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**Published in:** LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Verifying the metatheory of a formal system in Coq involves a lot of tedious "infrastructural" reasoning about variable binders. We present Tealeaves, a generic framework for first-order representations of variable binding that can be used to develop this sort of infrastructure once and for all. Given a particular strategy for representing binders concretely, such as locally nameless or de Bruijn indices, Tealeaves allows developers to implement modules of generic infrastructure called backends that end users can simply instantiate to their own syntax. Our framework rests on a novel abstraction of first-order abstract syntax called a decorated traversable monad (DTM) whose equational theory provides reasoning principles that replace tedious induction on terms. To evaluate Tealeaves, we have implemented a multisorted locally nameless backend providing generic versions of the lemmas generated by LNgen. We discuss case studies where we instantiate this generic infrastructure to simply-typed and polymorphic lambda calculi, comparing our approach to other utilities.

Lawrence Dunn, Val Tannen, and Steve Zdancewic. Tealeaves: Structured Monads for Generic First-Order Abstract Syntax Infrastructure. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dunn_et_al:LIPIcs.ITP.2023.14, author = {Dunn, Lawrence and Tannen, Val and Zdancewic, Steve}, title = {{Tealeaves: Structured Monads for Generic First-Order Abstract Syntax Infrastructure}}, booktitle = {14th International Conference on Interactive Theorem Proving (ITP 2023)}, pages = {14:1--14:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-284-6}, ISSN = {1868-8969}, year = {2023}, volume = {268}, editor = {Naumowicz, Adam and Thiemann, Ren\'{e}}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.14}, URN = {urn:nbn:de:0030-drops-183891}, doi = {10.4230/LIPIcs.ITP.2023.14}, annote = {Keywords: Coq, category theory, formal metatheory, raw syntax, locally nameless} }

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**Published in:** LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)

Semiring provenance is a successful approach, originating in database theory, to providing detailed information on how atomic facts combine to yield the result of a query. In particular, general provenance semirings of polynomials or formal power series provide precise descriptions of the evaluation strategies or "proof trees" for the query. By evaluating these descriptions in specific application semirings, one can extract practical information for instance about the confidence of a query or the cost of its evaluation.
This paper develops semiring provenance for very general logical languages featuring the full interaction between negation and fixed-point inductions or, equivalently, arbitrary interleavings of least and greatest fixed points. This also opens the door to provenance analysis applications for modal μ-calculus and temporal logics, as well as for finite and infinite model-checking games.
Interestingly, the common approach based on Kleene’s Fixed-Point Theorem for ω-continuous semirings is not sufficient for these general languages. We show that an adequate framework for the provenance analysis of full fixed-point logics is provided by semirings that are (1) fully continuous, and (2) absorptive. Full continuity guarantees that provenance values of least and greatest fixed-points are well-defined. Absorptive semirings provide a symmetry between least and greatest fixed-points and make sure that provenance values of greatest fixed points are informative.
We identify semirings of generalized absorptive polynomials S^{∞}[X] and prove universal properties that make them the most general appropriate semirings for our framework. These semirings have the further property of being (3) chain-positive, which is responsible for having truth-preserving interpretations that give non-zero values to all true formulae. We relate the provenance analysis of fixed-point formulae with provenance values of plays and strategies in the associated model-checking games. Specifically, we prove that the provenance value of a fixed point formula gives precise information on the evaluation strategies in these games.

Katrin M. Dannert, Erich Grädel, Matthias Naaf, and Val Tannen. Semiring Provenance for Fixed-Point Logic. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 17:1-17:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dannert_et_al:LIPIcs.CSL.2021.17, author = {Dannert, Katrin M. and Gr\"{a}del, Erich and Naaf, Matthias and Tannen, Val}, title = {{Semiring Provenance for Fixed-Point Logic}}, booktitle = {29th EACSL Annual Conference on Computer Science Logic (CSL 2021)}, pages = {17:1--17:22}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-175-7}, ISSN = {1868-8969}, year = {2021}, volume = {183}, editor = {Baier, Christel and Goubault-Larrecq, Jean}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.17}, URN = {urn:nbn:de:0030-drops-134518}, doi = {10.4230/LIPIcs.CSL.2021.17}, annote = {Keywords: Finite Model Theory, Semiring Provenance, Absorptive Semirings, Fixed-Point Logics} }

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**Published in:** LIPIcs, Volume 68, 20th International Conference on Database Theory (ICDT 2017)

Representation systems have been widely used to capture different forms of incomplete data in various settings. However, existing representation systems are not expressive enough to handle the more complex scenarios of missing data that can occur in practice: these could vary from missing attribute values, missing a known number of tuples, or even missing an unknown number of tuples. In this work, we propose a new representation system called m-tables, that can represent many different types of missing data. We show that m-tables form a closed, complete and strong representation system under both set and bag semantics and are strictly more expressive than conditional tables under both the closed and open world assumptions. We further study the complexity of computing certain and possible answers in m-tables. Finally, we discuss how to "interpret" m-tables through a novel labeling scheme that marks a type of generalized tuples as certain or possible.

Bruhathi Sundarmurthy, Paraschos Koutris, Willis Lang, Jeffrey Naughton, and Val Tannen. m-tables: Representing Missing Data. In 20th International Conference on Database Theory (ICDT 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 68, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{sundarmurthy_et_al:LIPIcs.ICDT.2017.21, author = {Sundarmurthy, Bruhathi and Koutris, Paraschos and Lang, Willis and Naughton, Jeffrey and Tannen, Val}, title = {{m-tables: Representing Missing Data}}, booktitle = {20th International Conference on Database Theory (ICDT 2017)}, pages = {21:1--21:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-024-8}, ISSN = {1868-8969}, year = {2017}, volume = {68}, editor = {Benedikt, Michael and Orsi, Giorgio}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2017.21}, URN = {urn:nbn:de:0030-drops-70618}, doi = {10.4230/LIPIcs.ICDT.2017.21}, annote = {Keywords: missing values, incomplete data, c tables, representation systems} }

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**Published in:** LIPIcs, Volume 48, 19th International Conference on Database Theory (ICDT 2016)

Provisioning is a technique for avoiding repeated expensive computations in what-if analysis. Given a query, an analyst formulates k hypotheticals, each retaining some of the tuples of a database instance, possibly overlapping, and she wishes to answer the query under scenarios, where a scenario is defined by a subset of the hypotheticals that are "turned on". We say that a query admits compact provisioning if given any database instance and any k hypotheticals, one can create a poly-size (in k) sketch that can then be used to answer the query under any of the 2^k possible scenarios without accessing the original instance.
In this paper, we focus on provisioning complex queries that combine relational algebra (the logical component), grouping, and statistics/analytics (the numerical component). We first show that queries that compute quantiles or linear regression (as well as simpler queries that compute count and sum/average of positive values) can be compactly provisioned to provide (multiplicative) approximate answers to an arbitrary precision. In contrast, exact provisioning for each of these statistics requires the sketch size to be exponential in k. We then establish that for any complex query whose logical component is a positive relational algebra query, as long as the numerical component can be compactly provisioned, the complex query itself can be compactly provisioned. On the other hand, introducing negation or recursion in the logical component again requires the sketch size to be exponential in k. While our positive results use algorithms that do not access the original instance after a scenario is known, we prove our lower bounds even for the case when, knowing the scenario, limited access to the instance is allowed.

Sepehr Assadi, Sanjeev Khanna, Yang Li, and Val Tannen. Algorithms for Provisioning Queries and Analytics. In 19th International Conference on Database Theory (ICDT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 48, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{assadi_et_al:LIPIcs.ICDT.2016.18, author = {Assadi, Sepehr and Khanna, Sanjeev and Li, Yang and Tannen, Val}, title = {{Algorithms for Provisioning Queries and Analytics}}, booktitle = {19th International Conference on Database Theory (ICDT 2016)}, pages = {18:1--18:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-002-6}, ISSN = {1868-8969}, year = {2016}, volume = {48}, editor = {Martens, Wim and Zeume, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2016.18}, URN = {urn:nbn:de:0030-drops-57877}, doi = {10.4230/LIPIcs.ICDT.2016.18}, annote = {Keywords: What-if Analysis, Provisioning, Data Compression, Approximate Query Answering} }

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**Published in:** LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

In this paper, we introduce a new model for sublinear algorithms called dynamic sketching. In this model, the underlying data is partitioned into a large static part and a small dynamic part and the goal is to compute a summary of the static part (i.e, a sketch) such that given any update for the dynamic part, one can combine it with the sketch to compute a given function. We say that a sketch is compact if its size is bounded by a polynomial function of the length of the dynamic data, (essentially) independent of the size of the static part.
A graph optimization problem P in this model is defined as follows. The input is a graph G(V,E) and a set T \subseteq V of k terminals; the edges between the terminals are the dynamic part and the other edges in G are the static part. The goal is to summarize the graph G into a compact sketch (of size poly(k)) such that given any set Q of edges between the terminals, one can answer the problem P for the graph obtained by inserting all edges in Q to G, using only the sketch.
We study the fundamental problem of computing a maximum matching and prove tight bounds on the sketch size. In particular, we show that there exists a (compact) dynamic sketch of size O(k^2) for the matching problem and any such sketch has to be of size \Omega(k^2). Our sketch for matchings can be further used to derive compact dynamic sketches for other fundamental graph problems involving cuts and connectivities. Interestingly, our sketch for matchings can also be used to give an elementary construction of a cut-preserving vertex sparsifier with space O(kC^2) for k-terminal graphs, which matches the best known upper bound; here C is the total capacity of the edges incident on the terminals. Additionally, we give an improved lower bound (in terms of C) of Omega(C/log{C}) on size of cut-preserving vertex sparsifiers, and establish that progress on dynamic sketching of the s-t max-flow problem (either upper bound or lower bound) immediately leads to better bounds for size of cut-preserving vertex sparsifiers.

Sepehr Assadi, Sanjeev Khanna, Yang Li, and Val Tannen. Dynamic Sketching for Graph Optimization Problems with Applications to Cut-Preserving Sketches. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 52-68, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{assadi_et_al:LIPIcs.FSTTCS.2015.52, author = {Assadi, Sepehr and Khanna, Sanjeev and Li, Yang and Tannen, Val}, title = {{Dynamic Sketching for Graph Optimization Problems with Applications to Cut-Preserving Sketches}}, booktitle = {35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)}, pages = {52--68}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-97-2}, ISSN = {1868-8969}, year = {2015}, volume = {45}, editor = {Harsha, Prahladh and Ramalingam, G.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.52}, URN = {urn:nbn:de:0030-drops-56361}, doi = {10.4230/LIPIcs.FSTTCS.2015.52}, annote = {Keywords: Small-space Algorithms, Maximum Matchings, Vertex Sparsifiers} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 4391, Semantic Interoperability and Integration (2005)

Semantic Web (SW) technology aims to facilitate the integration of legacy data sources spread worldwide. Despite the plethora of SW languages e.g., RDF/S, OWL recently proposed for
supporting large scale information interoperation, the vast majority of legacy sources still rely on relational databases RDB published on the
Web or corporate intranets as virtual XML. In this paper, we advocate a Datalog framework for mediating high level queries to relational and or
XML sources using community ontologies expressed in a SW language such as RDF/S. We describe the architecture and the reasoning services
of our SW integration middleware, called SWIM, and we present the main design choices and techniques for supporting powerful mappings between different data models, as well as reformulation and optimization of queries expressed against mediation schemas and views.

Ioanna Koffina, Giorgos Serfiotis, Vassilis Christophides, Val Tannen, and Alin Deutsch. Integrating XML Data Sources using RDF/S Schemas: The ICS-FORTH Semantic Web Integration Middleware (SWIM). In Semantic Interoperability and Integration. Dagstuhl Seminar Proceedings, Volume 4391, pp. 1-6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{koffina_et_al:DagSemProc.04391.9, author = {Koffina, Ioanna and Serfiotis, Giorgos and Christophides, Vassilis and Tannen, Val and Deutsch, Alin}, title = {{Integrating XML Data Sources using RDF/S Schemas: The ICS-FORTH Semantic Web Integration Middleware (SWIM)}}, booktitle = {Semantic Interoperability and Integration}, pages = {1--6}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2005}, volume = {4391}, editor = {Y. Kalfoglou and M. Schorlemmer and A. Sheth and S. Staab and M. Uschold}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04391.9}, URN = {urn:nbn:de:0030-drops-340}, doi = {10.4230/DagSemProc.04391.9}, annote = {Keywords: integration , xml , rdf schema} }