Relevant bibliographies by topics / Presheaf semantics

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Academic literature on the topic 'Presheaf semantics'

Author: Grafiati
Published: 7 June 2025
Last updated: 2 August 2025

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Journal articles on the topic "Presheaf semantics"

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Hildebrandt, Thomas T. "A Fully Abstract Presheaf Semantics of SCCS with Finite Delay." Electronic Notes in Theoretical Computer Science 29 (1999): 102–26. http://dx.doi.org/10.1016/s1571-0661(05)80311-1.

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Ghilardi, Silvio. "Presheaf semantics and independence results for some non-classical first-order logics." Archive for Mathematical Logic 29, no. 2 (1989): 125–36. http://dx.doi.org/10.1007/bf01620621.

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Bizjak, Aleš, and Rasmus Ejlers Møgelberg. "Denotational semantics for guarded dependent type theory." Mathematical Structures in Computer Science 30, no. 4 (2020): 342–78. http://dx.doi.org/10.1017/s0960129520000080.

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AbstractWe present a new model of guarded dependent type theory (GDTT), a type theory with guarded recursion and multiple clocks in which one can program with and reason about coinductive types. Productivity of recursively defined coinductive programs and proofs is encoded in types using guarded recursion and can therefore be checked modularly, unlike the syntactic checks implemented in modern proof assistants. The model is based on a category of covariant presheaves over a category of time objects, and quantification over clocks is modelled using a presheaf of clocks. To model the clock irrel
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Hildebrandt, Thomas T. "Towards categorical models for fairness: fully abstract presheaf semantics of SCCS with finite delay." Theoretical Computer Science 294, no. 1-2 (2003): 151–81. http://dx.doi.org/10.1016/s0304-3975(01)00247-x.

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Ceulemans, Joris, Andreas Nuyts, and Dominique Devriese. "BiSikkel: A Multimode Logical Framework in Agda." Proceedings of the ACM on Programming Languages 9, POPL (2025): 210–40. https://doi.org/10.1145/3704844.

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Embedding Multimode Type Theory (MTT) as a library enables the usage of additional reasoning principles in off-the-shelf proof assistants without risking soundness or compatibility. Moreover, by interpreting embedded MTT terms in an internally constructed model of MTT, we can extract programs and proofs to the metalanguage and obtain interoperability between the embedded language and the metalanguage. The existing Sikkel library for Agda achieves this for Multimode Simple Type Theory (MSTT) with an internal presheaf model of dependent MTT. In this work, we add, on top of the simply-typed layer
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Winskel, Glynn. "A Presheaf Semantics of Value-Passing Processes." BRICS Report Series 3, no. 44 (1996). http://dx.doi.org/10.7146/brics.v3i44.20046.

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This paper investigates presheaf models for process calculi with<br />value passing. Denotational semantics in presheaf models are shown<br />to correspond to operational semantics in that bisimulation obtained<br />from open maps is proved to coincide with bisimulation as defined<br />traditionally from the operational semantics. Both "early" and "late"<br />semantics are considered, though the more interesting "late" semantics<br />is emphasised. A presheaf model and denotational semantics is proposed<br />for a language allowing process passing, tho
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Hildebrandt, Thomas Troels. "A Fully Abstract Presheaf Semantics of SCCS with Finite Delay." BRICS Report Series 6, no. 28 (1999). http://dx.doi.org/10.7146/brics.v6i28.20097.

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We present a presheaf model for the observation of infinite as well<br />as finite computations. We apply it to give a denotational semantics of<br />SCCS with finite delay, in which the meanings of recursion are given by<br />final coalgebras and meanings of finite delay by initial algebras of the<br />process equations for delay. This can be viewed as a first step in representing<br />fairness in presheaf semantics. We give a concrete representation<br />of the presheaf model as a category of generalised synchronisation<br />trees and show that it is
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Cattani, Gian Luca, Ian Stark, and Glynn Winskel. "Presheaf Models for the pi-Calculus." BRICS Report Series 4, no. 34 (1997). http://dx.doi.org/10.7146/brics.v4i34.18960.

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<p>Recent work has shown that presheaf categories provide a general model of concurrency, with an inbuilt notion of bisimulation based on open maps. Here it is shown how this approach can also handle systems where the language of actions may change dynamically as a process evolves. The example is the pi-calculus, a calculus for `mobile processes' whose communication topology varies as channels are created and discarded. A denotational semantics is described for the pi-calculus within an indexed category of profunctors; the model is fully abstract for bisimilarity, in the sense that bisim
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Nuyts, Andreas, and Dominique Devriese. "Transpension: The Right Adjoint to the Pi-type." Logical Methods in Computer Science Volume 20, Issue 2 (June 19, 2024). http://dx.doi.org/10.46298/lmcs-20(2:16)2024.

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Presheaf models of dependent type theory have been successfully applied to model HoTT, parametricity, and directed, guarded and nominal type theory. There has been considerable interest in internalizing aspects of these presheaf models, either to make the resulting language more expressive, or in order to carry out further reasoning internally, allowing greater abstraction and sometimes automated verification. While the constructions of presheaf models largely follow a common pattern, approaches towards internalization do not. Throughout the literature, various internal presheaf operators ($\s
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König, Harald, and Uwe Wolter. "Van Kampen Colimits and Path Uniqueness." Logical Methods in Computer Science Volume 14, Issue 2 (April 25, 2018). https://doi.org/10.23638/lmcs-14(2:5)2018.

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Fibred semantics is the foundation of the model-instance pattern of software engineering. Software models can often be formalized as objects of presheaf topoi, i.e, categories of objects that can be represented as algebras as well as coalgebras, e.g., the category of directed graphs. Multimodeling requires to construct colimits of models, decomposition is given by pullback. Compositionality requires an exact interplay of these operations, i.e., diagrams must enjoy the Van Kampen property. However, checking the validity of the Van Kampen property algorithmically based on its definition is often
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Books on the topic "Presheaf semantics"

1

Caramello, Olivia. Some Applications. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0012.

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This chapter describes some applications of the theory developed in the previous chapters in a variety of different mathematical contexts. The main methodology used to generate such applications is the ‘bridge technique’ presented in Chapter 2. The discussed topics include restrictions of Morita equivalences to quotients of the two theories involved, give a solution to a prozblem of Lawvere concerning the boundary operator on subtoposes, establish syntax-semantics ‘bridges’ for quotients of theories of presheaf type, present topos-theoretic interpretations and generalizations of Fraïssé’s theo
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Caramello, Olivia. Quotients of a theory of presheaf type. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0010.

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In this chapter the quotients of a given theory of presheaf type are investigated by means of Grothendieck topologies that can be naturally attached to them, establishing a ‘semantic’ representation for the classifying topos of such a quotient as a subtopos of the classifying topos of the given theory of presheaf type. It is also shown that the models of such a quotient can be characterized among the models of the theory of presheaf type as those which satisfy a key property of homogeneity with respect to a Grothendieck topology associated with the quotient. A number of sufficient conditions f
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Book chapters on the topic "Presheaf semantics"

1

Gadducci, Fabio, and Davide Trotta. "A Presheaf Semantics for Quantified Temporal Logics." In Recent Trends in Algebraic Development Techniques. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-43345-0_4.

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Winskel, Glynn. "A presheaf semantics of value-passing processes." In CONCUR '96: Concurrency Theory. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/3-540-61604-7_50.

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Pientka, Brigitte, and Ulrich Schöpp. "Semantical Analysis of Contextual Types." In Lecture Notes in Computer Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45231-5_26.

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AbstractWe describe a category-theoretic semantics for a simply typed variant of Cocon, a contextual modal type theory where the box modality mediates between the weak function space that is used to represent higher-order abstract syntax (HOAS) trees and the strong function space that describes (recursive) computations about them. What makes Cocon different from standard type theories is the presence of first-class contexts and contextual objects to describe syntax trees that are closed with respect to a given context of assumptions. Following M. Hofmann’s work, we use a presheaf model to char
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Ahman, Danel. "When Programs Have to Watch Paint Dry." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30829-1_1.

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AbstractWe explore type systems and programming abstractions for the safe usage of resources. In particular, we investigate how to use types to modularly specify and check when programs are allowed to use their resources, e.g., when programming a robot arm on a production line, it is crucial that painted parts are given enough time to dry before assembly. We capture such temporal resources using a time-graded variant of Fitch-style modal type systems, develop a corresponding modally typed, effectful core calculus, and equip it with a graded-monadic denotational semantics illustrated by a concr
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