HOπ in Coq

Lenglet, Sergueï; Schmitt, Alan

doi:10.1145/3167083

Cited by 4 publications

(2 citation statements)

References 19 publications

(41 reference statements)

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“…Interestingly, it offers an elegant notion of concrete context (and thus of Morris approximation) that seems much easier to reason with than previous efforts (Ford and Mason 2003). Lenglet and Schmitt (2018) present a formalization of Sangiorgi's higher order πcalculus in Coq, using the locally nameless approach to representing name restriction and well-scoped de Bruijn indices for process variables. The formalization includes a proof that strong context bisimilarity is a congruence, via an adaptation to the concurrent setting of Howe's method.…”

Section: Related Workmentioning

confidence: 99%

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: Related Workmentioning

confidence: 99%

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

Momigliano¹,

Pientka²,

Thibodeau³

2018

Math. Struct. Comp. Sci.

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“…We compare the four formalizations in Section 8, and we discuss related and future work in respectively Sections 9 and 10. The locally nameless formalization has been first presented at CPP [31]; the de Bruijn, nominal, and HOAS formalizations are new. The formal developments are available at http://passivation.inria.fr/hopi/; a symbol in the paper indicates a link to the online proofs scripts.…”

Section: Introductionmentioning

confidence: 99%

HO$$\pi $$ in Coq

2020

Self Cite

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We present a formalization of HOπ in Coq, a process calculus where messages carry processes. Such a higher-order calculus features two very different kinds of binder: process input, similar to λ-abstraction, and name restriction, whose scope can be expanded by communication. For the latter, we compare four approaches to represent binders: locally nameless, de Bruijn indices, nominal, and Higher-Order Abstract Syntax. In each case, we formalize strong context bisimilarity and prove it is compatible, i.e., closed under every context, using Howe's method, based on several proof schemes we developed in a previous paper.

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POPLMark reloaded: Mechanizing proofs by logical relations

et al. 2019

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We propose a new collection of benchmark problems in mechanizing the metatheory of programming languages, in order to compare and push the state of the art of proof assistants. In particular, we focus on proofs using logical relations (LRs) and propose establishing strong normalization of a simply typed calculus with a proof by Kripke-style LRs as a benchmark. We give a modern view of this well-understood problem by formulating our LR on well-typed terms. Using this case study, we share some of the lessons learned tackling this problem in different dependently typed proof environments. In particular, we consider the mechanization in Beluga, a proof environment that supports higher-order abstract syntax encodings and contrast it to the development and strategies used in general-purpose proof assistants such as Coq and Agda. The goal of this paper is to engage the community in discussions on what support in proof environments is needed to truly bring mechanized metatheory to the masses and engage said community in the crafting of future benchmarks.

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HOπ in Coq

Cited by 4 publications

References 19 publications

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

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

HO$$\pi $$ in Coq

POPLMark reloaded: Mechanizing proofs by logical relations

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