to the data term language, giving sufficient criteria for subject reduction to hold. Our framework can accommodate several existing process calculi; the resulting transition systems are isomorphic to the originals up to strong bisimulation. We also demonstrate different notions of computation on data terms, including cryptographic primitives and a lambda-calculus with erratic choice. Substantial parts of the meta-theory of sorted psi-calculi have been machine-checked using Nominal Isabelle.

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Higher-order psi-calculi

Cited by 14 publications

References 18 publications

Psi-Calculi in Isabelle

Psi-Calculi in Isabelle

A Sorted Semantic Framework for Applied Process Calculi

A Sorted Semantic Framework for Applied Process Calculi (Extended Abstract)

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