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Documents authored by Lancelot, Adrienne

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Software
DOI: 10.4230/artifacts.23906
adrilancelot/Abella-lambda-Barendregt-theory

Authors: Adrienne Lancelot, Beniamino Accattoli, and Maxime Vemclefs

Abstract
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Adrienne Lancelot, Beniamino Accattoli, Maxime Vemclefs. adrilancelot/Abella-lambda-Barendregt-theory (Software, Abella formalization code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{AbellaSources,
   title = {{adrilancelot/Abella-lambda-Barendregt-theory}}, 
   author = {Lancelot, Adrienne and Accattoli, Beniamino and Vemclefs, Maxime},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:b20ffd2d8d946adac1eb2fffa72112d23a2deeed;origin=https://github.com/adrilancelot/Abella-lambda-Barendregt-theory;visit=swh:1:snp:51adf802a55fe82840e4e8d940b31babccdb58a2;anchor=swh:1:rev:07ea3f03983145ce1b7e070e3afbe9ff730d2531}{\texttt{swh:1:dir:b20ffd2d8d946adac1eb2fffa72112d23a2deeed}} (visited on 2025-09-22)},
   url = {https://github.com/adrilancelot/Abella-lambda-Barendregt-theory},
   doi = {10.4230/artifacts.23906},
}
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.
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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.
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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.2024.23
Mirroring Call-By-Need, or Values Acting Silly

Authors: Beniamino Accattoli and Adrienne Lancelot

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

Abstract
Call-by-need evaluation for the λ-calculus can be seen as merging the best of call-by-name and call-by-value, namely the wise erasing behaviour of the former and the wise duplicating behaviour of the latter. To better understand how duplication and erasure can be combined, we design a degenerated calculus, dubbed call-by-silly, that is symmetric to call-by-need in that it merges the worst of call-by-name and call-by-value, namely silly duplications by-name and silly erasures by-value. We validate the design of the call-by-silly calculus via rewriting properties and multi types. In particular, we mirror the main theorem about call-by-need - that is, its operational equivalence with call-by-name - showing that call-by-silly and call-by-value induce the same contextual equivalence. This fact shows the blindness with respect to efficiency of call-by-value contextual equivalence. We also define a call-by-silly strategy and measure its length via tight multi types. Lastly, we prove that the call-by-silly strategy computes evaluation sequences of maximal length in the calculus.
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Beniamino Accattoli and Adrienne Lancelot. Mirroring Call-By-Need, or Values Acting Silly. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{accattoli_et_al:LIPIcs.FSCD.2024.23,
  author =	{Accattoli, Beniamino and Lancelot, Adrienne},
  title =	{{Mirroring Call-By-Need, or Values Acting Silly}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{23:1--23:24},
  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.2024.23},
  URN =		{urn:nbn:de:0030-drops-203527},
  doi =		{10.4230/LIPIcs.FSCD.2024.23},
  annote =	{Keywords: Lambda calculus, intersection types, call-by-value, call-by-need}
}
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