Abstract
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.
Highlights
Motivation The QED manifesto [2] of 1994 urged the automated reasoning community to work toward a universal, computer-based database of all mathematical knowledge, strictly formalized in logic and supported by proofs that can be checked mechanically
Contribution In [37], we proposed a major project of extending representations of proof assistant logics in logical framework and exporting their entire libraries into a universal format
We have presented experiences from building exports of major theorem prover libraries spanning some five years
Summary
Motivation The QED manifesto [2] of 1994 urged the automated reasoning community to work toward a universal, computer-based database of all mathematical knowledge, strictly formalized in logic and supported by proofs that can be checked mechanically. The QED database was intended as a communal resource that would guide research and allow the evaluation of automated reasoning tools and systems This database was never realized, but the interoperability of proof assistants and the integration of their libraries has remained a highly valued but elusive goal. The logical framework can serve as a uniform intermediate data structure via which libraries can be moved into other proof assistants Such translations were built in [60] from a representation of HOL in LF to one of Nuprl and in [10] for a large set of logics. The entire text of this paper is new with the exception that the sections on the individual systems include short high-level summaries of the respective export to make the paper self-contained
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