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Titlebook: Certified Programs and Proofs; Third International Georges Gonthier,Michael Norrish Conference proceedings 2013 Springer International Pub

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Certified Parsing of Regular Languagess a regular expression if and only if the NFA accepts it. The proof of the if-part is effectively a function turning acceptance of a string into a parse tree while the only-if part gives a function turning rejection into a proof of impossibility of a parse tree.
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A Formal Proof of Borodin-Trakhtenbrot’s Gap Theoremons required to prove the result (smaller than expected, actually). The work is part of a long term . program, whose goal is to obtain, via a reverse methodological approach, a formal treatment of Complexity Theory at a comfortable level of abstraction and logical rigor.
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Episode I: The 1986 Legislation, polynomials and .-terms modulo .-equivalence. The many-sorted metatheory of nonfree datatypes is formalized as an ordinary Isabelle theory and is animated by the package into user-specified instances. HOL lacks a type of types, so we employ an ad hoc construction of a universe embedding the relevant parameter types.
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