9 research outputs found

    LF+ in Coq for fast-and-loose reasoning

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    We develop the metatheory and the implementation, in Coq, of the novel logical framework LF+ and discuss several of its applications. LF+ generalises research work, carried out by the authors over more than a decade, on Logical Frameworks conservatively extending LF and featuring lock-type constructors L-P(N:sigma)[center dot]. Lock-types capture monadically the concept of inhabitability up-to. They were originally introduced for factoring-out, postponing, or delegating to external tools the verification of time-consuming judgments, which are morally proof-irrelevant, thus allowing for integrating different sources of epistemic evidence in a unique Logical Framework. Besides introducing LF+ and its "shallow" implementation in Coq, the main novelty of the paper is to show that lock-types are also a very flexible tool for expressing in Type Theory several diverse cognitive attitudes and mental strategies used in ordinary reasoning, which essentially amount to reasoning up-to, as in e.g. Typical Ambiguity provisos or co-inductive Coq proofs. In particular we address the encoding of the emerging paradigm of fast-and-loose reasoning, which trades off efficiency for correctness. This paradigm, implicitly used normally in naive Set Theory, is producing considerable impact also in computer architecture and distributed systems, when branch prediction and optimistic concurrency control are implemented

    A definitional implementation of the LAX logical framework LLFP in CoQ, for supporting fast and loose reasoning

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    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

    Day v. Transportation Department Clerk\u27s Record Dckt. 45552

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    https://digitalcommons.law.uidaho.edu/idaho_supreme_court_record_briefs/8604/thumbnail.jp

    Hammer v. City of Sun Valley Clerk\u27s Record v. 9 Dckt. 43079

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    https://digitalcommons.law.uidaho.edu/idaho_supreme_court_record_briefs/7596/thumbnail.jp

    State, Dept. of Transp. v. Grathol Clerk\u27s Record Dckt. 40168

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    https://digitalcommons.law.uidaho.edu/idaho_supreme_court_record_briefs/5911/thumbnail.jp

    Journal of the House of Representatives, 1838-1841

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    The published daily journals of the transactions of the House of Representatives for the current legislative session and the official bound journals printed after adjournment for previous legislative sessions. Four consecutive volumes bound as one
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