10 Search Results for "Pérez, Jorge"

Document
DOI: 10.4230/LIPIcs.TYPES.2021.11
Types and Terms Translated: Unrestricted Resources in Encoding Functions as Processes

Authors: Joseph W. N. Paulus, Daniele Nantes-Sobrinho, and Jorge A. Pérez

Published in: LIPIcs, Volume 239, 27th International Conference on Types for Proofs and Programs (TYPES 2021)

Abstract
Type-preserving translations are effective rigorous tools in the study of core programming calculi. In this paper, we develop a new typed translation that connects sequential and concurrent calculi; it is governed by type systems that control resource consumption. Our main contribution is the source language, a new resource λ-calculus with non-collapsing non-determinism and failures, dubbed uλ^{↯}_{⊕}. In uλ^{↯}_{⊕}, resources are split into linear and unrestricted; failures are explicit and arise from this distinction. We define a type system based on intersection types to control resources and fail-prone computation. The target language is 𝗌π, an existing session-typed π-calculus that results from a Curry-Howard correspondence between linear logic and session types. Our typed translation subsumes our prior work; interestingly, it treats unrestricted resources in uλ^{↯}_{⊕} as client-server session behaviours in 𝗌π.
Cite as

Joseph W. N. Paulus, Daniele Nantes-Sobrinho, and Jorge A. Pérez. Types and Terms Translated: Unrestricted Resources in Encoding Functions as Processes. In 27th International Conference on Types for Proofs and Programs (TYPES 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 239, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{paulus_et_al:LIPIcs.TYPES.2021.11,
  author =	{Paulus, Joseph W. N. and Nantes-Sobrinho, Daniele and P\'{e}rez, Jorge A.},
  title =	{{Types and Terms Translated: Unrestricted Resources in Encoding Functions as Processes}},
  booktitle =	{27th International Conference on Types for Proofs and Programs (TYPES 2021)},
  pages =	{11:1--11:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-254-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{239},
  editor =	{Basold, Henning and Cockx, Jesper and Ghilezan, Silvia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2021.11},
  URN =		{urn:nbn:de:0030-drops-167808},
  doi =		{10.4230/LIPIcs.TYPES.2021.11},
  annote =	{Keywords: Resource \lambda-calculus, intersection types, session types, process calculi}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2022.23
A Self-Dual Distillation of Session Types

Authors: Jules Jacobs

Published in: LIPIcs, Volume 222, 36th European Conference on Object-Oriented Programming (ECOOP 2022)

Abstract
We introduce ƛ ("lambda-barrier"), a minimal extension of linear λ-calculus with concurrent communication, which adds only a single new fork construct for spawning threads. It is inspired by GV, a session-typed functional language also based on linear λ-calculus. Unlike GV, ƛ strives to be as simple as possible, and adds no new operations other than fork, no new type formers, and no explicit definition of session type duality. Instead, we use linear function function type τ₁ -∘ τ₂ for communication between threads, which is dual to τ₂ -∘ τ₁, i.e., the function type constructor is dual to itself. Nevertheless, we can encode session types as ƛ types, GV’s channel operations as ƛ terms, and show that this encoding is type-preserving. The linear type system of ƛ ensures that all programs are deadlock-free and satisfy global progress, which we prove in Coq. Because of ƛ’s minimality, these proofs are simpler than mechanized proofs of deadlock freedom for GV.
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Jules Jacobs. A Self-Dual Distillation of Session Types. In 36th European Conference on Object-Oriented Programming (ECOOP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 222, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{jacobs:LIPIcs.ECOOP.2022.23,
  author =	{Jacobs, Jules},
  title =	{{A Self-Dual Distillation of Session Types}},
  booktitle =	{36th European Conference on Object-Oriented Programming (ECOOP 2022)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-225-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{222},
  editor =	{Ali, Karim and Vitek, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2022.23},
  URN =		{urn:nbn:de:0030-drops-162518},
  doi =		{10.4230/LIPIcs.ECOOP.2022.23},
  annote =	{Keywords: Linear types, concurrency, lambda calculus, session types}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.21
Non-Deterministic Functions as Non-Deterministic Processes

Authors: Joseph W. N. Paulus, Daniele Nantes-Sobrinho, and Jorge A. Pérez

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
We study encodings of the λ-calculus into the π-calculus in the unexplored case of calculi with non-determinism and failures. On the sequential side, we consider λ^↯_⊕, a new non-deterministic calculus in which intersection types control resources (terms); on the concurrent side, we consider 𝗌π, a π-calculus in which non-determinism and failure rest upon a Curry-Howard correspondence between linear logic and session types. We present a typed encoding of λ^↯_⊕ into 𝗌π and establish its correctness. Our encoding precisely explains the interplay of non-deterministic and fail-prone evaluation in λ^↯_⊕ via typed processes in 𝗌π. In particular, it shows how failures in sequential evaluation (absence/excess of resources) can be neatly codified as interaction protocols.
Cite as

Joseph W. N. Paulus, Daniele Nantes-Sobrinho, and Jorge A. Pérez. Non-Deterministic Functions as Non-Deterministic Processes. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{paulus_et_al:LIPIcs.FSCD.2021.21,
  author =	{Paulus, Joseph W. N. and Nantes-Sobrinho, Daniele and P\'{e}rez, Jorge A.},
  title =	{{Non-Deterministic Functions as Non-Deterministic Processes}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.21},
  URN =		{urn:nbn:de:0030-drops-142598},
  doi =		{10.4230/LIPIcs.FSCD.2021.21},
  annote =	{Keywords: Resource calculi, \pi-calculus, intersection types, session types, linear logic}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.TIME.2020.2
Temporal Modalities in Answer Set Programming (Invited Talk)

Authors: Pedro Cabalar

Published in: LIPIcs, Volume 178, 27th International Symposium on Temporal Representation and Reasoning (TIME 2020)

Abstract
Based on the answer set (or stable model) semantics for logic programs, Answer Set Programming (ASP) has become one of the most successful paradigms for practical Knowledge Representation and problem solving. Although ASP is naturally equipped for solving static combinatorial problems up to NP complexity (or ΣP2 in the disjunctive case) its application to temporal scenarios has been frequent since its very beginning, partly due to its early use for reasoning about actions and change. Temporal problems normally suppose an extra challenge for ASP for several reasons. On the one hand, they normally raise the complexity (in the case of classical planning, for instance, it becomes PSPACE-complete), although this is usually accounted for by making repeated calls to an ASP solver. On the other hand, temporal scenarios also pose a representational challenge, since the basic ASP language does not support temporal expressions. To fill this representational gap, a temporal extension of ASP called Temporal Equilibrium Logic (TEL) was proposed in and extensively studied later. This formalism constitutes a modal, linear-time extension of Equilibrium Logic which, in its turn, is a complete logical characterisation of (standard) ASP based on the intermediate logic of Here-and-There (HT). As a result, TEL is an expressive non-monotonic modal logic that shares the syntax of Linear-Time Temporal Logic (LTL) but interprets temporal formulas under a non-monotonic semantics that properly extends stable models.
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Pedro Cabalar. Temporal Modalities in Answer Set Programming (Invited Talk). In 27th International Symposium on Temporal Representation and Reasoning (TIME 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 178, pp. 2:1-2:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cabalar:LIPIcs.TIME.2020.2,
  author =	{Cabalar, Pedro},
  title =	{{Temporal Modalities in Answer Set Programming}},
  booktitle =	{27th International Symposium on Temporal Representation and Reasoning (TIME 2020)},
  pages =	{2:1--2:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-167-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{178},
  editor =	{Mu\~{n}oz-Velasco, Emilio and Ozaki, Ana and Theobald, Martin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2020.2},
  URN =		{urn:nbn:de:0030-drops-129707},
  doi =		{10.4230/LIPIcs.TIME.2020.2},
  annote =	{Keywords: Logic Programming, Temporal Logic, Answer Set Programming, Modal Logic}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2020.6
On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra

Authors: Pablo Barceló, Nelson Higuera, Jorge Pérez, and Bernardo Subercaseaux

Published in: LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)

Abstract
We study the expressive power of the Lara language - a recently proposed unified model for expressing relational and linear algebra operations - both in terms of traditional database query languages and some analytic tasks often performed in machine learning pipelines. We start by showing Lara to be expressive complete with respect to first-order logic with aggregation. Since Lara is parameterized by a set of user-defined functions which allow to transform values in tables, the exact expressive power of the language depends on how these functions are defined. We distinguish two main cases depending on the level of genericity queries are enforced to satisfy. Under strong genericity assumptions the language cannot express matrix convolution, a very important operation in current machine learning operations. This language is also local, and thus cannot express operations such as matrix inverse that exhibit a recursive behavior. For expressing convolution, one can relax the genericity requirement by adding an underlying linear order on the domain. This, however, destroys locality and turns the expressive power of the language much more difficult to understand. In particular, although under complexity assumptions the resulting language can still not express matrix inverse, a proof of this fact without such assumptions seems challenging to obtain.
Cite as

Pablo Barceló, Nelson Higuera, Jorge Pérez, and Bernardo Subercaseaux. On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{barcelo_et_al:LIPIcs.ICDT.2020.6,
  author =	{Barcel\'{o}, Pablo and Higuera, Nelson and P\'{e}rez, Jorge and Subercaseaux, Bernardo},
  title =	{{On the Expressiveness of LARA: A Unified Language for Linear and Relational Algebra}},
  booktitle =	{23rd International Conference on Database Theory (ICDT 2020)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-139-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{155},
  editor =	{Lutz, Carsten and Jung, Jean Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.6},
  URN =		{urn:nbn:de:0030-drops-119305},
  doi =		{10.4230/LIPIcs.ICDT.2020.6},
  annote =	{Keywords: languages for linear and relational algebra, expressive power, first order logic with aggregation, matrix convolution, matrix inverse, query genericity, locality of queries, safety}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2019.39
Domain-Aware Session Types

Authors: Luís Caires, Jorge A. Pérez, Frank Pfenning, and Bernardo Toninho

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Abstract
We develop a generalization of existing Curry-Howard interpretations of (binary) session types by relying on an extension of linear logic with features from hybrid logic, in particular modal worlds that indicate domains. These worlds govern domain migration, subject to a parametric accessibility relation familiar from the Kripke semantics of modal logic. The result is an expressive new typed process framework for domain-aware, message-passing concurrency. Its logical foundations ensure that well-typed processes enjoy session fidelity, global progress, and termination. Typing also ensures that processes only communicate with accessible domains and so respect the accessibility relation. Remarkably, our domain-aware framework can specify scenarios in which domain information is available only at runtime; flexible accessibility relations can be cleanly defined and statically enforced. As a specific application, we introduce domain-aware multiparty session types, in which global protocols can express arbitrarily nested sub-protocols via domain migration. We develop a precise analysis of these multiparty protocols by reduction to our binary domain-aware framework: complex domain-aware protocols can be reasoned about at the right level of abstraction, ensuring also the principled transfer of key correctness properties from the binary to the multiparty setting.
Cite as

Luís Caires, Jorge A. Pérez, Frank Pfenning, and Bernardo Toninho. Domain-Aware Session Types. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{caires_et_al:LIPIcs.CONCUR.2019.39,
  author =	{Caires, Lu{\'\i}s and P\'{e}rez, Jorge A. and Pfenning, Frank and Toninho, Bernardo},
  title =	{{Domain-Aware Session Types}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.39},
  URN =		{urn:nbn:de:0030-drops-109417},
  doi =		{10.4230/LIPIcs.CONCUR.2019.39},
  annote =	{Keywords: Session Types, Linear Logic, Process Calculi, Hybrid Logic}
}
Document
Artifact
DOI: 10.4230/DARTS.5.2.5
Minimal Session Types (Artifact)

Authors: Alen Arslanagić, Jorge A. Pérez, and Erik Voogd

Published in: DARTS, Volume 5, Issue 2, Special Issue of the 33rd European Conference on Object-Oriented Programming (ECOOP 2019)

Abstract
This artifact contains MISTY, a tool that decomposes message-passing programs with session types into programs typable with the minimal session types we introduce in our ECOOP paper. MISTY incorporates a domain-specific language for message-passing concurrency based on a higher-order process calculus with {session types}. Given a source program in this language, MISTY follows the results in our ECOOP paper to produce LaTeX code for its corresponding decomposition. To demonstrate the tight connection between source and decomposed programs, MISTY also allows users to simulate their corresponding reductions.
Cite as

Alen Arslanagić, Jorge A. Pérez, and Erik Voogd. Minimal Session Types (Artifact). In Special Issue of the 33rd European Conference on Object-Oriented Programming (ECOOP 2019). Dagstuhl Artifacts Series (DARTS), Volume 5, Issue 2, pp. 5:1-5:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Article{arslanagic_et_al:DARTS.5.2.5,
  author =	{Arslanagi\'{c}, Alen and P\'{e}rez, Jorge A. and Voogd, Erik},
  title =	{{Minimal Session Types}},
  pages =	{5:1--5:3},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2019},
  volume =	{5},
  number =	{2},
  editor =	{Arslanagi\'{c}, Alen and P\'{e}rez, Jorge A. and Voogd, Erik},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DARTS.5.2.5},
  URN =		{urn:nbn:de:0030-drops-107825},
  doi =		{10.4230/DARTS.5.2.5},
  annote =	{Keywords: Session types, process calculi, pi-calculus}
}
Document
Pearl
DOI: 10.4230/LIPIcs.ECOOP.2019.23
Minimal Session Types (Pearl)

Authors: Alen Arslanagić, Jorge A. Pérez, and Erik Voogd

Published in: LIPIcs, Volume 134, 33rd European Conference on Object-Oriented Programming (ECOOP 2019)

Abstract
Session types are a type-based approach to the verification of message-passing programs. They have been much studied as type systems for the pi-calculus and for languages such as Java. A session type specifies what and when should be exchanged through a channel. Central to session-typed languages are constructs in types and processes that specify sequencing in protocols. Here we study minimal session types, session types without sequencing. This is arguably the simplest form of session types. By relying on a core process calculus with sessions and higher-order concurrency (abstraction-passing), we prove that every process typable with standard (non minimal) session types can be compiled down into a process typed with minimal session types. This means that having sequencing constructs in both processes and session types is redundant; only sequentiality in processes is indispensable, as it can precisely codify sequentiality in types. Our developments draw inspiration from work by Parrow on behavior-preserving decompositions of untyped processes. By casting Parrow’s results in the realm of typed processes, our results reveal a conceptually simple formulation of session types and a principled avenue to the integration of session types into languages without sequencing in types.
Cite as

Alen Arslanagić, Jorge A. Pérez, and Erik Voogd. Minimal Session Types (Pearl). In 33rd European Conference on Object-Oriented Programming (ECOOP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 134, pp. 23:1-23:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{arslanagic_et_al:LIPIcs.ECOOP.2019.23,
  author =	{Arslanagi\'{c}, Alen and P\'{e}rez, Jorge A. and Voogd, Erik},
  title =	{{Minimal Session Types}},
  booktitle =	{33rd European Conference on Object-Oriented Programming (ECOOP 2019)},
  pages =	{23:1--23:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-111-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{134},
  editor =	{Donaldson, Alastair F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2019.23},
  URN =		{urn:nbn:de:0030-drops-108151},
  doi =		{10.4230/LIPIcs.ECOOP.2019.23},
  annote =	{Keywords: Session types, process calculi, pi-calculus}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2015.398
Characteristic Bisimulation for Higher-Order Session Processes

Authors: Dimitrios Kouzapas, Jorge A. Pérez, and Nobuko Yoshida

Published in: LIPIcs, Volume 42, 26th International Conference on Concurrency Theory (CONCUR 2015)

Abstract
Characterising contextual equivalence is a long-standing issue for higher-order (process) languages. In the setting of a higher-order pi-calculus with sessions, we develop characteristic bisimilarity, a typed bisimilarity which fully characterises contextual equivalence. To our knowledge, ours is the first characterisation of its kind. Using simple values inhabiting (session) types, our approach distinguishes from untyped methods for characterising contextual equivalence in higher-order processes: we show that observing as inputs only a precise finite set of higher-order values suffices to reason about higher-order session processes. We demonstrate how characteristic bisimilarity can be used to justify optimisations in session protocols with mobile code communication.
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Dimitrios Kouzapas, Jorge A. Pérez, and Nobuko Yoshida. Characteristic Bisimulation for Higher-Order Session Processes. In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 398-411, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{kouzapas_et_al:LIPIcs.CONCUR.2015.398,
  author =	{Kouzapas, Dimitrios and P\'{e}rez, Jorge A. and Yoshida, Nobuko},
  title =	{{Characteristic Bisimulation for Higher-Order Session Processes}},
  booktitle =	{26th International Conference on Concurrency Theory (CONCUR 2015)},
  pages =	{398--411},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-91-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{42},
  editor =	{Aceto, Luca and de Frutos Escrig, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.398},
  URN =		{urn:nbn:de:0030-drops-53659},
  doi =		{10.4230/LIPIcs.CONCUR.2015.398},
  annote =	{Keywords: Behavioural equivalences, session types, higher-order process calculi}
}
Document
DOI: 10.4230/DFU.Vol5.10452.69
The Inverse of a Schema Mapping

Authors: Jorge Pérez

Published in: Dagstuhl Follow-Ups, Volume 5, Data Exchange, Integration, and Streams (2013)

Abstract
The inversion of schema mappings has been identified as one of the fundamental operators for the development of a general framework for data exchange, data integration, and more generally, for metadata management. Given a mapping M from a schema S to a schema T, an inverse of M is a new mapping that describes the reverse relationship fromT to S, and that is semantically consistent with the relationship previously established by M. In practical scenarios, the inversion of a schema mapping can have several applications. For example, in a data exchange context, if a mapping M is used to exchange data from a source to a target schema, an inverse of M can be used to exchange the data back to the source, thus reversing the application of M. The formalization of a clear semantics for the inverse operator has proved to be a very difficult task. In fact, during the last years, several alternative notions of inversion for schema mappings have been proposed in the literature. This chapter provides a survey on the different formalizations for the inverse operator and the main theoretical and practical results obtained so far. In particular, we present and compare the main proposals for inverting schema mappings that have been considered in the literature. For each one of them we present their formal semantics and characterizations of their existence. We also present algorithms to compute inverses and study the language needed to express such inverses.
Cite as

Jorge Pérez. The Inverse of a Schema Mapping. In Data Exchange, Integration, and Streams. Dagstuhl Follow-Ups, Volume 5, pp. 69-95, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InCollection{perez:DFU.Vol5.10452.69,
  author =	{P\'{e}rez, Jorge},
  title =	{{The Inverse of a Schema Mapping}},
  booktitle =	{Data Exchange, Integration, and Streams},
  pages =	{69--95},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-61-3},
  ISSN =	{1868-8977},
  year =	{2013},
  volume =	{5},
  editor =	{Kolaitis, Phokion G. and Lenzerini, Maurizio and Schweikardt, Nicole},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DFU.Vol5.10452.69},
  URN =		{urn:nbn:de:0030-drops-42909},
  doi =		{10.4230/DFU.Vol5.10452.69},
  annote =	{Keywords: Schema mappings, data exchange, inverse}
}
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