Adequate and Computational Encodings in the Logical Framework Dedukti

Author Thiago Felicissimo

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Author Details

Thiago Felicissimo
  • Université Paris-Saclay, INRIA project Deducteam, Laboratoire de Méthodes Formelles, ENS Paris-Saclay, 91190, France


I would like to thank my PhD advisors Frédéric Blanqui and Gilles Dowek for the helpful discussions and comments on this paper. I would also like to thank the anonymous reviewers for their very helpful comments and suggestions.

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Thiago Felicissimo. Adequate and Computational Encodings in the Logical Framework Dedukti. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Dedukti is a very expressive logical framework which unlike most frameworks, such as the Edinburgh Logical Framework (LF), allows for the representation of computation alongside deduction. However, unlike LF encodings, Dedukti encodings proposed until now do not feature an adequacy theorem - i.e., a bijection between terms in the encoded system and in its encoding. Moreover, many of them also do not have a conservativity result, which compromises the ability of Dedukti to check proofs written in such encodings. We propose a different approach for Dedukti encodings which do not only allow for simpler conservativity proofs, but which also restore the adequacy of encodings. More precisely, we propose in this work adequate (and thus conservative) encodings for Functional Pure Type Systems. However, in contrast with LF encodings, ours is computational - that is, represents computation directly as computation. Therefore, our work is the first to present and prove correct an approach allowing for encodings that are both adequate and computational in Dedukti.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
  • Theory of computation → Equational logic and rewriting
  • Type Theory
  • Logical Frameworks
  • Rewriting
  • Dedukti
  • Pure Type Systems


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