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Journal articles on the topic 'Presheaf semantics'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Hamana, Makoto. "Complete algebraic semantics for second-order rewriting systems based on abstract syntax with variable binding." Mathematical Structures in Computer Science, October 14, 2022, 1–32. http://dx.doi.org/10.1017/s0960129522000287.

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Abstract By using algebraic structures in a presheaf category over finite sets, following Fiore, Plotkin and Turi, we develop sound and complete models of second-order rewriting systems called second-order computation systems (CSs). Restricting the algebraic structures to those equipped with well-founded relations, we obtain a complete characterisation of terminating CSs. We also extend the characterisation to rewriting on meta-terms using the notion of $\Sigma$ -monoid.

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12

Nygaard, Mikkel, and Glynn Winskel. "Domain Theory for Concurrency." BRICS Report Series 10, no. 43 (2003). http://dx.doi.org/10.7146/brics.v10i43.21815.

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A simple domain theory for concurrency is presented. Based on a categorical model of linear logic and associated comonads, it highlights the role of linearity in concurrent computation. Two choices of comonad yield two expressive metalanguages for higher-order processes, both arising from canonical constructions in the model. Their denotational semantics are fully abstract with respect to contextual equivalence. One language derives from an exponential of linear logic; it supports a straightforward operational semantics with simple proofs of soundness and adequacy. The other choice of comonad

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13

Kaddar, Younesse, and Sam Staton. "A model of stochastic memoization and name generation in probabilistic programming: categorical semantics via monads on presheaf categories." Electronic Notes in Theoretical Informatics and Computer Science Volume 3 - Proceedings of... (November 23, 2023). http://dx.doi.org/10.46298/entics.12291.

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Stochastic memoization is a higher-order construct of probabilistic programming languages that is key in Bayesian nonparametrics, a modular approach that allows us to extend models beyond their parametric limitations and compose them in an elegant and principled manner. Stochastic memoization is simple and useful in practice, but semantically elusive, particularly regarding dataflow transformations. As the naive implementation resorts to the state monad, which is not commutative, it is not clear if stochastic memoization preserves the dataflow property -- i.e., whether we can reorder the lines

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14

Aagaard, Frederik Lerbjerg, Magnus Baunsgaard Kristensen, Daniel Gratzer, and Lars Birkedal. "Unifying cubical and multimodal type theory." Logical Methods in Computer Science Volume 20, Issue 4 (December 12, 2024). https://doi.org/10.46298/lmcs-20(4:25)2024.

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In this paper we combine the principled approach to modalities from multimodal type theory (MTT) with the computationally well-behaved realization of identity types from cubical type theory (CTT). The result -- cubical modal type theory (Cubical MTT) -- has the desirable features of both systems. In fact, the whole is more than the sum of its parts: Cubical MTT validates desirable extensionality principles for modalities that MTT only supported through ad hoc means. We investigate the semantics of Cubical MTT and provide an axiomatic approach to producing models of Cubical MTT based on the int

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15

Hu, Jason Z. S., and Brigitte Pientka. "A Categorical Normalization Proof for the Modal Lambda-Calculus." Electronic Notes in Theoretical Informatics and Computer Science Volume 1 - Proceedings of... (February 22, 2023). http://dx.doi.org/10.46298/entics.10360.

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We investigate a simply typed modal $\lambda$-calculus, $\lambda^{\to\square}$, due to Pfenning, Wong and Davies, where we define a well-typed term with respect to a context stack that captures the possible world semantics in a syntactic way. It provides logical foundation for multi-staged meta-programming. Our main contribution in this paper is a normalization by evaluation (NbE) algorithm for $\lambda^{\to\square}$ which we prove sound and complete. The NbE algorithm is a moderate extension to the standard presheaf model of simply typed $\lambda$-calculus. However, central to the model const

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16

Cattani, Gian Luca, and Glynn Winskel. "Profunctors, Open Maps and Bisimulation." BRICS Report Series 11, no. 22 (2004). http://dx.doi.org/10.7146/brics.v11i22.21847.

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This paper studies fundamental connections between profunctors (i.e., distributors, or bimodules), open maps and bisimulation. In particular, it proves that a colimit preserving functor between presheaf categories (corresponding to a profunctor) preserves open maps and open map bisimulation. Consequently, the composition of profunctors preserves open maps as 2-cells. A guiding idea is the view that profunctors, and colimit preserving functors, are linear maps in a model of classical linear logic. But profunctors, and colimit preserving functors, as linear maps, are too restrictive for many app

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17

Cattani, Gian Luca, and Glynn Winskel. "Profunctors, Open Maps and Bisimulation." February 22, 2016. https://doi.org/10.7146/brics.v11i22.21847.

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This paper studies fundamental connections between profunctors (i.e., distributors, or bimodules), open maps and bisimulation. In particular, it proves that a colimit preserving functor between presheaf categories (corresponding to a profunctor) preserves open maps and open map bisimulation. Consequently, the composition of profunctors preserves open maps as 2-cells. A guiding idea is the view that profunctors, and colimit preserving functors, are linear maps in a model of classical linear logic. But profunctors, and colimit preserving functors, as linear maps, are too restrictive for many app

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18

Emmerson, Parker Yehushuason, and J. Buchanan Buchanan Ryan. "Potentiation vs. Permission: Formalizing Implicit Associations in Mathematical Structures." May 6, 2025. https://doi.org/10.5281/zenodo.15347483.

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This paper investigates the formalization of implicit associations within mathematical structures through the contrasting lenses of <em>potentiation</em> and <em>permission</em>. While implicit associations—underlying, often non-definitional relationships between structural elements—play a critical role in shaping mathematical behavior, their abstract nature has hindered systematic analysis. We propose a dual framework where <em>potentiation</em> characterizes the inherent capacity of elements to enable or amplify specific properties or operations, while&nb

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