4 Search Results for "Šinkarovs, Artjoms"

Document
DOI: 10.4230/LIPIcs.ITP.2025.33
Scott’s Representation Theorem and the Univalent Karoubi Envelope

Authors: Arnoud van der Leer, Kobe Wullaert, and Benedikt Ahrens

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Lambek and Scott constructed a correspondence between simply-typed lambda calculi and Cartesian closed categories. Scott’s Representation Theorem is a cousin to this result for untyped lambda calculi. It states that every untyped lambda calculus arises from a reflexive object in some category. We present a formalization of Scott’s Representation Theorem in univalent foundations, in the (Rocq-)UniMath library. Specifically, we implement two proofs of that theorem, one by Scott and one by Hyland. We also explain the role of the Karoubi envelope - a categorical construction - in the proofs and the impact the chosen foundation has on this construction. Finally, we report on some automation we have implemented for the reduction of λ-terms.
Cite as

Arnoud van der Leer, Kobe Wullaert, and Benedikt Ahrens. Scott’s Representation Theorem and the Univalent Karoubi Envelope. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 33:1-33:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanderleer_et_al:LIPIcs.ITP.2025.33,
  author =	{van der Leer, Arnoud and Wullaert, Kobe and Ahrens, Benedikt},
  title =	{{Scott’s Representation Theorem and the Univalent Karoubi Envelope}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{33:1--33:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.33},
  URN =		{urn:nbn:de:0030-drops-246318},
  doi =		{10.4230/LIPIcs.ITP.2025.33},
  annote =	{Keywords: Lambda calculi, algebraic theories, categorical semantics, Karoubi envelope, formalization, Rocq-UniMath, univalent foundations}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2025.2
Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs (Invited Talk)

Authors: Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, and Luca Arnaboldi

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Neuro-symbolic programs, i.e. programs containing both machine learning components and traditional symbolic code, are becoming increasingly widespread. Finding a general methodology for verifying such programs is challenging due to both the number of different tools involved and the intricate interface between the "neural" and "symbolic" program components. In this paper we present a general decomposition of the neuro-symbolic verification problem into parts, and examine the problem of the embedding gap that occurs when one tries to combine proofs about the neural and symbolic components. To address this problem we then introduce Vehicle - standing as an abbreviation for a "verification condition language" - an intermediate programming language interface between machine learning frameworks, automated theorem provers, and dependently-typed formalisations of neuro-symbolic programs. Vehicle allows users to specify the properties of the neural components of neuro-symbolic programs once, and then safely compile the specification to each interface using a tailored typing and compilation procedure. We give a high-level overview of Vehicle’s overall design, its interfaces and compilation & type-checking procedures, and then demonstrate its utility by formally verifying the safety of a simple autonomous car controlled by a neural network, operating in a stochastic environment with imperfect information.
Cite as

Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, and Luca Arnaboldi. Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs (Invited Talk). In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 2:1-2:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{daggitt_et_al:LIPIcs.FSCD.2025.2,
  author =	{Daggitt, Matthew L. and Kokke, Wen and Atkey, Robert and Komendantskaya, Ekaterina and Slusarz, Natalia and Arnaboldi, Luca},
  title =	{{Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{2:1--2:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.2},
  URN =		{urn:nbn:de:0030-drops-236172},
  doi =		{10.4230/LIPIcs.FSCD.2025.2},
  annote =	{Keywords: Neural Network Verification, Types, Interactive Theorem Provers}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2022.10
The Münchhausen Method in Type Theory

Authors: Thorsten Altenkirch, Ambrus Kaposi, Artjoms Šinkarovs, and Tamás Végh

Published in: LIPIcs, Volume 269, 28th International Conference on Types for Proofs and Programs (TYPES 2022)

Abstract
In one of his long tales, after falling into a swamp, Baron Münchhausen salvaged himself and the horse by lifting them both up by his hair. Inspired by this, the paper presents a technique to justify very dependent types. Such types reference the term that they classify, e.g. x : F x. While in most type theories this is not allowed, we propose a technique on salvaging the meaning of both the term and the type. The proposed technique does not refer to preterms or typing relations and works in a completely algebraic setting, e.g categories with families. With a series of examples we demonstrate our technique. We use Agda to demonstrate that our examples are implementable within a proof assistant.
Cite as

Thorsten Altenkirch, Ambrus Kaposi, Artjoms Šinkarovs, and Tamás Végh. The Münchhausen Method in Type Theory. In 28th International Conference on Types for Proofs and Programs (TYPES 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 269, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{altenkirch_et_al:LIPIcs.TYPES.2022.10,
  author =	{Altenkirch, Thorsten and Kaposi, Ambrus and \v{S}inkarovs, Artjoms and V\'{e}gh, Tam\'{a}s},
  title =	{{The M\"{u}nchhausen Method in Type Theory}},
  booktitle =	{28th International Conference on Types for Proofs and Programs (TYPES 2022)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-285-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{269},
  editor =	{Kesner, Delia and P\'{e}drot, Pierre-Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2022.10},
  URN =		{urn:nbn:de:0030-drops-184534},
  doi =		{10.4230/LIPIcs.TYPES.2022.10},
  annote =	{Keywords: type theory, proof assistants, very dependent types}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2023.24
Combinatory Logic and Lambda Calculus Are Equal, Algebraically

Authors: Thorsten Altenkirch, Ambrus Kaposi, Artjoms Šinkarovs, and Tamás Végh

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
It is well-known that extensional lambda calculus is equivalent to extensional combinatory logic. In this paper we describe a formalisation of this fact in Cubical Agda. The distinguishing features of our formalisation are the following: (i) Both languages are defined as generalised algebraic theories, the syntaxes are intrinsically typed and quotiented by conversion; we never mention preterms or break the quotients in our construction. (ii) Typing is a parameter, thus the un(i)typed and simply typed variants are special cases of the same proof. (iii) We define syntaxes as quotient inductive-inductive types (QIITs) in Cubical Agda; we prove the equivalence and (via univalence) the equality of these QIITs; we do not rely on any axioms, the conversion functions all compute and can be experimented with.
Cite as

Thorsten Altenkirch, Ambrus Kaposi, Artjoms Šinkarovs, and Tamás Végh. Combinatory Logic and Lambda Calculus Are Equal, Algebraically. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{altenkirch_et_al:LIPIcs.FSCD.2023.24,
  author =	{Altenkirch, Thorsten and Kaposi, Ambrus and \v{S}inkarovs, Artjoms and V\'{e}gh, Tam\'{a}s},
  title =	{{Combinatory Logic and Lambda Calculus Are Equal, Algebraically}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.24},
  URN =		{urn:nbn:de:0030-drops-180086},
  doi =		{10.4230/LIPIcs.FSCD.2023.24},
  annote =	{Keywords: Combinatory logic, lambda calculus, quotient inductive types, Cubical Agda}
}
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