π-calculus in (Co)inductive-type theory

Honsell, Furio; Miculan, Marino; Scagnetto, Ivan

doi:10.1016/s0304-3975(00)00095-5

Cited by 84 publications

(113 citation statements)

References 15 publications

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“…HOAS has been used to model the π-calculus in both Coq [25], by Honsell et. al., and in Isabelle by Röckl and Hirschkoff [39].…”

Section: Results and Conclusionmentioning

confidence: 99%

“…al., and in Isabelle by Röckl and Hirschkoff [39]. In [25] the late operational semantics is encoded together with late strong bisimulation. The proved results include that the algebraic laws presented in [30] are sound where the non-trivial proofs include preservation results for bisimulation and the results for structural congruence.…”

Section: Results and Conclusionmentioning

confidence: 99%

“…Another problem is that since abstraction is handled by the meta-logic of the theorem prover, reasoning about binders at the object level can become problematic. In [25] we can read:…”

Section: Results and Conclusionmentioning

confidence: 99%

“…As we shall see in a moment, an alternative definition using direct coinduction, similar to the approach in [25], yields shorter proofs. Our main improvement, however, is in the treatment of the bound name x.…”

Section: Strong Bisimulationmentioning

confidence: 99%

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Formalising the pi-calculus using nominal logic

Bengtson¹,

Parrow²

2009

Logical Methods in Computer Science

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Abstract. We formalise the pi-calculus using the nominal datatype package, based on ideas from the nominal logic by Pitts et al., and demonstrate an implementation in Isabelle/HOL. The purpose is to derive powerful induction rules for the semantics in order to conduct machine checkable proofs, closely following the intuitive arguments found in manual proofs. In this way we have covered many of the standard theorems of bisimulation equivalence and congruence, both late and early, and both strong and weak in a uniform manner. We thus provide one of the most extensive formalisations of a process calculus ever done inside a theorem prover.A significant gain in our formulation is that agents are identified up to alpha-equivalence, thereby greatly reducing the arguments about bound names. This is a normal strategy for manual proofs about the pi-calculus, but that kind of hand waving has previously been difficult to incorporate smoothly in an interactive theorem prover. We show how the nominal logic formalism and its support in Isabelle accomplishes this and thus significantly reduces the tedium of conducting completely formal proofs. This improves on previous work using weak higher order abstract syntax since we do not need extra assumptions to filter out exotic terms and can keep all arguments within a familiar first-order logic.

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“…HOAS has been used to model the π-calculus in both Coq [25], by Honsell et. al., and in Isabelle by Röckl and Hirschkoff [39].…”

Section: Results and Conclusionmentioning

confidence: 99%

Section: Results and Conclusionmentioning

confidence: 99%

“…Another problem is that since abstraction is handled by the meta-logic of the theorem prover, reasoning about binders at the object level can become problematic. In [25] we can read:…”

Section: Results and Conclusionmentioning

confidence: 99%

Section: Strong Bisimulationmentioning

confidence: 99%

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Formalising the pi-calculus using nominal logic

Bengtson¹,

Parrow²

2009

Logical Methods in Computer Science

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“…The closest development to ours is [4], where Bengtson and Parrow have formalised the π-calculus in Isabelle/HOL using the Nominal package, providing a library which allows users to carry proofs about π-calculus. Other approaches to binding management are de Bruijn indexes [12], and (weak) higher order abstract syntax [13]. De Bruijn indexes are quite cumbersome to use in interactive proofs, because names disappear completely.…”

Section: Discussionmentioning

confidence: 99%

Implementing Spi Calculus Using Nominal Techniques

Kahsai

Miculan

Logic and Theory of Algorithms

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Abstract. The aim of this work is to obtain an interactive proof environment based on Isabelle/HOL for reasoning formally about cryptographic protocols, expressed as processes of the spi calculus (a π-calculus with cryptographic primitives). To this end, we formalise syntax, semantics, and hedged bisimulation, an environment-sensitive bisimulation which can be used for proving security properties of protocols. In order to deal smoothly with binding operators and reason up-to α-equivalence of bound names, we adopt the new Nominal datatype package. This simplifies both the encoding, and the formal proofs, which turn out to correspond closely to "manual proofs".

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