6 Search Results for "Polesiuk, Piotr"

Document
DOI: 10.4230/LIPIcs.ITP.2025.13
Barendregt’s Theory of the λ-Calculus, Refreshed and Formalized

Authors: Adrienne Lancelot, Beniamino Accattoli, and Maxime Vemclefs

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

Abstract
Barendregt’s book on the untyped λ-calculus refines the inconsistent view of β-divergence as representation of the undefined via the key concept of head reduction. In this paper, we put together recent revisitations of some key theorems laid out in Barendregt’s book, and we formalize them in the Abella proof assistant. Our work provides a compact and refreshed presentation of the core of the book. The formalization faithfully mimics pen-and-paper proofs. Two interesting aspects are the manipulation of contexts for the study of contextual equivalence and a formal alternative to the informal trick at work in Takahashi’s proof of the genericity lemma. As a by-product, we obtain an alternative definition of contextual equivalence that does not mention contexts.
Cite as

Adrienne Lancelot, Beniamino Accattoli, and Maxime Vemclefs. Barendregt’s Theory of the λ-Calculus, Refreshed and Formalized. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lancelot_et_al:LIPIcs.ITP.2025.13,
  author =	{Lancelot, Adrienne and Accattoli, Beniamino and Vemclefs, Maxime},
  title =	{{Barendregt’s Theory of the \lambda-Calculus, Refreshed and Formalized}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{13:1--13:22},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-246114},
  doi =		{10.4230/LIPIcs.ITP.2025.13},
  annote =	{Keywords: lambda-calculus, head reduction, equational theory}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2024.4
Separating Terms by Means of Multi Types, Coinductively

Authors: Adrienne Lancelot

Published in: LIPIcs, Volume 336, 30th International Conference on Types for Proofs and Programs (TYPES 2024)

Abstract
Intersection type systems, as adequate models of the λ-calculus, induce an equational theory on terms, that we refer to as type equivalence. We give a new proof technique to coinductively characterize type equivalence. To do so, we explore a simple setting, namely weak head type equivalence, which is the equational theory induced by a weak head non-idempotent intersection type system. We prove a folklore result: weak head type equivalence coincides with Sangiorgi’s normal form bisimilarity. What is new in our development is that we only rely on coinductive program equivalences, bypassing the need to introduce term approximants, which were used in previous works characterizing type equivalence. The crucial part of this characterization is to show that type equivalent terms are normal form bisimilar: we do so by constructing shape typings that can only type terms of a specific normal form structure. Shape typings are a light form of principal types, a technique often used in intersection types to generate from one or few principal typing all possible typings of a term.
Cite as

Adrienne Lancelot. Separating Terms by Means of Multi Types, Coinductively. In 30th International Conference on Types for Proofs and Programs (TYPES 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 336, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lancelot:LIPIcs.TYPES.2024.4,
  author =	{Lancelot, Adrienne},
  title =	{{Separating Terms by Means of Multi Types, Coinductively}},
  booktitle =	{30th International Conference on Types for Proofs and Programs (TYPES 2024)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-376-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{336},
  editor =	{M{\o}gelberg, Rasmus Ejlers and van den Berg, Benno},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2024.4},
  URN =		{urn:nbn:de:0030-drops-233660},
  doi =		{10.4230/LIPIcs.TYPES.2024.4},
  annote =	{Keywords: lambda calculus, intersection types, program equivalence}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2020.7
A Complete Normal-Form Bisimilarity for Algebraic Effects and Handlers

Authors: Dariusz Biernacki, Sergueï Lenglet, and Piotr Polesiuk

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
We present a complete coinductive syntactic theory for an untyped calculus of algebraic operations and handlers, a relatively recent concept that augments a programming language with unprecedented flexibility to define, combine and interpret computational effects. Our theory takes the form of a normal-form bisimilarity and its soundness w.r.t. contextual equivalence hinges on using so-called context variables to test evaluation contexts comprising normal forms other than values. The theory is formulated in purely syntactic elementary terms and its completeness demonstrates the discriminating power of handlers. It crucially takes advantage of the clean separation of effect handling code from effect raising construct, a distinctive feature of algebraic effects, not present in other closely related control structures such as delimited-control operators.
Cite as

Dariusz Biernacki, Sergueï Lenglet, and Piotr Polesiuk. A Complete Normal-Form Bisimilarity for Algebraic Effects and Handlers. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{biernacki_et_al:LIPIcs.FSCD.2020.7,
  author =	{Biernacki, Dariusz and Lenglet, Sergue\"{i} and Polesiuk, Piotr},
  title =	{{A Complete Normal-Form Bisimilarity for Algebraic Effects and Handlers}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.7},
  URN =		{urn:nbn:de:0030-drops-123295},
  doi =		{10.4230/LIPIcs.FSCD.2020.7},
  annote =	{Keywords: algebraic effect, handler, behavioral equivalence, bisimilarity}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2019.30
Typed Equivalence of Effect Handlers and Delimited Control

Authors: Maciej Piróg, Piotr Polesiuk, and Filip Sieczkowski

Published in: LIPIcs, Volume 131, 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)

Abstract
It is folklore that effect handlers and delimited control operators are closely related: recently, this relationship has been proved in an untyped setting for deep handlers and the shift_0 delimited control operator. We positively resolve the conjecture that in an appropriately polymorphic type system this relationship can be extended to the level of types, by identifying the necessary forms of polymorphism, thus extending the definability result to the typed context. In the process, we identify a novel and potentially interesting type system feature for delimited control operators. Moreover, we extend these results to substantiate the folklore connection between shallow handlers and control_0 flavour of delimited control, both in an untyped and typed settings.
Cite as

Maciej Piróg, Piotr Polesiuk, and Filip Sieczkowski. Typed Equivalence of Effect Handlers and Delimited Control. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{pirog_et_al:LIPIcs.FSCD.2019.30,
  author =	{Pir\'{o}g, Maciej and Polesiuk, Piotr and Sieczkowski, Filip},
  title =	{{Typed Equivalence of Effect Handlers and Delimited Control}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Geuvers, Herman},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.30},
  URN =		{urn:nbn:de:0030-drops-105376},
  doi =		{10.4230/LIPIcs.FSCD.2019.30},
  annote =	{Keywords: type-and-effect systems, algebraic effects, delimited control, macro expressibility}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2016.9
Environmental Bisimulations for Delimited-Control Operators with Dynamic Prompt Generation

Authors: Andrés Aristizábal, Dariusz Biernacki, Sergueï Lenglet, and Piotr Polesiuk

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)

Abstract
We present sound and complete environmental bisimilarities for a variant of Dybvig et al.'s calculus of multi-prompted delimited-control operators with dynamic prompt generation. The reasoning principles that we obtain generalize and advance the existing techniques for establishing program equivalence in calculi with single-prompted delimited control. The basic theory that we develop is presented using Madiot et al.'s framework that allows for smooth integration and composition of up-to techniques facilitating bisimulation proofs. We also generalize the framework in order to express environmental bisimulations that support equivalence proofs of evaluation contexts representing continuations. This change leads to a novel and powerful up-to technique enhancing bisimulation proofs in the presence of control operators.
Cite as

Andrés Aristizábal, Dariusz Biernacki, Sergueï Lenglet, and Piotr Polesiuk. Environmental Bisimulations for Delimited-Control Operators with Dynamic Prompt Generation. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{aristizabal_et_al:LIPIcs.FSCD.2016.9,
  author =	{Aristiz\'{a}bal, Andr\'{e}s and Biernacki, Dariusz and Lenglet, Sergue\"{i} and Polesiuk, Piotr},
  title =	{{Environmental Bisimulations for Delimited-Control Operators with Dynamic Prompt Generation}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.9},
  URN =		{urn:nbn:de:0030-drops-59756},
  doi =		{10.4230/LIPIcs.FSCD.2016.9},
  annote =	{Keywords: delimited continuation, dynamic prompt generation, contextual equivalence, environmental bisimulation, up-to technique}
}
Document
DOI: 10.4230/LIPIcs.TLCA.2015.107
Logical Relations for Coherence of Effect Subtyping

Authors: Dariusz Biernacki and Piotr Polesiuk

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

Abstract
A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the typing derivation for a given typing judgment. In this article we present heterogeneous, biorthogonal, step-indexed logical relations for establishing the coherence of coercion semantics of programming languages with subtyping. To illustrate the effectiveness of the proof method, we develop a proof of coherence of a type-directed, selective CPS translation from a typed call-by-value lambda calculus with delimited continuations and control-effect subtyping. The article is accompanied by a Coq formalization that relies on a novel shallow embedding of a logic for reasoning about step-indexing.
Cite as

Dariusz Biernacki and Piotr Polesiuk. Logical Relations for Coherence of Effect Subtyping. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 107-122, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{biernacki_et_al:LIPIcs.TLCA.2015.107,
  author =	{Biernacki, Dariusz and Polesiuk, Piotr},
  title =	{{Logical Relations for Coherence of Effect Subtyping}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{107--122},
  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.2015.107},
  URN =		{urn:nbn:de:0030-drops-51580},
  doi =		{10.4230/LIPIcs.TLCA.2015.107},
  annote =	{Keywords: type system, coherence of subtyping, logical relation, control effect, continuation-passing style}
}
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