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DOI: 10.4230/LIPIcs.CSL.2026.47

Useful Call-by-Value: A Semantic Interpretation via Quantitative Types

Authors: Pablo Barenbaum, Delia Kesner, and Mariana Milicich

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

Abstract

Useful evaluation is an optimised evaluation mechanism for functional programming languages. It relies on representing terms with sharing and imposing a restricted notion of useful substitutions, that intuitively disallows copying subterms that do not contribute to the progress of the computation. In particular, useful call-by-value evaluation optimises the standard call-by-value strategy by preserving its original semantics. This preservation result has been shown by means of syntactical rewriting techniques, difficult to adapt to alternative variants of the calculi at play. In this work, we present the first semantic model of useful call-by-value evaluation through the non-idempotent intersection type system 𝒰. Our first contribution is a characterisation of termination for useful call-by-value evaluation via system 𝒰. That is, a term is typable in system 𝒰 if and only if it terminates in the useful call-by-value strategy. As a second contribution, we show that system 𝒰 provides a quantitative interpretation for useful call-by-value evaluation, offering exact step-count information for program evaluation. Our third contribution is that termination in call-by-value and useful call-by-value are equivalent. This ensures in particular that call-by-value, which is (potentially) erasing, and useful call-by-value, which is non-erasing, are observationally equivalent. Even though the specification of the operational semantics of useful evaluation is highly complex, system 𝒰 is notably simple. As far as we know, system 𝒰 is one of the scarce quantitative type systems capturing exactly the substitution step-count for variables and abstractions in an open call-by-value strategy.

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Pablo Barenbaum, Delia Kesner, and Mariana Milicich. Useful Call-by-Value: A Semantic Interpretation via Quantitative Types. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 47:1-47:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{barenbaum_et_al:LIPIcs.CSL.2026.47,
  author =	{Barenbaum, Pablo and Kesner, Delia and Milicich, Mariana},
  title =	{{Useful Call-by-Value: A Semantic Interpretation via Quantitative Types}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{47:1--47:24},
  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.2026.47},
  URN =		{urn:nbn:de:0030-drops-254721},
  doi =		{10.4230/LIPIcs.CSL.2026.47},
  annote =	{Keywords: Lambda calculus, Evaluation strategies, Call-by-Value, Useful Evaluation, Intersection types, Quantitative models}
}

Document

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.2024.8

Optimal Multilevel Slashing for Blockchains

Authors: Kenan Wood, Hammurabi Mendes, and Jonad Pulaj

Published in: LIPIcs, Volume 324, 28th International Conference on Principles of Distributed Systems (OPODIS 2024)

Abstract

We present the notion of multilevel slashing, where proof-of-stake blockchain validators can obtain gradual levels of assurance that a certain block is bound to be finalized in a global consensus procedure, unless an increasing and optimally large number of Byzantine processes have their staked assets slashed - that is, deducted - due to provably incorrect behavior. Our construction is a highly parameterized generalization of combinatorial intersection systems based on finite projective spaces, with asymptotic high availability and optimal slashing properties. Even under weak conditions, we show that our construction has asymptotically optimal slashing properties with respect to message complexity and validator load; this result also illustrates a fundamental trade off between message complexity, load, and slashing. In addition, we show that any intersection system whose ground elements are disjoint subsets of nodes (e.g. "committees" in committee-based consensus protocols) has asymptotic high availability under similarly weak conditions. Finally, our multilevel construction gives the flexibility to blockchain validators to decide how many "levels" of finalization assurance they wish to obtain. This functionality can be seen either as (i) a form of an early, slashing-based block finalization; or (ii) a service to support reorg tolerance.

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Kenan Wood, Hammurabi Mendes, and Jonad Pulaj. Optimal Multilevel Slashing for Blockchains. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{wood_et_al:LIPIcs.OPODIS.2024.8,
  author =	{Wood, Kenan and Mendes, Hammurabi and Pulaj, Jonad},
  title =	{{Optimal Multilevel Slashing for Blockchains}},
  booktitle =	{28th International Conference on Principles of Distributed Systems (OPODIS 2024)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-360-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{324},
  editor =	{Bonomi, Silvia and Galletta, Letterio and Rivi\`{e}re, Etienne and Schiavoni, Valerio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2024.8},
  URN =		{urn:nbn:de:0030-drops-225445},
  doi =		{10.4230/LIPIcs.OPODIS.2024.8},
  annote =	{Keywords: Blockchains, Finality, Slashablility, Committees, Availability}
}

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}
}

6 Search Results for "García-Pérez, Álvaro"

Useful Call-by-Value: A Semantic Interpretation via Quantitative Types

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Towards the Type Safety of Pure Subtype Systems

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Optimal Multilevel Slashing for Blockchains

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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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