A Definitional Implementation of the Lax Logical Framework LLFP in Coq, for Supporting Fast and Loose Reasoning

Fabio Alessi
(Department of Mathematics, Computer Science and Physics - University of Udine, Italy)
Alberto Ciaffaglione
(Department of Mathematics, Computer Science and Physics - University of Udine, Italy)
Pietro Di Gianantonio
(Department of Mathematics, Computer Science and Physics - University of Udine, Italy)
Furio Honsell
(Department of Mathematics, Computer Science and Physics - University of Udine, Italy)
Marina Lenisa
(Department of Mathematics, Computer Science and Physics - University of Udine, Italy)

The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to provide a conceptual framework for integrating different proof development tools, thus allowing for external evidence and for postponing, delegating, or factoring-out side conditions. In particular, LLFP allows for reducing the number of times a proof-irrelevant check is performed. In this paper we give a shallow, actually definitional, implementation of LLFP in Coq, i.e. we use Coq both as host framework and oracle for LLFP. This illuminates the principles underpinning the mechanism of Lock-types and also suggests how to possibly extend Coq with the features of LLFP. The derived proof editor is then put to use for developing case-studies on an emerging paradigm, both at logical and implementation level, which we call fast and loose reasoning following Danielsson et alii [6]. This paradigm trades off efficiency for correctness and amounts to postponing, or running in parallel, tedious or computationally demanding checks, until we are really sure that the intended goal can be achieved. Typical examples are branch-prediction in CPUs and optimistic concurrency control.

In Dale Miller and Ivan Scagnetto: Proceedings of the Fourteenth Workshop on Logical Frameworks and Meta-Languages: Theory and Practice (LFMTP 2019), Vancouver, Canada, 22nd June 2019, Electronic Proceedings in Theoretical Computer Science 307, pp. 8–23.
Published: 12th October 2019.

ArXived at: http://dx.doi.org/10.4204/EPTCS.307.3 bibtex PDF
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