Encoding Transition Systems in Sequent Calculus: Preliminary Report

McDowell, Raymond; Miller, Dale; Palamidessi, Catuscia

doi:10.1016/s1571-0661(05)80412-8

Cited by 4 publications

(1 citation statement)

References 9 publications

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“…This brought to the forefront the issue of representing and reasoning about infinite behaviour. In fact, McDowell et al (1996) were concerned with the representation of transition systems and their bisimulation: in agreement with Milner's original presentation in A Calculus of Communicating Systems, bisimilarity was captured inductively by computing the greatest fixed point starting from the universal relation and closing downwards by intersection. This is doable, but notoriously awkward to work with and in fact Milner swiftly adopted the notion of coinduction in his subsequent Communication and Concurrency.…”

Section: Introductionmentioning

confidence: 87%

A case study in programming coinductive proofs: Howe’s method

Momigliano¹,

Pientka²,

Thibodeau³

2018

Math. Struct. Comp. Sci.

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Bisimulation proofs play a central role in programming languages in establishing rich properties such as contextual equivalence. They are also challenging to mechanize, since they require a combination of inductive and coinductive reasoning on open terms. In this paper, we describe mechanizing the property that similarity in the call-by-name lambda calculus is a pre-congruence using Howe’s method in the Beluga formal reasoning system. The development relies on three key ingredients: (1) we give a higher order abstract syntax (HOAS) encoding of lambda terms together with their operational semantics as intrinsically typed terms, thereby avoiding not only the need to deal with binders, renaming and substitutions, but keeping all typing invariants implicit; (2) we take advantage of Beluga’s support for representing open terms using built-in contexts and simultaneous substitutions: this allows us to directly state central definitions such as open simulation without resorting to the usual inductive closure operation and to encode very elegantly notoriously painful proofs such as the substitutivity of the Howe relation; (3) we exploit the possibility of reasoning by coinduction in Beluga’s reasoning logic. The end result is succinct and elegant, thanks to the high-level abstractions and primitives Beluga provides. We believe that this mechanization is a significant example that illustrates Beluga’s strength at mechanizing challenging (co)inductive proofs using HOAS encodings.

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Section: Introductionmentioning

confidence: 87%