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Documents authored by Timany, Amin

Document
DOI: 10.4230/LIPIcs.ECOOP.2023.22
Modular Verification of State-Based CRDTs in Separation Logic

Authors: Abel Nieto, Arnaud Daby-Seesaram, Léon Gondelman, Amin Timany, and Lars Birkedal

Published in: LIPIcs, Volume 263, 37th European Conference on Object-Oriented Programming (ECOOP 2023)

Abstract
Conflict-free Replicated Datatypes (CRDTs) are a class of distributed data structures that are highly-available and weakly consistent. The CRDT taxonomy is further divided into two subclasses: state-based and operation-based (op-based). Recent prior work showed how to use separation logic to verify convergence and functional correctness of op-based CRDTs while (a) verifying implementations (as opposed to high-level protocols), (b) giving high level specifications that abstract from low-level implementation details, and (c) providing specifications that are modular (i.e. allow client code to use the CRDT like an abstract data type). We extend this separation logic approach to verification of CRDTs to handle state-based CRDTs, while respecting the desiderata (a)-(c). The key idea is to track the state of a CRDT as a function of the set of operations that produced that state. Using the observation that state-based CRDTs are automatically causally-consistent, we obtain CRDT specifications that are agnostic to whether a CRDT is state- or op-based. When taken together with prior work, our technique thus provides a unified approach to specification and verification of op- and state-based CRDTs. We have tested our approach by verifying StateLib, a library for building state-based CRDTs. Using StateLib, we have further verified convergence and functional correctness of multiple example CRDTs from the literature. Our proofs are written in the Aneris distributed separation logic and are mechanized in Coq.
Cite as

Abel Nieto, Arnaud Daby-Seesaram, Léon Gondelman, Amin Timany, and Lars Birkedal. Modular Verification of State-Based CRDTs in Separation Logic. In 37th European Conference on Object-Oriented Programming (ECOOP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 263, pp. 22:1-22:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{nieto_et_al:LIPIcs.ECOOP.2023.22,
  author =	{Nieto, Abel and Daby-Seesaram, Arnaud and Gondelman, L\'{e}on and Timany, Amin and Birkedal, Lars},
  title =	{{Modular Verification of State-Based CRDTs in Separation Logic}},
  booktitle =	{37th European Conference on Object-Oriented Programming (ECOOP 2023)},
  pages =	{22:1--22:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-281-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{263},
  editor =	{Ali, Karim and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2023.22},
  URN =		{urn:nbn:de:0030-drops-182154},
  doi =		{10.4230/LIPIcs.ECOOP.2023.22},
  annote =	{Keywords: separation logic, distributed systems, CRDT, replicated data type, formal verification}
}
Document
Artifact
DOI: 10.4230/DARTS.9.2.15
Modular Verification of State-Based CRDTs in Separation Logic (Artifact)

Authors: Abel Nieto, Arnaud Daby-Seesaram, Léon Gondelman, Amin Timany, and Lars Birkedal

Published in: DARTS, Volume 9, Issue 2, Special Issue of the 37th European Conference on Object-Oriented Programming (ECOOP 2023)

Abstract
This is the documentation of the artifact for the paper "Modular Verification of State-Based CRDTs in Separation Logic". The artifact consists of a Coq formalization of the safety proofs for state-based CRDTs described in the paper. The Coq proofs are written in the Aneris distributed separation logic.
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Abel Nieto, Arnaud Daby-Seesaram, Léon Gondelman, Amin Timany, and Lars Birkedal. Modular Verification of State-Based CRDTs in Separation Logic (Artifact). In Special Issue of the 37th European Conference on Object-Oriented Programming (ECOOP 2023). Dagstuhl Artifacts Series (DARTS), Volume 9, Issue 2, pp. 15:1-15:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{nieto_et_al:DARTS.9.2.15,
  author =	{Nieto, Abel and Daby-Seesaram, Arnaud and Gondelman, L\'{e}on and Timany, Amin and Birkedal, Lars},
  title =	{{Modular Verification of State-Based CRDTs in Separation Logic (Artifact)}},
  pages =	{15:1--15:5},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2023},
  volume =	{9},
  number =	{2},
  editor =	{Nieto, Abel and Daby-Seesaram, Arnaud and Gondelman, L\'{e}on and Timany, Amin and Birkedal, Lars},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DARTS.9.2.15},
  URN =		{urn:nbn:de:0030-drops-182553},
  doi =		{10.4230/DARTS.9.2.15},
  annote =	{Keywords: separation logic, distributed systems, CRDT, replicated data type, formal verification}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2018.29
Cumulative Inductive Types In Coq

Authors: Amin Timany and Matthieu Sozeau

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract
In order to avoid well-known paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type_0 : Type_1 : *s. Such type systems are called cumulative if for any type A we have that A : Type_i implies A : Type_{i+1}. The Predicative Calculus of Inductive Constructions (pCIC) which forms the basis of the Coq proof assistant, is one such system. In this paper we present the Predicative Calculus of Cumulative Inductive Constructions (pCuIC) which extends the cumulativity relation to inductive types. We discuss cumulative inductive types as present in Coq 8.7 and their application to formalization and definitional translations.
Cite as

Amin Timany and Matthieu Sozeau. Cumulative Inductive Types In Coq. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{timany_et_al:LIPIcs.FSCD.2018.29,
  author =	{Timany, Amin and Sozeau, Matthieu},
  title =	{{Cumulative Inductive Types In Coq}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.29},
  URN =		{urn:nbn:de:0030-drops-91991},
  doi =		{10.4230/LIPIcs.FSCD.2018.29},
  annote =	{Keywords: Coq, Proof Assistants, Inductive Types, Universes, Cumulativity}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2016.30
Category Theory in Coq 8.5

Authors: Amin Timany and Bart Jacobs

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

Abstract
We report on our experience implementing category theory in Coq 8.5. Our work formalizes most of basic category theory, including concepts not covered by existing formalizations, in a library that is fit to be used as a general-purpose category-theoretical foundation. Our development particularly takes advantage of two features new to Coq 8.5: primitive projections for records and universe polymorphism. Primitive projections allow for well-behaved dualities while universe polymorphism provides a relative notion of largeness and smallness. The latter is one of the main contributions of this paper. It pushes the limits of the new universe polymorphism and constraint inference algorithm of Coq 8.5. In this paper we present in detail smallness and largeness in categories and the foundation they are built on top of. We furthermore explain how we have used the universe polymorphism of Coq 8.5 to represent smallness and largeness arguments by simply ignoring them and entrusting them to the universe inference algorithm of Coq 8.5. We also briefly discuss our experience throughout this implementation, discuss concepts formalized in this development and give a comparison with a few other developments of similar extent.
Cite as

Amin Timany and Bart Jacobs. Category Theory in Coq 8.5. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{timany_et_al:LIPIcs.FSCD.2016.30,
  author =	{Timany, Amin and Jacobs, Bart},
  title =	{{Category Theory in Coq 8.5}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{30:1--30:18},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.30},
  URN =		{urn:nbn:de:0030-drops-60003},
  doi =		{10.4230/LIPIcs.FSCD.2016.30},
  annote =	{Keywords: Category Theory, Coq 8.5, Universe Polymorphism, Homotopy Type Theory}
}
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