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Formal Metatheory of Programming Languages in the Matita Interactive Theorem Prover

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Abstract

This paper is a report about the use of Matita, an interactive theorem prover under development at the University of Bologna, for the solution of the POPLmark Challenge, part 1a. We provide three different formalizations, including two direct solutions using pure de Bruijn and locally nameless encodings of bound variables, and a formalization using named variables, obtained by means of a sound translation to the locally nameless encoding. According to this experience, we also discuss some of the proof principles used in our solutions, which have led to the development of a generalized inversion tactic for Matita.

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Authors and Affiliations

  1. Department of Computer Science, University of Bologna, Mura Anteo Zamboni, 7, 40127, Bologna, Italy

    Andrea Asperti, Wilmer Ricciotti & Claudio Sacerdoti Coen

  2. Microsoft Research - INRIA Joint Centre, Parc Orsay Université 28, rue Jean Rostand, 91893, Orsay, France

    Enrico Tassi

Authors
  1. Andrea Asperti
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  2. Wilmer Ricciotti
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  3. Claudio Sacerdoti Coen
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  4. Enrico Tassi
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Correspondence to Wilmer Ricciotti.

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Asperti, A., Ricciotti, W., Sacerdoti Coen, C. et al. Formal Metatheory of Programming Languages in the Matita Interactive Theorem Prover. J Autom Reasoning 49, 427–451 (2012). https://doi.org/10.1007/s10817-011-9228-z

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  • DOI: https://doi.org/10.1007/s10817-011-9228-z

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