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Documents authored by Åman Pohjola, Johannes

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Software
DOI: 10.4230/artifacts.24718
cbpv-reasonable-HOL

Authors: Zhuo Zoey Chen, Johannes Åman Pohjola, and Christine Rizkallah

Abstract
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Zhuo Zoey Chen, Johannes Åman Pohjola, Christine Rizkallah. cbpv-reasonable-HOL (Software, Mechanised Proof). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-24718,
   title = {{cbpv-reasonable-HOL}}, 
   author = {Chen, Zhuo Zoey and \r{A}man Pohjola, Johannes and Rizkallah, Christine},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:df18377e9fa5e35255f2687ad66ddbc2f010b934;origin=https://github.com/ZhuoZoeyChen/cbpv-reasonable-HOL;visit=swh:1:snp:9fefd6f03db3694a8bdc7e5ea8ff0f4a1fbde680;anchor=swh:1:rev:4e4f4692c9e6e1e23c566ec4730f81eafde32f3c}{\texttt{swh:1:dir:df18377e9fa5e35255f2687ad66ddbc2f010b934}} (visited on 2025-09-22)},
   url = {https://github.com/ZhuoZoeyChen/cbpv-reasonable-HOL/},
   doi = {10.4230/artifacts.24718},
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.7
A Verified Cost Model for Call-By-Push-Value

Authors: Zhuo Zoey Chen, Johannes Åman Pohjola, and Christine Rizkallah

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

Abstract
The call-by-push-value λ-calculus allows for syntactically specifying the order of evaluation as part of the term language. Hence, it serves as a unifying language for embedding various evaluation strategies including call-by-value and call-by-name. Given the impact of call-by-push-value, it is remarkable that its adequacy as a model for computational complexity theory has not yet been studied. In this paper, we show that the call-by-push-value λ-calculus is reasonable for both time and space complexity. A reasonable cost model can encode other reasonable cost models with polynomial overhead in time and constant factor overhead in space. We achieve this by encoding call-by-push-value λ-calculus into Turing machines, following a simulation strategy by Forster et al.; for the converse direction, we prove that Levy’s encoding of the call-by-value λ-calculus has reasonable complexity bounds. The main results have been formalised in the HOL4 theorem prover.
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Zhuo Zoey Chen, Johannes Åman Pohjola, and Christine Rizkallah. A Verified Cost Model for Call-By-Push-Value. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ITP.2025.7,
  author =	{Chen, Zhuo Zoey and \r{A}man Pohjola, Johannes and Rizkallah, Christine},
  title =	{{A Verified Cost Model for Call-By-Push-Value}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{7:1--7:19},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-246067},
  doi =		{10.4230/LIPIcs.ITP.2025.7},
  annote =	{Keywords: lambda calculus, formalizations of computational models, computability theory, HOL, call-by-push-value reduction, time and space complexity, abstract machines}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.15
A Verified Cyclicity Checker: For Theories with Overloaded Constants

Authors: Arve Gengelbach and Johannes Åman Pohjola

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
Non-terminating (dependencies of) definitions can lead to logical contradictions, for example when defining a boolean constant as its own negation. Some proof assistants thus detect and disallow non-terminating definitions. Termination is generally undecidable when constants may have different definitions at different type instances, which is called (ad-hoc) overloading. The Isabelle/HOL proof assistant supports overloading of constant definitions, but relies on an unclear foundation for this critical termination check. With this paper we aim to close this gap: we present a mechanised proof that, for restricted overloading, non-terminating definitions are of a detectable cyclic shape, and we describe a mechanised algorithm with its correctness proof. In addition we demonstrate this cyclicity checker on parts of the Isabelle/HOL main library. Furthermore, we introduce the first-ever formally verified kernel of a proof assistant for higher-order logic with overloaded definitions. All our results are formalised in the HOL4 theorem prover.
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Arve Gengelbach and Johannes Åman Pohjola. A Verified Cyclicity Checker: For Theories with Overloaded Constants. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gengelbach_et_al:LIPIcs.ITP.2022.15,
  author =	{Gengelbach, Arve and \r{A}man Pohjola, Johannes},
  title =	{{A Verified Cyclicity Checker: For Theories with Overloaded Constants}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.15},
  URN =		{urn:nbn:de:0030-drops-167240},
  doi =		{10.4230/LIPIcs.ITP.2022.15},
  annote =	{Keywords: cyclicity, non-termination, ad-hoc overloading, definitions, Isabelle/HOL}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.32
Characteristic Formulae for Liveness Properties of Non-Terminating CakeML Programs

Authors: Johannes Åman Pohjola, Henrik Rostedt, and Magnus O. Myreen

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
There are useful programs that do not terminate, and yet standard Hoare logics are not able to prove liveness properties about non-terminating programs. This paper shows how a Hoare-like programming logic framework (characteristic formulae) can be extended to enable reasoning about the I/O behaviour of programs that do not terminate. The approach is inspired by transfinite induction rather than coinduction, and does not require non-terminating loops to be productive. This work has been developed in the HOL4 theorem prover and has been integrated into the ecosystem of proof tools surrounding the CakeML programming language.
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Johannes Åman Pohjola, Henrik Rostedt, and Magnus O. Myreen. Characteristic Formulae for Liveness Properties of Non-Terminating CakeML Programs. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{amanpohjola_et_al:LIPIcs.ITP.2019.32,
  author =	{\r{A}man Pohjola, Johannes and Rostedt, Henrik and Myreen, Magnus O.},
  title =	{{Characteristic Formulae for Liveness Properties of Non-Terminating CakeML Programs}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{32:1--32:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.32},
  URN =		{urn:nbn:de:0030-drops-110872},
  doi =		{10.4230/LIPIcs.ITP.2019.32},
  annote =	{Keywords: Program verification, non-termination, liveness, Hoare logic}
}
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