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DOI: 10.4230/LIPIcs.CSL.2026.37

Towards the Type Safety of Pure Subtype Systems

Authors: Valentin Pasquale and Álvaro García-Pérez

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract

Hutchins' Pure Subtype Systems (PSS) offer a unified framework for types and terms, promising significant advancements in language design for features like dependent types and higher-order subtyping. However, the theory has been hampered by a critical gap: a proof of type safety has remained an open problem for over a decade. The original attempt to prove this property relied on the conjectured commutativity of two fundamental reduction relations, equivalence and subtyping. Proving transitivity elimination, however, requires this commutativity, a property that is notoriously difficult to establish for higher-order subtyping systems. In this paper, we address this issue by introducing Machine-Based PSS (MPSS), a novel reformulation of the original system. MPSS integrates a continuation stack mechanism, reminiscent of the Krivine Abstract Machine, to keep track of arguments that are passed during function application, enabling more fine-grained reductions. This architectural change exposes crucial intermediate reduction steps that were absent in the original PSS. The primary contribution of our work is a direct proof that the equivalence and subtyping reductions in MPSS commute. This result formally establishes transitivity elimination, which is the cornerstone of the inversion lemma required for type safety. We conclude by outlining a pathway from our foundational result to a complete, type-safe system, thereby paving the way for the practical realization of PSS-based languages.

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Valentin Pasquale and Álvaro García-Pérez. Towards the Type Safety of Pure Subtype Systems. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{pasquale_et_al:LIPIcs.CSL.2026.37,
  author =	{Pasquale, Valentin and Garc{\'\i}a-P\'{e}rez, \'{A}lvaro},
  title =	{{Towards the Type Safety of Pure Subtype Systems}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{37:1--37:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.37},
  URN =		{urn:nbn:de:0030-drops-254626},
  doi =		{10.4230/LIPIcs.CSL.2026.37},
  annote =	{Keywords: Lambda calculus, Pure subtype systems, Dependent types, Higher-order subtyping, Type safety}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2019.5

Deconstructing Stellar Consensus

Authors: Álvaro García-Pérez and Maria A. Schett

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

Abstract

Some of the recent blockchain proposals, such as Stellar and Ripple, allow for open membership while using quorum-like structures typical for classical Byzantine consensus with closed membership. This is achieved by constructing quorums in a decentralised way: each participant independently chooses whom to trust, and quorums arise from these individual decisions. Unfortunately, the consensus protocols underlying such blockchains are poorly understood, and their correctness has not been rigorously investigated. In this paper we rigorously prove correct the Stellar Consensus Protocol (SCP), with our proof giving insights into the protocol structure and its use of lower-level abstractions. To this end, we first propose an abstract version of SCP that uses as a black box Stellar’s federated voting primitive (analogous to reliable Byzantine broadcast), previously investigated by García-Pérez and Gotsman [Álvaro García-Pérez and Alexey Gotsman, 2018]. The abstract consensus protocol highlights a modular structure in Stellar and can be proved correct by reusing the previous results on federated voting. However, it is unsuited for realistic implementations, since its processes maintain infinite state. We thus establish a refinement between the abstract protocol and the concrete SCP that uses only finite state, thereby carrying over the result about the correctness of former to the latter. Our results help establish the theoretical foundations of decentralised blockchains like Stellar and gain confidence in their correctness.

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Álvaro García-Pérez and Maria A. Schett. Deconstructing Stellar Consensus. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{garciaperez_et_al:LIPIcs.OPODIS.2019.5,
  author =	{Garc{\'\i}a-P\'{e}rez, \'{A}lvaro and Schett, Maria A.},
  title =	{{Deconstructing Stellar Consensus}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.5},
  URN =		{urn:nbn:de:0030-drops-117910},
  doi =		{10.4230/LIPIcs.OPODIS.2019.5},
  annote =	{Keywords: Blockchain, Consensus protocol, Stellar, Byzantine quorum systems}
}

Document

DOI: 10.4230/LIPIcs.OPODIS.2018.17

Federated Byzantine Quorum Systems

Authors: Álvaro García-Pérez and Alexey Gotsman

Published in: LIPIcs, Volume 125, 22nd International Conference on Principles of Distributed Systems (OPODIS 2018)

Abstract

Some of the recent blockchain proposals, such as Stellar and Ripple, use quorum-like structures typical for Byzantine consensus while allowing for open membership. This is achieved by constructing quorums in a decentralised way: each participant independently chooses whom to trust, and quorums arise from these individual decisions. Unfortunately, the theoretical foundations underlying such blockchains have not been thoroughly investigated. To close this gap, in this paper we study decentralised quorum construction by means of federated Byzantine quorum systems, used by Stellar. We rigorously prove the correctness of basic broadcast abstractions over federated quorum systems and establish their relationship to the classical Byzantine quorum systems. In particular, we prove correctness in the realistic setting where Byzantine nodes may lie about their trust choices. We show that this setting leads to a novel variant of Byzantine quorum systems where different nodes may have different understanding of what constitutes a quorum.

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Álvaro García-Pérez and Alexey Gotsman. Federated Byzantine Quorum Systems. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{garciaperez_et_al:LIPIcs.OPODIS.2018.17,
  author =	{Garc{\'\i}a-P\'{e}rez, \'{A}lvaro and Gotsman, Alexey},
  title =	{{Federated Byzantine Quorum Systems}},
  booktitle =	{22nd International Conference on Principles of Distributed Systems (OPODIS 2018)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-098-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{125},
  editor =	{Cao, Jiannong and Ellen, Faith and Rodrigues, Luis and Ferreira, Bernardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2018.17},
  URN =		{urn:nbn:de:0030-drops-100772},
  doi =		{10.4230/LIPIcs.OPODIS.2018.17},
  annote =	{Keywords: Blockchain, Stellar, Byzantine quorum systems}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2017.10

Rule Formats for Nominal Process Calculi

Authors: Luca Aceto, Ignacio Fábregas, Álvaro García-Pérez, Anna Ingólfsdóttir, and Yolanda Ortega-Mallén

Published in: LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Abstract

The nominal transition systems (NTSs) of Parrow et al. describe the operational semantics of nominal process calculi. We study NTSs in terms of the nominal residual transition systems (NRTSs) that we introduce. We provide rule formats for the specifications of NRTSs that ensure that the associated NRTS is an NTS and apply them to the operational specification of the early pi-calculus. Our study stems from the recent Nominal SOS of Cimini et al. and from earlier works in nominal sets and nominal logic by Gabbay, Pitts and their collaborators.

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Luca Aceto, Ignacio Fábregas, Álvaro García-Pérez, Anna Ingólfsdóttir, and Yolanda Ortega-Mallén. Rule Formats for Nominal Process Calculi. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{aceto_et_al:LIPIcs.CONCUR.2017.10,
  author =	{Aceto, Luca and F\'{a}bregas, Ignacio and Garc{\'\i}a-P\'{e}rez, \'{A}lvaro and Ing\'{o}lfsd\'{o}ttir, Anna and Ortega-Mall\'{e}n, Yolanda},
  title =	{{Rule Formats for Nominal Process Calculi}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-048-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{85},
  editor =	{Meyer, Roland and Nestmann, Uwe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.10},
  URN =		{urn:nbn:de:0030-drops-77869},
  doi =		{10.4230/LIPIcs.CONCUR.2017.10},
  annote =	{Keywords: nominal sets, nominal structural operational semantics, process algebra, nominal transition systems, scope opening, rule formats}
}

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Documents authored by García-Pérez, Álvaro

Towards the Type Safety of Pure Subtype Systems

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Deconstructing Stellar Consensus

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Federated Byzantine Quorum Systems

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Rule Formats for Nominal Process Calculi

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