Related papers: Higher category models of the pi-calculus
Lawvere observed in his celebrated work on hyperdoctrines that the set-theoretic schema of comprehension can be elegantly expressed in the functorial language of categorical logic, as a comprehension structure on the functor…
Bi-factor and second-order models based on copulas are proposed for item response data, where the items can be split into non-overlapping groups such that there is a homogeneous dependence within each group. Our general models include the…
This paper provides an abstract definition of some kinds of logics, called diagrammatic logics, together with a definition of morphisms and of 2-morphisms between diagrammatic logics. The definition of the 2-category of diagrammatic logics…
Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the…
This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition…
We consider two characterisations of the may and must testing preorders for a probabilistic extension of the finite pi-calculus: one based on notions of probabilistic weak simulations, and the other on a probabilistic extension of a…
We give a new treatment of the pi-calculus based on the semantic theory of separation logic, continuing a research program begun by Hoare and O'Hearn. Using a novel resource model that distinguishes between public and private ownership, we…
Shape types are a general concept of process types which work for many process calculi. We extend the previously published Poly* system of shape types to support name restriction. We evaluate the expressiveness of the extended system by…
Operations on the cohomology of spaces are important tools enhancing the descriptive power of this computable invariant. For cohomology with mod 2 coefficients, Steenrod squares are the most significant of these operations. Their effective…
The paper discusses the role of interpretations, understood as multifunctions that preserve and reflect logical consequence, as refinement witnesses in the general setting of pi-institutions. This leads to a smooth generalization of the…
The lambda-Pi-calculus Modulo is a variant of the lambda-calculus with dependent types where beta-conversion is extended with user-defined rewrite rules. It is an expressive logical framework and has been used to encode logics and type…
Session types model structured communication-based programming. In particular, binary session types for the pi-calculus describe communication between exactly two participants in a distributed scenario. Adding sessions to the pi-calculus…
The $\pi$-calculus is the paradigmatical name-passing calculus. While being purely name-passing, it allows the representation of higher-order functions and store. We study how $\pi$-calculus processes can be controlled so that computations…
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…
Computation can be considered by taking into account two dimensions: extensional versus intensional, and sequential versus concurrent. Traditionally sequential extensional computation can be captured by the lambda-calculus. However, recent…
In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs,…
Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework…
We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as a potential yoga for dealing with processes and processes of…
We study encodings of the lambda-calculus into the pi-calculus in the unexplored case of calculi with non-determinism and failures. On the sequential side, we consider lambdafail, a new non-deterministic calculus in which intersection types…