The Structure of Concurrent Process Histories

Nester, Chad

doi:10.1007/978-3-030-78142-2_13

Cited by 6 publications

(12 citation statements)

References 19 publications

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“…String diagrams for monoidal categories are dealt with rigorously in [14]. The use of "corners" in single object double categories to allow the concurrent decomposition of resource transformations is due to [19]. Double categories first appear in [5].…”

Section: Contributions and Related Workmentioning

confidence: 99%

“…The resource theoretic interpretation of symmetric strict monoidal categories can be extended to allow the decomposition of material histories into their concurrent components [19]. Specifically, we augment the string diagrams for a given resource theory A with corners for each object A of A:…”

Section: Cornering and Concurrent Transformationsmentioning

confidence: 99%

“…The double category A is more thoroughly investigated in [19]. For our purposes we need only mention that A always contains crossing cells, pictured below on the left for an arbitrary B ∈ A 0 and X ∈ A •• .…”

Section: Cornering and Concurrent Transformationsmentioning

confidence: 99%

“…The horizontal cells of A form a monoidal category H A , with composition given by horizontal composition in A and the tensor product given by vertical composition in A . Think of H A as a category of exchanges -a point of view is developed in [19]. Isomorphic objects of H A correspond to equivalent exchanges ( [19], Lemma 3).…”

Section: Compact Closure and Accountingmentioning

confidence: 99%

“…Our point of departure is to replace the theory of partita-doppia ledgers with an arbitrary resource theory (symmetric strict monoidal category) in the sense of [3]. Augmenting our resource theories with corners [19] allows us to assign material history to a transition in a compositional way: material history generated by a composite transition system is the composite of material history generated by its components. We call the resulting notion a situated transition system, and we show that for any resource theory A the A-situated transition systems form a monoidal category.…”

Section: Introductionmentioning

confidence: 99%

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Situated Transition Sytems

Nester¹

2021

Preprint

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We construct a monoidal category of open transition systems that generate material history as transitions unfold, which we call situated transition systems. The material history generated by a composite system is composed of the material history generated by each component. The construction is parameterized by a symmetric strict monoidal category, understood as a resource theory, from which material histories are drawn. We pay special attention to the case in which this category is compact closed. In particular, if we begin with a compact closed category of integers then the resulting situated transition systems can be understood as systems of double-entry bookkeeping accounts.

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Section: Contributions and Related Workmentioning

confidence: 99%

Section: Cornering and Concurrent Transformationsmentioning

confidence: 99%

Section: Cornering and Concurrent Transformationsmentioning

confidence: 99%

Section: Compact Closure and Accountingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Situated Transition Sytems

Nester¹

2021

Preprint

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Inductive Diagrams for Causal Reasoning

Castello,

Redmond,

Kuper

2024

Proc. ACM Program. Lang.

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The Lamport diagram is a pervasive and intuitive tool for informal reasoning about “happens-before” relationships in a concurrent system. However, traditional axiomatic formalizations of Lamport diagrams can be painful to work with in a mechanized setting like Agda. We propose an alternative, inductive formalization — the causal separation diagram (CSD) — that takes inspiration from string diagrams and concurrent separation logic, but enjoys a graphical syntax similar to Lamport diagrams. Critically, CSDs are based on the idea that causal relationships between events are witnessed by the paths that information follows between them. To that end, we model “happens-before” as a dependent type of paths between events. The inductive formulation of CSDs enables their interpretation into a variety of semantic domains. We demonstrate the interpretability of CSDs with a case study on properties of logical clocks , widely-used mechanisms for reifying causal relationships as data. We carry out this study by implementing a series of interpreters for CSDs, culminating in a generic proof of Lamport’s clock condition that is parametric in a choice of clock. We instantiate this proof on Lamport’s scalar clock, on Mattern’s vector clock, and on the matrix clocks of Raynal et al. and of Wuu and Bernstein, yielding verified implementations of each. The CSD formalism and our case study are mechanized in the Agda proof assistant.

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