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Documents authored by Atkey, Robert

Artifact
Software
DOI: 10.4230/artifacts.23126
vehicle-lang/vehicle

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

Abstract
Cite as

Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, Luca Arnaboldi. vehicle-lang/vehicle (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{AtkeyVehicleForm23,
   title = {{vehicle-lang/vehicle}}, 
   author = {Daggitt, Matthew L. and Kokke, Wen and Atkey, Robert and Komendantskaya, Ekaterina and Slusarz, Natalia and Arnaboldi, Luca},
   note = {Software, version 0.16.1., EPSRC grant AISEC: AI Secure and Explainable by Construction (EP/T026960/1, EP/T027037/1, EP/T026960/1), swhId: \href{https://archive.softwareheritage.org/swh:1:dir:0fa35e993030867ae24451f644c7c296c0f70f22;origin=https://github.com/vehicle-lang/vehicle;visit=swh:1:snp:a878c982596b8bfb093b9e4710463b94df33e699;anchor=swh:1:rev:9d607a0fffb599b31f53b13d06474dbdec41f2aa}{\texttt{swh:1:dir:0fa35e993030867ae24451f644c7c296c0f70f22}} (visited on 2025-07-07)},
   url = {https://github.com/vehicle-lang/vehicle},
   doi = {10.4230/artifacts.23126},
}
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.FSCD.2017.18
Continuation Passing Style for Effect Handlers

Authors: Daniel Hillerström, Sam Lindley, Robert Atkey, and K. C. Sivaramakrishnan

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
We present Continuation Passing Style (CPS) translations for Plotkin and Pretnar's effect handlers with Hillerström and Lindley's row-typed fine-grain call-by-value calculus of effect handlers as the source language. CPS translations of handlers are interesting theoretically, to explain the semantics of handlers, and also offer a practical implementation technique that does not require special support in the target language's runtime. We begin with a first-order CPS translation into untyped lambda calculus which manages a stack of continuations and handlers as a curried sequence of arguments. We then refine the initial CPS translation first by uncurrying it to yield a properly tail-recursive translation and second by making it higher-order in order to contract administrative redexes at translation time. We prove that the higher-order CPS translation simulates effect handler reduction. We have implemented the higher-order CPS translation as a JavaScript backend for the Links programming language.
Cite as

Daniel Hillerström, Sam Lindley, Robert Atkey, and K. C. Sivaramakrishnan. Continuation Passing Style for Effect Handlers. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{hillerstrom_et_al:LIPIcs.FSCD.2017.18,
  author =	{Hillerstr\"{o}m, Daniel and Lindley, Sam and Atkey, Robert and Sivaramakrishnan, K. C.},
  title =	{{Continuation Passing Style for Effect Handlers}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{18:1--18:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.18},
  URN =		{urn:nbn:de:0030-drops-77394},
  doi =		{10.4230/LIPIcs.FSCD.2017.18},
  annote =	{Keywords: effect handlers, delimited control, continuation passing style}
}
Document
DOI: 10.4230/LIPIcs.TLCA.2015.45
Models for Polymorphism over Physical Dimension

Authors: Robert Atkey, Neil Ghani, Fredrik Nordvall Forsberg, Timothy Revell, and Sam Staton

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)

Abstract
We provide a categorical framework for models of a type theory that has special types for physical quantities. The types are indexed by the physical dimensions that they involve. Fibrations are used to organize this index structure in the models of the type theory. We develop some informative models of this type theory: firstly, a model based on group actions, which captures invariance under scaling, and secondly, a way of constructing new models using relational parametricity.
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Robert Atkey, Neil Ghani, Fredrik Nordvall Forsberg, Timothy Revell, and Sam Staton. Models for Polymorphism over Physical Dimension. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 45-59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{atkey_et_al:LIPIcs.TLCA.2015.45,
  author =	{Atkey, Robert and Ghani, Neil and Nordvall Forsberg, Fredrik and Revell, Timothy and Staton, Sam},
  title =	{{Models for Polymorphism over Physical Dimension}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{45--59},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.45},
  URN =		{urn:nbn:de:0030-drops-51547},
  doi =		{10.4230/LIPIcs.TLCA.2015.45},
  annote =	{Keywords: Category Theory, Units of Measure, Dimension Types, Type Theory}
}
Document
DOI: 10.4230/LIPIcs.CSL.2012.46
Relational Parametricity for Higher Kinds

Authors: Robert Atkey

Published in: LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012)

Abstract
Reynolds' notion of relational parametricity has been extremely influential and well studied for polymorphic programming languages and type theories based on System F. The extension of relational parametricity to higher kinded polymorphism, which allows quantification over type operators as well as types, has not received as much attention. We present a model of relational parametricity for System Fomega, within the impredicative Calculus of Inductive Constructions, and show how it forms an instance of a general class of models defined by Hasegawa. We investigate some of the consequences of our model and show that it supports the definition of inductive types, indexed by an arbitrary kind, and with reasoning principles provided by initiality.
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Robert Atkey. Relational Parametricity for Higher Kinds. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 46-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{atkey:LIPIcs.CSL.2012.46,
  author =	{Atkey, Robert},
  title =	{{Relational Parametricity for Higher Kinds}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{46--61},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{C\'{e}gielski, Patrick and Durand, Arnaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.46},
  URN =		{urn:nbn:de:0030-drops-36638},
  doi =		{10.4230/LIPIcs.CSL.2012.46},
  annote =	{Keywords: Relational Parametricity, Higher Kinds, Polymorphism}
}
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