41 Search Results for "Felty, Amy P."

Volume

LIPIcs, Volume 228

7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

FSCD 2022, August 2-5, 2022, Haifa, Israel

Editors: Amy P. Felty

Document
DOI: 10.4230/LIPIcs.ITP.2024.23
A Generalised Union of Rely-Guarantee and Separation Logic Using Permission Algebras

Authors: Vincent Jackson, Toby Murray, and Christine Rizkallah

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
This paper describes GenRGSep, an Isabelle/HOL library for the development of RGSep logics using a general algebraic state model. In particular, we develop an algebraic state models based on resource algebras that assume neither the presence of unit resources or the cancellativity law. If a new resource model is required, its components need only be proven an instance of a permission algebra, and then they can be composed together using tuples and functions. The proof of soundness is performed by Vafeiadis' operational soundness method. This method was originally formulated with respect to a concrete heap model. This paper adapts it to account for the absence of both units as well as the cancellativity law.
Cite as

Vincent Jackson, Toby Murray, and Christine Rizkallah. A Generalised Union of Rely-Guarantee and Separation Logic Using Permission Algebras. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 23:1-23:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jackson_et_al:LIPIcs.ITP.2024.23,
  author =	{Jackson, Vincent and Murray, Toby and Rizkallah, Christine},
  title =	{{A Generalised Union of Rely-Guarantee and Separation Logic Using Permission Algebras}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{23:1--23:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.23},
  URN =		{urn:nbn:de:0030-drops-207510},
  doi =		{10.4230/LIPIcs.ITP.2024.23},
  annote =	{Keywords: verification, concurrency, rely-guarantee, separation logic, resource algebras}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.8
The Directed Van Kampen Theorem in Lean

Authors: Henning Basold, Peter Bruin, and Dominique Lawson

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
Directed topology augments the concept of a topological space with a notion of directed paths. This leads to a category of directed spaces, in which the morphisms are continuous maps respecting directed paths. Directed topology thereby enables an accurate representation of computation paths in concurrent systems that usually cannot be reversed. Even though ideas from algebraic topology have analogues in directed topology, the directedness drastically changes how spaces can be characterised. For instance, while an important homotopy invariant of a topological space is its fundamental groupoid, for directed spaces this has to be replaced by the fundamental category because directed paths are not necessarily reversible. In this paper, we present a Lean 4 formalisation of directed spaces and of a Van Kampen theorem for them, which allows the fundamental category of a directed space to be computed in terms of the fundamental categories of subspaces. Part of this formalisation is also a significant theory of directed spaces, directed homotopy theory and path coverings, which can serve as basis for future formalisations of directed topology. The formalisation in Lean can also be used in computer-assisted reasoning about the behaviour of concurrent systems that have been represented as directed spaces.
Cite as

Henning Basold, Peter Bruin, and Dominique Lawson. The Directed Van Kampen Theorem in Lean. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{basold_et_al:LIPIcs.ITP.2024.8,
  author =	{Basold, Henning and Bruin, Peter and Lawson, Dominique},
  title =	{{The Directed Van Kampen Theorem in Lean}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.8},
  URN =		{urn:nbn:de:0030-drops-207368},
  doi =		{10.4230/LIPIcs.ITP.2024.8},
  annote =	{Keywords: Lean, Directed Topology, Van Kampen Theorem, Directed Homotopy Theory, Formalised Mathematics}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.4
Taming Differentiable Logics with Coq Formalisation

Authors: Reynald Affeldt, Alessandro Bruni, Ekaterina Komendantskaya, Natalia Ślusarz, and Kathrin Stark

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to translate propositional or first-order formulae into loss functions deployed for optimisation in machine learning. At the same time, recent attempts to give programming language support for verification of neural networks showed that DLs can be used to compile verification properties to machine-learning backends. This situation is calling for stronger guarantees about the soundness of such compilers, the soundness and compositionality of DLs, and the differentiability and performance of the resulting loss functions. In this paper, we propose an approach to formalise existing DLs using the Mathematical Components library in the Coq proof assistant. Thanks to this formalisation, we are able to give uniform semantics to otherwise disparate DLs, give formal proofs to existing informal arguments, find errors in previous work, and provide formal proofs to missing conjectured properties. This work is meant as a stepping stone for the development of programming language support for verification of machine learning.
Cite as

Reynald Affeldt, Alessandro Bruni, Ekaterina Komendantskaya, Natalia Ślusarz, and Kathrin Stark. Taming Differentiable Logics with Coq Formalisation. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{affeldt_et_al:LIPIcs.ITP.2024.4,
  author =	{Affeldt, Reynald and Bruni, Alessandro and Komendantskaya, Ekaterina and \'{S}lusarz, Natalia and Stark, Kathrin},
  title =	{{Taming Differentiable Logics with Coq Formalisation}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{4:1--4:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.4},
  URN =		{urn:nbn:de:0030-drops-207325},
  doi =		{10.4230/LIPIcs.ITP.2024.4},
  annote =	{Keywords: Machine Learning, Loss Functions, Differentiable Logics, Logic and Semantics, Interactive Theorem Proving}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.35
Formal Verification of the Empty Hexagon Number

Authors: Bernardo Subercaseaux, Wojciech Nawrocki, James Gallicchio, Cayden Codel, Mario Carneiro, and Marijn J. H. Heule

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
A recent breakthrough in computer-assisted mathematics showed that every set of 30 points in the plane in general position (i.e., no three points on a common line) contains an empty convex hexagon. Heule and Scheucher solved this problem with a combination of geometric insights and automated reasoning techniques by constructing CNF formulas ϕ_n, with O(n⁴) clauses, such that if ϕ_n is unsatisfiable then every set of n points in general position must contain an empty convex hexagon. An unsatisfiability proof for n = 30 was then found with a SAT solver using 17 300 CPU hours of parallel computation. In this paper, we formalize and verify this result in the Lean theorem prover. Our formalization covers ideas in discrete computational geometry and SAT encoding techniques by introducing a framework that connects geometric objects to propositional assignments. We see this as a key step towards the formal verification of other SAT-based results in geometry, since the abstractions we use have been successfully applied to similar problems. Overall, we hope that our work sets a new standard for the verification of geometry problems relying on extensive computation, and that it increases the trust the mathematical community places in computer-assisted proofs.
Cite as

Bernardo Subercaseaux, Wojciech Nawrocki, James Gallicchio, Cayden Codel, Mario Carneiro, and Marijn J. H. Heule. Formal Verification of the Empty Hexagon Number. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{subercaseaux_et_al:LIPIcs.ITP.2024.35,
  author =	{Subercaseaux, Bernardo and Nawrocki, Wojciech and Gallicchio, James and Codel, Cayden and Carneiro, Mario and Heule, Marijn J. H.},
  title =	{{Formal Verification of the Empty Hexagon Number}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.35},
  URN =		{urn:nbn:de:0030-drops-207633},
  doi =		{10.4230/LIPIcs.ITP.2024.35},
  annote =	{Keywords: Empty Hexagon Number, Discrete Computational Geometry, Erd\H{o}s-Szekeres}
}
Document
DOI: 10.4230/OASIcs.FMBC.2024.2
Formal Specification of the Cardano Blockchain Ledger, Mechanized in Agda

Authors: Andre Knispel, Orestis Melkonian, James Chapman, Alasdair Hill, Joosep Jääger, William DeMeo, and Ulf Norell

Published in: OASIcs, Volume 118, 5th International Workshop on Formal Methods for Blockchains (FMBC 2024)

Abstract
Blockchain systems comprise critical software that handle substantial monetary funds, rendering them excellent candidates for formal verification. One of their core components is the underlying ledger that does all the accounting: keeping track of transactions and their validity, etc. Unfortunately, previous theoretical studies are typically confined to an idealized setting, while specifications for real implementations are scarce; either the functionality is directly implemented without a proper specification, or at best an informal specification is written on paper. The present work expands beyond prior meta-theoretical investigations of the EUTxO model to encompass the full scale of the Cardano blockchain: our formal specification describes a hierarchy of modular transitions that covers all the intricacies of a realistic blockchain, such as fully expressive smart contracts and decentralized governance. It is mechanized in a proof assistant, thus enjoys a higher standard of rigor: type-checking prevents minor oversights that were frequent in previous informal approaches; key meta-theoretical properties can now be formally proven; it is an executable specification against which the implementation in production is being tested for conformance; and it provides firm foundations for smart contract verification. Apart from a safety net to keep us in check, the formalization also provides a guideline for the ledger design: one informs the other in a symbiotic way, especially in the case of state-of-the-art features like decentralized governance, which is an emerging sub-field of blockchain research that however mandates a more exploratory approach. All the results presented in this paper have been mechanized in the Agda proof assistant and are publicly available. In fact, this document is itself a literate Agda script and all rendered code has been successfully type-checked.
Cite as

Andre Knispel, Orestis Melkonian, James Chapman, Alasdair Hill, Joosep Jääger, William DeMeo, and Ulf Norell. Formal Specification of the Cardano Blockchain Ledger, Mechanized in Agda. In 5th International Workshop on Formal Methods for Blockchains (FMBC 2024). Open Access Series in Informatics (OASIcs), Volume 118, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{knispel_et_al:OASIcs.FMBC.2024.2,
  author =	{Knispel, Andre and Melkonian, Orestis and Chapman, James and Hill, Alasdair and J\"{a}\"{a}ger, Joosep and DeMeo, William and Norell, Ulf},
  title =	{{Formal Specification of the Cardano Blockchain Ledger, Mechanized in Agda}},
  booktitle =	{5th International Workshop on Formal Methods for Blockchains (FMBC 2024)},
  pages =	{2:1--2:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-317-1},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{118},
  editor =	{Bernardo, Bruno and Marmsoler, Diego},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.FMBC.2024.2},
  URN =		{urn:nbn:de:0030-drops-198673},
  doi =		{10.4230/OASIcs.FMBC.2024.2},
  annote =	{Keywords: blockchain, distributed ledgers, UTxO, Cardano, formal verification, Agda}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.FSCD.2022
LIPIcs, Volume 228, FSCD 2022, Complete Volume

Authors: Amy P. Felty

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
LIPIcs, Volume 228, FSCD 2022, Complete Volume
Cite as

7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 1-652, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Proceedings{felty:LIPIcs.FSCD.2022,
  title =	{{LIPIcs, Volume 228, FSCD 2022, Complete Volume}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{1--652},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022},
  URN =		{urn:nbn:de:0030-drops-162803},
  doi =		{10.4230/LIPIcs.FSCD.2022},
  annote =	{Keywords: LIPIcs, Volume 228, FSCD 2022, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.FSCD.2022.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Amy P. Felty

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{felty:LIPIcs.FSCD.2022.0,
  author =	{Felty, Amy P.},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.0},
  URN =		{urn:nbn:de:0030-drops-162814},
  doi =		{10.4230/LIPIcs.FSCD.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2022.1
Cutting a Proof into Bite-Sized Chunks: Incrementally proving termination in higher-order term rewriting (Invited Talk)

Authors: Cynthia Kop

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
This paper discusses a number of methods to prove termination of higher-order term rewriting systems, with a particular focus on large systems. In first-order term rewriting, the dependency pair framework can be used to split up a large termination problem into multiple (much) smaller components that can be solved individually. This is important because a large problem may take exponentially longer to solve in one go than solving each of its components. Unfortunately, while there are higher-order versions of several of these methods, they often fail to simplify a problem enough. Here, we will explore some of these techniques and their limitations, and discuss what else can be done to incrementally build a termination proof for higher-order systems.
Cite as

Cynthia Kop. Cutting a Proof into Bite-Sized Chunks: Incrementally proving termination in higher-order term rewriting (Invited Talk). In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kop:LIPIcs.FSCD.2022.1,
  author =	{Kop, Cynthia},
  title =	{{Cutting a Proof into Bite-Sized Chunks: Incrementally proving termination in higher-order term rewriting}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{1:1--1:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.1},
  URN =		{urn:nbn:de:0030-drops-162827},
  doi =		{10.4230/LIPIcs.FSCD.2022.1},
  annote =	{Keywords: Termination, Modularity, Higher-order term rewriting, Dependency Pairs, Algebra Interpretations}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2022.2
A Methodology for Designing Proof Search Calculi for Non-Classical Logics (Invited Talk)

Authors: Alwen Tiu

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
In this talk I present a methodology for designing proof search calculi for a wide range of non-classical logics, such as modal and tense logics, bi-intuitionistic (linear) logics and grammar logics. Most of these logics cannot be easily formalised in the traditional Gentzen-style sequent calculus; various structural extensions to sequent calculus seem to be required. One of the more expressive extensions of sequent calculus is Belnap’s display calculus, which allows one to formalise a very wide range of logics and which provides a generic cut-elimination method for logics formalised in the calculus. The generality of display calculus derives partly from the pervasive use of structural rules to capture properties of the underlying semantics of the logic of interest, such as various frame conditions in normal modal logics, that are not easily captured by introduction rules alone. Unlike traditional sequent calculi, the subformula property in display calculi does not typically give an immediate bound on the search space (assuming contraction is absent) in proof search, as new structures may be created and their creation may not be driven by any introduction rules for logical connectives. This line of work started out as an attempt to "tame" display calculus, to make it more proof search friendly, by eliminating or restricting the use of structural rules. Two key ideas that make this possible are the adoption of deep inference, allowing inference rules to be applied inside a nested structure, and the use of propagation rules in place of structural rules. A brief survey of the applications of this methodology to a wide range of logics is presented, along with some directions for future work.
Cite as

Alwen Tiu. A Methodology for Designing Proof Search Calculi for Non-Classical Logics (Invited Talk). In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 2:1-2:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{tiu:LIPIcs.FSCD.2022.2,
  author =	{Tiu, Alwen},
  title =	{{A Methodology for Designing Proof Search Calculi for Non-Classical Logics}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{2:1--2:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.2},
  URN =		{urn:nbn:de:0030-drops-162834},
  doi =		{10.4230/LIPIcs.FSCD.2022.2},
  annote =	{Keywords: Proof theory, Sequent calculus, Display calculus, Nested sequent calculus, Deep inference}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.3
A Fibrational Tale of Operational Logical Relations

Authors: Francesco Dagnino and Francesco Gavazzo

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been designed and applied to specific families of languages. However, a unifying abstract framework for operationally-based logical relations is still missing. We show how fibrations can provide a uniform treatment of operational logical relations, using as reference example a λ-calculus with generic effects endowed with a novel, abstract operational semantics defined on a large class of categories. Moreover, this abstract perspective allows us to give a solid mathematical ground also to differential logical relations - a recently introduced notion of higher-order distance between programs - both pure and effectful, bringing them back to a common picture with traditional ones.
Cite as

Francesco Dagnino and Francesco Gavazzo. A Fibrational Tale of Operational Logical Relations. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dagnino_et_al:LIPIcs.FSCD.2022.3,
  author =	{Dagnino, Francesco and Gavazzo, Francesco},
  title =	{{A Fibrational Tale of Operational Logical Relations}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{3:1--3:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.3},
  URN =		{urn:nbn:de:0030-drops-162840},
  doi =		{10.4230/LIPIcs.FSCD.2022.3},
  annote =	{Keywords: logical relations, operational semantics, fibrations, generic effects, program distance}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.4
On Quantitative Algebraic Higher-Order Theories

Authors: Ugo Dal Lago, Furio Honsell, Marina Lenisa, and Paolo Pistone

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
We explore the possibility of extending Mardare et al.’s quantitative algebras to the structures which naturally emerge from Combinatory Logic and the λ-calculus. First of all, we show that the framework is indeed applicable to those structures, and give soundness and completeness results. Then, we prove some negative results clearly delineating to which extent categories of metric spaces can be models of such theories. We conclude by giving several examples of non-trivial higher-order quantitative algebras.
Cite as

Ugo Dal Lago, Furio Honsell, Marina Lenisa, and Paolo Pistone. On Quantitative Algebraic Higher-Order Theories. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dallago_et_al:LIPIcs.FSCD.2022.4,
  author =	{Dal Lago, Ugo and Honsell, Furio and Lenisa, Marina and Pistone, Paolo},
  title =	{{On Quantitative Algebraic Higher-Order Theories}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.4},
  URN =		{urn:nbn:de:0030-drops-162851},
  doi =		{10.4230/LIPIcs.FSCD.2022.4},
  annote =	{Keywords: Quantitative Algebras, Lambda Calculus, Combinatory Logic, Metric Spaces}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.5
Sheaf Semantics of Termination-Insensitive Noninterference

Authors: Jonathan Sterling and Robert Harper

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
We propose a new sheaf semantics for secure information flow over a space of abstract behaviors, based on synthetic domain theory: security classes are open/closed partitions, types are sheaves, and redaction of sensitive information corresponds to restricting a sheaf to a closed subspace. Our security-aware computational model satisfies termination-insensitive noninterference automatically, and therefore constitutes an intrinsic alternative to state of the art extrinsic/relational models of noninterference. Our semantics is the latest application of Sterling and Harper’s recent re-interpretation of phase distinctions and noninterference in programming languages in terms of Artin gluing and topos-theoretic open/closed modalities. Prior applications include parametricity for ML modules, the proof of normalization for cubical type theory by Sterling and Angiuli, and the cost-aware logical framework of Niu et al. In this paper we employ the phase distinction perspective twice: first to reconstruct the syntax and semantics of secure information flow as a lattice of phase distinctions between "higher" and "lower" security, and second to verify the computational adequacy of our sheaf semantics with respect to a version of Abadi et al.’s dependency core calculus to which we have added a construct for declassifying termination channels.
Cite as

Jonathan Sterling and Robert Harper. Sheaf Semantics of Termination-Insensitive Noninterference. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{sterling_et_al:LIPIcs.FSCD.2022.5,
  author =	{Sterling, Jonathan and Harper, Robert},
  title =	{{Sheaf Semantics of Termination-Insensitive Noninterference}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.5},
  URN =		{urn:nbn:de:0030-drops-162869},
  doi =		{10.4230/LIPIcs.FSCD.2022.5},
  annote =	{Keywords: information flow, noninterference, denotational semantics, phase distinction, Artin gluing, modal type theory, topos theory, synthetic domain theory, synthetic Tait computability}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.6
Combined Hierarchical Matching: the Regular Case

Authors: Serdar Erbatur, Andrew M. Marshall, and Christophe Ringeissen

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
Matching algorithms are often central sub-routines in many areas of automated reasoning. They are used in areas such as functional programming, rule-based programming, automated theorem proving, and the symbolic analysis of security protocols. Matching is related to unification but provides a somewhat simplified problem. Thus, in some cases, we can obtain a matching algorithm even if the unification problem is undecidable. In this paper we consider a hierarchical approach to constructing matching algorithms. The hierarchical method has been successful for developing unification algorithms for theories defined over a constructor sub-theory. We show how the approach can be extended to matching problems which allows for the development, in a modular way, of hierarchical matching algorithms. Here we focus on regular theories, where both sides of each equational axiom have the same set of variables. We show that the combination of two hierarchical matching algorithms leads to a hierarchical matching algorithm for the union of regular theories sharing only a common constructor sub-theory.
Cite as

Serdar Erbatur, Andrew M. Marshall, and Christophe Ringeissen. Combined Hierarchical Matching: the Regular Case. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{erbatur_et_al:LIPIcs.FSCD.2022.6,
  author =	{Erbatur, Serdar and Marshall, Andrew M. and Ringeissen, Christophe},
  title =	{{Combined Hierarchical Matching: the Regular Case}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{6:1--6:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.6},
  URN =		{urn:nbn:de:0030-drops-162879},
  doi =		{10.4230/LIPIcs.FSCD.2022.6},
  annote =	{Keywords: Matching, combination problem, equational theories}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.7
Nominal Anti-Unification with Atom-Variables

Authors: Manfred Schmidt-Schauß and Daniele Nantes-Sobrinho

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
Anti-unification is the task of generalizing a set of expressions in the most specific way. It was extended to the nominal framework by Baumgarter, Kutsia, Levy and Villaret, who defined an algorithm solving the nominal anti-unification problem, which runs in polynomial time. Unfortunately, when an infinite set of atoms are allowed in generalizations, a minimal complete set of solutions in nominal anti-unification does not exist, in general. In this paper, we present a more general approach to nominal anti-unification that uses atom-variables instead of explicit atoms, and two variants of freshness constraints: NL_A-constraints (with atom-variables), and Eqr-constraints based on Equivalence relations on atom-variables. The idea of atom-variables is that different atom-variables may be instantiated with identical or different atoms. Albeit simple, this freedom in the formulation increases its application potential: we provide an algorithm that is finitary for the NL_A-freshness constraints, and for Eqr-freshness constraints it computes a unique least general generalization. There is a price to pay in the general case: checking freshness constraints and other related logical questions will require exponential time. The setting of Baumgartner et al. is improved by the atom-only case, which runs in polynomial time and computes a unique least general generalization.
Cite as

Manfred Schmidt-Schauß and Daniele Nantes-Sobrinho. Nominal Anti-Unification with Atom-Variables. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{schmidtschau_et_al:LIPIcs.FSCD.2022.7,
  author =	{Schmidt-Schau{\ss}, Manfred and Nantes-Sobrinho, Daniele},
  title =	{{Nominal Anti-Unification with Atom-Variables}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.7},
  URN =		{urn:nbn:de:0030-drops-162885},
  doi =		{10.4230/LIPIcs.FSCD.2022.7},
  annote =	{Keywords: Generalization, anti-unification, nominal algorithms, higher-order deduction}
}
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