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Documents authored by Pfenning, Frank

Document
DOI: 10.4230/LIPIcs.FSCD.2024.15
Adjoint Natural Deduction

Authors: Junyoung Jang, Sophia Roshal, Frank Pfenning, and Brigitte Pientka

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has been defined in the form of a sequent calculus because the central concept of independence is most clearly understood in this form, and because it permits a proof of cut elimination following standard techniques. In this paper we present a natural deduction formulation of adjoint logic and show how it is related to the sequent calculus. As a consequence, every provable proposition has a verification (sometimes called a long normal form). We also give a computational interpretation of adjoint logic in the form of a functional language and prove properties of computations that derive from the structure of modes, including freedom from garbage (for modes without weakening and contraction), strictness (for modes disallowing weakening), and erasure (based on a preorder between modes). Finally, we present a surprisingly subtle algorithm for type checking.
Cite as

Junyoung Jang, Sophia Roshal, Frank Pfenning, and Brigitte Pientka. Adjoint Natural Deduction. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 15:1-15:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jang_et_al:LIPIcs.FSCD.2024.15,
  author =	{Jang, Junyoung and Roshal, Sophia and Pfenning, Frank and Pientka, Brigitte},
  title =	{{Adjoint Natural Deduction}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{15:1--15:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.15},
  URN =		{urn:nbn:de:0030-drops-203441},
  doi =		{10.4230/LIPIcs.FSCD.2024.15},
  annote =	{Keywords: Substructural Logic, Type Systems, Functional Programming}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.12
Type-Based Termination for Futures

Authors: Siva Somayyajula and Frank Pfenning

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

Abstract
In sequential functional languages, sized types enable termination checking of programs with complex patterns of recursion in the presence of mixed inductive-coinductive types. In this paper, we adapt sized types and their metatheory to the concurrent setting. We extend the semi-axiomatic sequent calculus, a subsuming paradigm for futures-based functional concurrency, and its underlying operational semantics with recursion and arithmetic refinements. The latter enables a new and highly general sized type scheme we call sized type refinements. As a widely applicable technical device, we type recursive programs with infinitely deep typing derivations that unfold all recursive calls. Then, we observe that certain such derivations can be made infinitely wide but finitely deep. The resulting trees serve as the induction target of our strong normalization result, which we develop via a novel logical relations argument.
Cite as

Siva Somayyajula and Frank Pfenning. Type-Based Termination for Futures. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 12:1-12:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{somayyajula_et_al:LIPIcs.FSCD.2022.12,
  author =	{Somayyajula, Siva and Pfenning, Frank},
  title =	{{Type-Based Termination for Futures}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{12:1--12:21},
  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.2022.12},
  URN =		{urn:nbn:de:0030-drops-162931},
  doi =		{10.4230/LIPIcs.FSCD.2022.12},
  annote =	{Keywords: type-based termination, sized types, futures, concurrency, infinite proofs}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2020.13
Session Types with Arithmetic Refinements

Authors: Ankush Das and Frank Pfenning

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)

Abstract
Session types statically prescribe bidirectional communication protocols for message-passing processes. However, simple session types cannot specify properties beyond the type of exchanged messages. In this paper we extend the type system by using index refinements from linear arithmetic capturing intrinsic attributes of data structures and algorithms. We show that, despite the decidability of Presburger arithmetic, type equality and therefore also subtyping and type checking are now undecidable, which stands in contrast to analogous dependent refinement type systems from functional languages. We also present a practical, but incomplete algorithm for type equality, which we have used in our implementation of Rast, a concurrent session-typed language with arithmetic index refinements as well as ergometric and temporal types. Moreover, if necessary, the programmer can propose additional type bisimulations that are smoothly integrated into the type equality algorithm.
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Ankush Das and Frank Pfenning. Session Types with Arithmetic Refinements. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{das_et_al:LIPIcs.CONCUR.2020.13,
  author =	{Das, Ankush and Pfenning, Frank},
  title =	{{Session Types with Arithmetic Refinements}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.13},
  URN =		{urn:nbn:de:0030-drops-128252},
  doi =		{10.4230/LIPIcs.CONCUR.2020.13},
  annote =	{Keywords: Session Types, Refinement Types, Type Equality}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2020.29
Semi-Axiomatic Sequent Calculus

Authors: Henry DeYoung, Frank Pfenning, and Klaas Pruiksma

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
We present the semi-axiomatic sequent calculus (SAX) that blends features of Gentzen’s sequent calculus with an axiomatic formulation of intuitionistic logic. We develop and prove a suitable analogue to cut elimination and then show that a natural computational interpretation of SAX provides a simple form of shared memory concurrency.
Cite as

Henry DeYoung, Frank Pfenning, and Klaas Pruiksma. Semi-Axiomatic Sequent Calculus. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 29:1-29:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{deyoung_et_al:LIPIcs.FSCD.2020.29,
  author =	{DeYoung, Henry and Pfenning, Frank and Pruiksma, Klaas},
  title =	{{Semi-Axiomatic Sequent Calculus}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{29:1--29:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.29},
  URN =		{urn:nbn:de:0030-drops-123515},
  doi =		{10.4230/LIPIcs.FSCD.2020.29},
  annote =	{Keywords: Sequent calculus, Curry-Howard isomorphism, shared memory concurrency}
}
Document
System Description
DOI: 10.4230/LIPIcs.FSCD.2020.33
Rast: Resource-Aware Session Types with Arithmetic Refinements (System Description)

Authors: Ankush Das and Frank Pfenning

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
Traditional session types prescribe bidirectional communication protocols for concurrent computations, where well-typed programs are guaranteed to adhere to the protocols. Recent work has extended session types with refinements from linear arithmetic, capturing intrinsic properties of processes and data. These refinements then play a central role in describing sequential and parallel complexity bounds on session-typed programs. The Rast language and system provide an open-source implementation of session-typed concurrent programs extended with arithmetic refinements as well as ergometric and temporal types to capture work and span of program execution. Type checking relies on Cooper’s algorithm for quantifier elimination in Presburger arithmetic with a few significant optimizations, and a heuristic extension to nonlinear constraints. Rast furthermore includes a reconstruction engine so that most program constructs pertaining the layers of refinements and resources are inserted automatically. We provide a variety of examples to demonstrate the expressivity of the language.
Cite as

Ankush Das and Frank Pfenning. Rast: Resource-Aware Session Types with Arithmetic Refinements (System Description). In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 33:1-33:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{das_et_al:LIPIcs.FSCD.2020.33,
  author =	{Das, Ankush and Pfenning, Frank},
  title =	{{Rast: Resource-Aware Session Types with Arithmetic Refinements}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{33:1--33:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.33},
  URN =		{urn:nbn:de:0030-drops-123558},
  doi =		{10.4230/LIPIcs.FSCD.2020.33},
  annote =	{Keywords: Session Types, Resource Analysis, Refinement Types}
}
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.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
DOI: 10.4230/LIPIcs.CONCUR.2018.30
A Universal Session Type for Untyped Asynchronous Communication

Authors: Stephanie Balzer, Frank Pfenning, and Bernardo Toninho

Published in: LIPIcs, Volume 118, 29th International Conference on Concurrency Theory (CONCUR 2018)

Abstract
In the simply-typed lambda-calculus we can recover the full range of expressiveness of the untyped lambda-calculus solely by adding a single recursive type U = U -> U. In contrast, in the session-typed pi-calculus, recursion alone is insufficient to recover the untyped pi-calculus, primarily due to linearity: each channel just has two unique endpoints. In this paper, we show that shared channels with a corresponding sharing semantics (based on the language SILL_S developed in prior work) are enough to embed the untyped asynchronous pi-calculus via a universal shared session type U_S. We show that our encoding of the asynchronous pi-calculus satisfies operational correspondence and preserves observable actions (i.e., processes are weakly bisimilar to their encoding). Moreover, we clarify the expressiveness of SILL_S by developing an operationally correct encoding of SILL_S in the asynchronous pi-calculus.
Cite as

Stephanie Balzer, Frank Pfenning, and Bernardo Toninho. A Universal Session Type for Untyped Asynchronous Communication. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{balzer_et_al:LIPIcs.CONCUR.2018.30,
  author =	{Balzer, Stephanie and Pfenning, Frank and Toninho, Bernardo},
  title =	{{A Universal Session Type for Untyped Asynchronous Communication}},
  booktitle =	{29th International Conference on Concurrency Theory (CONCUR 2018)},
  pages =	{30:1--30:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-087-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{118},
  editor =	{Schewe, Sven and Zhang, Lijun},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2018.30},
  URN =		{urn:nbn:de:0030-drops-95681},
  doi =		{10.4230/LIPIcs.CONCUR.2018.30},
  annote =	{Keywords: Session types, sharing, pi-calculus, bisimulation}
}
Document
DOI: 10.4230/LIPIcs.CSL.2012.228
Cut Reduction in Linear Logic as Asynchronous Session-Typed Communication

Authors: Henry DeYoung, Luís Caires, Frank Pfenning, and Bernardo Toninho

Published in: LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012)

Abstract
Prior work has shown that intuitionistic linear logic can be seen as a session-type discipline for the pi-calculus, where cut reduction in the sequent calculus corresponds to synchronous process reduction. In this paper, we exhibit a new process assignment from the asynchronous, polyadic pi-calculus to exactly the same proof rules. Proof-theoretically, the difference between these interpretations can be understood through permutations of inference rules that preserve observational equivalence of closed processes in the synchronous case. We also show that, under this new asynchronous interpretation, cut reductions correspond to a natural asynchronous buffered session semantics, where each session is allocated a separate communication buffer.
Cite as

Henry DeYoung, Luís Caires, Frank Pfenning, and Bernardo Toninho. Cut Reduction in Linear Logic as Asynchronous Session-Typed Communication. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 228-242, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{deyoung_et_al:LIPIcs.CSL.2012.228,
  author =	{DeYoung, Henry and Caires, Lu{\'\i}s and Pfenning, Frank and Toninho, Bernardo},
  title =	{{Cut Reduction in Linear Logic as Asynchronous Session-Typed Communication}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{228--242},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{C\'{e}gielski, Patrick and Durand, Arnaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.228},
  URN =		{urn:nbn:de:0030-drops-36753},
  doi =		{10.4230/LIPIcs.CSL.2012.228},
  annote =	{Keywords: linear logic, cut reduction, asynchronous pi-calculus, session types}
}
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