Making PVS Accessible to Generic Services by Interpretation in a Universal Format

Kohlhase, Michael; Müller, Dennis; Owre, Sam; Rabe, Florian

doi:10.1007/978-3-319-66107-0_21

Cited by 13 publications

(13 citation statements)

References 19 publications

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“…To use resources efficiently, we chose representative theorem provers: one each based on higher-order logic (HOL Light [22]), constructive type theory (Coq [12]), an undecidable type theory (PVS [51]), and set theory (Mizar [62]), as well as one based on a logical framework (Isabelle [53]) and one based on axiomatic specification (IMPS [16]). All six exports were presented individually before: HOL Light in [31], Mizar in [27], PVS in [36], IMPS in [8], Coq in [46], and Isabelle in [38]. For simplicity, we will refer to these as "our exports" in the sequel even though each one was developed with different collaborators.…”

Section: Problem and Related Workmentioning

confidence: 99%

“…Our PVS export was carried out together with Sam Owre, Natarajan Shankar, and Dennis Müller. The details were published in [36].…”

Section: The Pvs Prelude and The Nasa Librarymentioning

confidence: 99%

“…Our export [36] used the generated XML files for both libraries. As a part of this export collaboration, the XML schema was heavily debugged and well-documented.…”

Section: Librariesmentioning

confidence: 99%

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Experiences from Exporting Major Proof Assistant Libraries

Kohlhase

Rabe

2021

J Autom Reasoning

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The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof assistants, specifically the ones of Coq, HOL Light, IMPS, Isabelle, Mizar, and PVS into a universal format: OMDoc/MMT. Each translation presented great theoretical, technical, and social challenges, some universal and some system-specific, some solvable and some still open. In this paper, we survey these challenges and compare and evaluate the solutions we chose. We believe similar library translations will be an essential part of any future system interoperability solution, and our experiences will prove valuable to others undertaking such efforts.

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Section: Problem and Related Workmentioning

confidence: 99%

“…Our PVS export was carried out together with Sam Owre, Natarajan Shankar, and Dennis Müller. The details were published in [36].…”

Section: The Pvs Prelude and The Nasa Librarymentioning

confidence: 99%

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Experiences from Exporting Major Proof Assistant Libraries

Kohlhase

Rabe

2021

J Autom Reasoning

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“…Additionally, several theorem prover libraries have been translated to OMDOC and integrated in the MMT system, e.g. Kohlhase et al (2017b); (for a detailed overview, see Müller (2019) and Kohlhase & Rabe (2020)). Extending these integrations to enable exporting from MMT as well (and in conjunction with natural language processing), this could enable verifying informal mathematics imported via sT E X using external state-of-the-art theorem prover systems.…”

Section: Mmtmentioning

confidence: 99%

Disambiguating Symbolic Expressions in Informal Documents

Müller¹,

Kaliszyk²

2021

Preprint

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We propose the task of disambiguating symbolic expressions in informal STEM documents in the form of L A T E X files -that is, determining their precise semantics and abstract syntax tree -as a neural machine translation task. We discuss the distinct challenges involved and present a dataset with roughly 33,000 entries. We evaluated several baseline models on this dataset, which failed to yield even syntactically valid L A T E X before overfitting. Consequently, we describe a methodology using a transformer language model pre-trained on sources obtained from arxiv.org, which yields promising results despite the small size of the dataset. We evaluate our model using a plurality of dedicated techniques, taking the syntax and semantics of symbolic expressions into account.

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“…Secondly, we can use a logical framework that provides a uniform intermediate data structure, in which we can specify the respective foundations and their libraries. This approach has been used by the authors' research group in [IKR11] for Mizar, in [KR14] for HOL Light and in [KMOR17] for PVS, using the MMT framework [RK13]. A similar approach is currently underway using Dedukti [BCH12] as the framework system.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Alignment-based Translations Across Formal Systems Using Interface Theories

Müller

Rothgang

Liu

et al. 2017

Electron. Proc. Theor. Comput. Sci.

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Translating expressions between different logics and theorem provers is notoriously and often prohibitively difficult, due to the large differences between the logical foundations, the implementations of the systems, and the structure of the respective libraries. Practical solutions for exchanging theorems across theorem provers have remained both weak and brittle. Consequently, libraries are not easily reusable across systems, and substantial effort must be spent on reformalizing and proving basic results in each system. Notably, this problem exists already if we only try to exchange theorem statements and forgo exchanging proofs.In previous work we introduced alignments as a lightweight standard for relating concepts across libraries and conjectured that it would provide a good base for translating expressions. In this paper, we demonstrate the feasibility of this approach. We use a foundationally uncommitted framework to write interface theories that abstract from logical foundation, implementation, and library structure. Then we use alignments to record how the concepts in the interface theories are realized in several major proof assistant libraries, and we use that information to translate expressions across libraries. Concretely, we present exemplary interface theories for several areas of mathematics and -in total -several hundred alignments that were found manually.

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Making PVS Accessible to Generic Services by Interpretation in a Universal Format

Cited by 13 publications

References 19 publications

Experiences from Exporting Major Proof Assistant Libraries

Experiences from Exporting Major Proof Assistant Libraries

Disambiguating Symbolic Expressions in Informal Documents

Alignment-based Translations Across Formal Systems Using Interface Theories

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