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Documents authored by Biernacka, Małgorzata

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.ITP.2022.7
The Zoo of Lambda-Calculus Reduction Strategies, And Coq

Authors: Małgorzata Biernacka, Witold Charatonik, and Tomasz Drab

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

Abstract
We present a generic framework for the specification and reasoning about reduction strategies in the lambda calculus, representable as sets of term decompositions. It is provided as a Coq formalization that features a novel format of phased strategies. It facilitates concise description and algebraic reasoning about properties of reduction strategies. The formalization accommodates many well-known strategies, both weak and strong, such as call by name, call by value, head reduction, normal order, full β-reduction, etc. We illustrate the use of the framework as a tool to inspect and categorize the "zoo" of existing strategies, as well as to discover and study new ones with particular properties.
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Małgorzata Biernacka, Witold Charatonik, and Tomasz Drab. The Zoo of Lambda-Calculus Reduction Strategies, And Coq. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{biernacka_et_al:LIPIcs.ITP.2022.7,
  author =	{Biernacka, Ma{\l}gorzata and Charatonik, Witold and Drab, Tomasz},
  title =	{{The Zoo of Lambda-Calculus Reduction Strategies, And Coq}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{7:1--7:19},
  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.2022.7},
  URN =		{urn:nbn:de:0030-drops-167165},
  doi =		{10.4230/LIPIcs.ITP.2022.7},
  annote =	{Keywords: Lambda calculus, Reduction strategies, Coq}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2019.8
Deriving an Abstract Machine for Strong Call by Need

Authors: Małgorzata Biernacka and Witold Charatonik

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

Abstract
Strong call by need is a reduction strategy for computing strong normal forms in the lambda calculus, where terms are fully normalized inside the bodies of lambda abstractions and open terms are allowed. As typical for a call-by-need strategy, the arguments of a function call are evaluated at most once, only when they are needed. This strategy has been introduced recently by Balabonski et al., who proved it complete with respect to full beta-reduction and conservative over weak call by need. We show a novel reduction semantics and the first abstract machine for the strong call-by-need strategy. The reduction semantics incorporates syntactic distinction between strict and non-strict let constructs and is geared towards an efficient implementation. It has been defined within the framework of generalized refocusing, i.e., a generic method that allows to go from a reduction semantics instrumented with context kinds to the corresponding abstract machine; the machine is thus correct by construction. The format of the semantics that we use makes it explicit that strong call by need is an example of a hybrid strategy with an infinite number of substrategies.
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Małgorzata Biernacka and Witold Charatonik. Deriving an Abstract Machine for Strong Call by Need. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{biernacka_et_al:LIPIcs.FSCD.2019.8,
  author =	{Biernacka, Ma{\l}gorzata and Charatonik, Witold},
  title =	{{Deriving an Abstract Machine for Strong Call by Need}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{8:1--8:20},
  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.2019.8},
  URN =		{urn:nbn:de:0030-drops-105159},
  doi =		{10.4230/LIPIcs.FSCD.2019.8},
  annote =	{Keywords: abstract machines, reduction semantics}
}
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