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Documents authored by Timany, Amin

Document
DOI: 10.4230/LIPIcs.ECOOP.2026.20
Verifying Wait-Freedom for Concurrent Higher-Order Programs

Authors: Egor Namakonov, Lars Birkedal, and Amin Timany

Published in: LIPIcs, Volume 372, 40th European Conference on Object-Oriented Programming (ECOOP 2026)

Abstract
Wait-freedom is the strongest non-blocking progress guarantee for concurrent data structures, ensuring that every operation completes in a finite number of steps regardless of interference from other threads. While verification of wait-freedom has been studied for first-order languages, verifying it for higher-order programming languages with general references remains an open challenge. In such languages, operations may be used by arbitrary, unverified higher-order clients, making it unclear how to even define wait-freedom formally in terms of programs' semantics, let alone prove it. In this paper, we present the first framework for verifying wait-freedom of concurrent programs written in a higher-order language with general references. Our approach is based on the Lawyer concurrent separation logic which has been recently introduced for termination verification. We identify a specification pattern in the Lawyer logic that captures wait-freedom. To establish this connection formally, we prove a novel adequacy theorem for Lawyer which states that programs which are proven correct in the Lawyer logic against a specification in the aforementioned specification pattern are wait-free. Proving wait-freedom requires to show that all calls made to operations by any arbitrary client terminate. Thus, as a part of proving the adequacy theorem above, we need to prove that the behavior of the client of the data structure is safe in the sense that it does not break the internal invariants of the data structure, e.g., by directly manipulating the data structure’s internal state. To this end, we develop a logical relations model that establishes safety for all clients once and for all. We demonstrate the effectiveness of our approach by proving wait-freedom for several representative examples, including a higher-order list map function, and a memory-efficient single-producer, single-consumer queue. For the latter, wait-freedom is conditional in that, as the name suggests, there can be at most one enqueuer thread and one dequeuer thread. To capture this formally, we introduce the notion of restricted wait-freedom as a variant of wait-freedom that restricts the number of concurrent threads, and show how our approach can support reasoning about restricted wait-freedom. All our results have been mechanized on top of the Rocq Prover and using the Iris separation logic framework that Lawyer is also based on.
Cite as

Egor Namakonov, Lars Birkedal, and Amin Timany. Verifying Wait-Freedom for Concurrent Higher-Order Programs. In 40th European Conference on Object-Oriented Programming (ECOOP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 372, pp. 20:1-20:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{namakonov_et_al:LIPIcs.ECOOP.2026.20,
  author =	{Namakonov, Egor and Birkedal, Lars and Timany, Amin},
  title =	{{Verifying Wait-Freedom for Concurrent Higher-Order Programs}},
  booktitle =	{40th European Conference on Object-Oriented Programming (ECOOP 2026)},
  pages =	{20:1--20:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-423-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{372},
  editor =	{Krebbers, Robbert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2026.20},
  URN =		{urn:nbn:de:0030-drops-261164},
  doi =		{10.4230/LIPIcs.ECOOP.2026.20},
  annote =	{Keywords: separation logic, higher-order logic, concurrency, formal verification}
}
Document
Artifact
DOI: 10.4230/DARTS.12.1.21
Verifying Wait-Freedom for Concurrent Higher-Order Programs (Artifact)

Authors: Egor Namakonov, Lars Birkedal, and Amin Timany

Published in: DARTS, Volume 12, Issue 1, Special Issue of the 40th European Conference on Object-Oriented Programming (ECOOP 2026)

Abstract
Wait-freedom is the strongest non-blocking progress guarantee for concurrent data structures, ensuring that every operation completes in a finite number of steps regardless of interference from other threads. While verification of wait-freedom has been studied for first-order languages, verifying it for higher-order programming languages with general references remains an open challenge. In such languages, operations may be used by arbitrary, unverified higher-order clients, making it unclear how to even define wait-freedom formally in terms of programs' semantics, let alone prove it. In this paper, we present the first framework for verifying wait-freedom of concurrent programs written in a higher-order language with general references. Our approach is based on the Lawyer concurrent separation logic which has been recently introduced for termination verification. We identify a specification pattern in the Lawyer logic that captures wait-freedom. To establish this connection formally, we extend Lawyer with a novel adequacy theorem that proves that programs which are proven correct in the Lawyer logic against a specification in this aforementioned specification pattern are wait-free. Proving wait-freedom requires us to show that all calls made to operations by any arbitrary client terminate. Thus, as part of formally proving wait-freedom, i.e., as part of the proof of the adequacy theorem above, we need to prove that the behavior of the client of the data structure is safe in the sense that it does not break the internal invariants of the data structure, e.g., by directly manipulating the data structure’s internal state. To this end, we develop a logical relations model that establishes safety for all clients once and for all. We demonstrate the effectiveness of our approach by proving wait-freedom for several representative examples, including higher-order functions such as the list map function, and a memory-efficient single-producer, single-consumer queue. For the latter, wait-freedom is conditional in that as the name suggests there can be at most one enqueuer thread and one dequeuer thread. To capture this formally we introduce the notion of restricted wait-freedom as a variant of wait-freedom that restricts the number of concurrent threads, and show how our approach can support reasoning about restricted wait-freedom. All our results have been mechanized on top of the Rocq Prover and using the Iris separation logic framework that Lawyer is also based on.
Cite as

Egor Namakonov, Lars Birkedal, and Amin Timany. Verifying Wait-Freedom for Concurrent Higher-Order Programs (Artifact). In Special Issue of the 40th European Conference on Object-Oriented Programming (ECOOP 2026). Dagstuhl Artifacts Series (DARTS), Volume 12, Issue 1, pp. 21:1-21:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{namakonov_et_al:DARTS.12.1.21,
  author =	{Namakonov, Egor and Birkedal, Lars and Timany, Amin},
  title =	{{Verifying Wait-Freedom for Concurrent Higher-Order Programs (Artifact)}},
  pages =	{21:1--21:8},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2026},
  volume =	{12},
  number =	{1},
  editor =	{Namakonov, Egor and Birkedal, Lars and Timany, Amin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.12.1.21},
  URN =		{urn:nbn:de:0030-drops-261581},
  doi =		{10.4230/DARTS.12.1.21},
  annote =	{Keywords: separation logic, higher-order logic, concurrency, formal verification}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.33
Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It

Authors: Sergei Stepanenko and Amin Timany

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Constructing solutions to recursive domain equations is a well-known, important problem in the study of programs and programming languages. Mathematically speaking, the problem is finding a fixed point (up to isomorphism) of a suitable functor over a suitable category. A particularly useful instance, inspired by the step-indexing technique, is where the functor is over (a subcategory of) the category of presheaves over the ordinal ω and the functors are locally-contractive, also known as guarded functors. This corresponds to step-indexing over natural numbers. However, for certain problems, e.g., when dealing with infinite non-determinism, one needs to employ trans-finite step-indexing, i.e., consider presheaf categories over higher ordinals. Prior work on trans-finite step-indexing either only considers a very narrow class of functors over a particularly restricted subcategory of presheaves over higher ordinals, or treats the problem very generally working with sheaves over an arbitrary complete Heyting algebra with a well-founded basis. In this paper we present a solution to the guarded domain equations problem over all guarded functors over the category of presheaves over ordinal numbers, as well as its mechanization in the Rocq Prover. As the categories of sheaves and presheaves over ordinals are equivalent, our main contribution is simplifying prior work from the setting of the category of sheaves to the setting of the category of presheaves and mechanizing it - presheaves are more amenable to mechanization in a proof assistant.
Cite as

Sergei Stepanenko and Amin Timany. Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 33:1-33:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{stepanenko_et_al:LIPIcs.FSCD.2025.33,
  author =	{Stepanenko, Sergei and Timany, Amin},
  title =	{{Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{33:1--33:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.33},
  URN =		{urn:nbn:de:0030-drops-236486},
  doi =		{10.4230/LIPIcs.FSCD.2025.33},
  annote =	{Keywords: Domain Equations, Guarded Fixed Points, Fixed Points, Category Theory, Rocq, Presheaves, Ordinals}
}
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.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.
Cite as

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.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.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.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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