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Documents authored by Felicissimo, Thiago

Document
DOI: 10.4230/LIPIcs.LICS.2026.41
Definitional Proof Irrelevance Made Accessible

Authors: Thiago Felicissimo, Yann Leray, Loïc Pujet, Nicolas Tabareau, Éric Tanter, and Théo Winterhalter

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
A universe of propositions equipped with definitional proof irrelevance constitutes a convenient medium to express properties and proofs in type-theoretic proof assistants such as Lean, Rocq, and Agda. However, allowing accessibility predicates - used to establish semantic termination arguments - to inhabit such a universe yields undecidable typechecking, hampering the predictability and foundational bases of a proof assistant. To effectively reconcile definitional proof irrelevance and accessibility predicates with both theoretical foundations and practicality in mind, we describe a type theory that extends the Calculus of Inductive Constructions featuring observational equality in a universe of strict propositions, with two variants for handling the elimination principle of accessibility predicates: one variant safeguards decidability by sticking to propositional unfolding, and the other variant favors flexibility with definitional unfolding, at the expense of a potentially diverging typechecking procedure. Crucially, the metatheory of this dual approach establishes that any proof made in the definitional variant of the theory can be translated into a proof of the same statement in the propositional variant, all while preserving the decidability of the latter. Moreover, we prove the two variants to be consistent and to satisfy forms of canonicity, ensuring that programs can indeed be properly evaluated. We present an implementation in Rocq and compare it with existing approaches. Overall, this work introduces an effective technique that informs the design of proof assistants with strict propositions, enabling local computation with accessibility predicates without compromising the ambient type theory.
Cite as

Thiago Felicissimo, Yann Leray, Loïc Pujet, Nicolas Tabareau, Éric Tanter, and Théo Winterhalter. Definitional Proof Irrelevance Made Accessible. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 41:1-41:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{felicissimo_et_al:LIPIcs.LICS.2026.41,
  author =	{Felicissimo, Thiago and Leray, Yann and Pujet, Lo\"{i}c and Tabareau, Nicolas and Tanter, \'{E}ric and Winterhalter, Th\'{e}o},
  title =	{{Definitional Proof Irrelevance Made Accessible}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{41:1--41:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.41},
  URN =		{urn:nbn:de:0030-drops-268289},
  doi =		{10.4230/LIPIcs.LICS.2026.41},
  annote =	{Keywords: Dependent type theory, proof assistants, Rocq, proof irrelevance, accessibility predicates, observational equality, canonicity, set-theoretic models}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.21
Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti

Authors: Thiago Felicissimo and Théo Winterhalter

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
Proof assistants such as Coq implement a type theory featuring three important features: impredicativity, cumulativity and product covariance. This combination has proven difficult to be expressed in the logical framework Dedukti, and previous attempts have failed in providing an encoding that is proven confluent, sound and conservative. In this work we solve this longstanding open problem by providing an encoding of these three features that we prove to be confluent, sound and to satisfy a restricted (but, we argue, strong enough) form of conservativity. Our proof of confluence is a contribution by itself, and combines various criteria and proof techniques from rewriting theory. Our proof of soundness also contributes a new strategy in which the result is shown in terms of an inverse translation function, fixing a common flaw made in some previous encoding attempts.
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Thiago Felicissimo and Théo Winterhalter. Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{felicissimo_et_al:LIPIcs.FSCD.2024.21,
  author =	{Felicissimo, Thiago and Winterhalter, Th\'{e}o},
  title =	{{Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{21:1--21:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.21},
  URN =		{urn:nbn:de:0030-drops-203503},
  doi =		{10.4230/LIPIcs.FSCD.2024.21},
  annote =	{Keywords: Dedukti, Rewriting, Confluence, Dependent types, Cumulativity, Universes}
}
Document
DOI: 10.4230/LIPIcs.CSL.2023.19
Translating Proofs from an Impredicative Type System to a Predicative One

Authors: Thiago Felicissimo, Frédéric Blanqui, and Ashish Kumar Barnawal

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
As the development of formal proofs is a time-consuming task, it is important to devise ways of sharing the already written proofs to prevent wasting time redoing them. One of the challenges in this domain is to translate proofs written in proof assistants based on impredicative logics, such as Coq, Matita and the HOL family, to proof assistants based on predicative logics like Agda, whenever impredicativity is not used in an essential way. In this paper we present an algorithm to do such a translation between a core impredicative type system and a core predicative one allowing prenex universe polymorphism like in Agda. It consists in trying to turn a potentially impredicative term into a universe polymorphic term as general as possible. The use of universe polymorphism is justified by the fact that mapping an impredicative universe to a fixed predicative one is not sufficient in most cases. During the algorithm, we need to solve unification problems modulo the max-successor algebra on universe levels. But, in this algebra, there are solvable problems having no most general solution. We however provide an incomplete algorithm whose solutions, when it succeeds, are most general ones. The proposed translation is of course partial, but in practice allows one to translate many proofs that do not use impredicativity in an essential way. Indeed, it was implemented in the tool Predicativize and then used to translate semi-automatically many non-trivial developments from Matita’s arithmetic library to Agda, including Bertrand’s Postulate and Fermat’s Little Theorem, which were not available in Agda yet.
Cite as

Thiago Felicissimo, Frédéric Blanqui, and Ashish Kumar Barnawal. Translating Proofs from an Impredicative Type System to a Predicative One. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{felicissimo_et_al:LIPIcs.CSL.2023.19,
  author =	{Felicissimo, Thiago and Blanqui, Fr\'{e}d\'{e}ric and Barnawal, Ashish Kumar},
  title =	{{Translating Proofs from an Impredicative Type System to a Predicative One}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.19},
  URN =		{urn:nbn:de:0030-drops-174801},
  doi =		{10.4230/LIPIcs.CSL.2023.19},
  annote =	{Keywords: Type Theory, Impredicativity, Predicativity, Proof Translation, Universe Polymorphism, Unification Modulo Max, Agda, Dedukti}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.25
Adequate and Computational Encodings in the Logical Framework Dedukti

Authors: Thiago Felicissimo

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
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.
Cite as

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)

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@InProceedings{felicissimo:LIPIcs.FSCD.2022.25,
  author =	{Felicissimo, Thiago},
  title =	{{Adequate and Computational Encodings in the Logical Framework Dedukti}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.25},
  URN =		{urn:nbn:de:0030-drops-163064},
  doi =		{10.4230/LIPIcs.FSCD.2022.25},
  annote =	{Keywords: Type Theory, Logical Frameworks, Rewriting, Dedukti, Pure Type Systems}
}
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