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Documents authored by Biernacki, Dariusz

Document
DOI: 10.4230/LIPIcs.FSCD.2024.11
Optimizing a Non-Deterministic Abstract Machine with Environments

Authors: Małgorzata Biernacka, Dariusz Biernacki, Sergueï Lenglet, and Alan Schmitt

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

Abstract
Non-deterministic abstract machine (NDAM) is a recent implementation model for programming languages where one must choose among several redexes at each reduction step, like process calculi. These machines can be derived from a zipper semantics, a mix between structural operational semantics and context-based reduction semantics. Such a machine has been generated also for the λ-calculus without a fixed reduction strategy, i.e., with the full non-deterministic β-reduction. In that machine, substitution is an external operation that replaces all the occurrences of a variable at once. Implementing substitution with environments is more low-level and more efficient as variables are replaced only when needed. In this paper, we define a NDAM with environments for the λ-calculus without a fixed reduction strategy. We also introduce other optimizations, including a form of refocusing, and we show that we can restrict our optimized NDAM to recover some of the usual λ-calculus machines, e.g., the Krivine Abstract Machine. Most of the improvements we propose in this work could be applied to other NDAMs as well.
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Małgorzata Biernacka, Dariusz Biernacki, Sergueï Lenglet, and Alan Schmitt. Optimizing a Non-Deterministic Abstract Machine with Environments. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{biernacka_et_al:LIPIcs.FSCD.2024.11,
  author =	{Biernacka, Ma{\l}gorzata and Biernacki, Dariusz and Lenglet, Sergue\"{i} and Schmitt, Alan},
  title =	{{Optimizing a Non-Deterministic Abstract Machine with Environments}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{11:1--11:22},
  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.2024.11},
  URN =		{urn:nbn:de:0030-drops-203409},
  doi =		{10.4230/LIPIcs.FSCD.2024.11},
  annote =	{Keywords: Abstract machine, Explicit substitutions, Refocusing}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2022.7
Non-Deterministic Abstract Machines

Authors: Małgorzata Biernacka, Dariusz Biernacki, Sergueï Lenglet, and Alan Schmitt

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)

Abstract
We present a generic design of abstract machines for non-deterministic programming languages, such as process calculi or concurrent lambda calculi, that provides a simple way to implement them. Such a machine traverses a term in the search for a redex, making non-deterministic choices when several paths are possible and backtracking when it reaches a dead end, i.e., an irreducible subterm. The search is guaranteed to terminate thanks to term annotations the machine introduces along the way. We show how to automatically derive a non-deterministic abstract machine from a zipper semantics - a form of structural operational semantics in which the decomposition process of a term into a context and a redex is made explicit. The derivation method ensures the soundness and completeness of the machines w.r.t. the zipper semantics.
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Małgorzata Biernacka, Dariusz Biernacki, Sergueï Lenglet, and Alan Schmitt. Non-Deterministic Abstract Machines. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 7:1-7:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{biernacka_et_al:LIPIcs.CONCUR.2022.7,
  author =	{Biernacka, Ma{\l}gorzata and Biernacki, Dariusz and Lenglet, Sergue\"{i} and Schmitt, Alan},
  title =	{{Non-Deterministic Abstract Machines}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{7:1--7:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.7},
  URN =		{urn:nbn:de:0030-drops-170705},
  doi =		{10.4230/LIPIcs.CONCUR.2022.7},
  annote =	{Keywords: Abstract machines, non-determinism, lambda-calculus, process calculi}
}
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.
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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.2020.18
A Reflection on Continuation-Composing Style

Authors: Dariusz Biernacki, Mateusz Pyzik, and Filip Sieczkowski

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

Abstract
We present a study of the continuation-composing style (CCS) that describes the image of the CPS translation of Danvy and Filinski’s shift and reset delimited-control operators. In CCS continuations are composable rather than abortive as in the traditional CPS, and, therefore, the structure of terms is considerably more complex. We show that the CPS translation from Moggi’s computational lambda calculus extended with shift and reset has a right inverse and that the two translations form a reflection i.e., a Galois connection in which the target is isomorphic to a subset of the source (the orders are given by the reduction relations). Furthermore, we use this result to show that Plotkin’s call-by-value lambda calculus extended with shift and reset is isomorphic to the image of the CPS translation. This result, in particular, provides a first direct-style transformation for delimited continuations that is an inverse of the CPS transformation up to syntactic identity.
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Dariusz Biernacki, Mateusz Pyzik, and Filip Sieczkowski. A Reflection on Continuation-Composing Style. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{biernacki_et_al:LIPIcs.FSCD.2020.18,
  author =	{Biernacki, Dariusz and Pyzik, Mateusz and Sieczkowski, Filip},
  title =	{{A Reflection on Continuation-Composing Style}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{18:1--18:17},
  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.2020.18},
  URN =		{urn:nbn:de:0030-drops-123402},
  doi =		{10.4230/LIPIcs.FSCD.2020.18},
  annote =	{Keywords: delimited control, continuation-passing style, reflection, call-by-value lambda calculus, computational lambda calculus}
}
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.
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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.
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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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