Related papers: Higher category models of the pi-calculus
We introduce a novel approach to studying properties of processes in the {\pi}-calculus based on a processes-as-formulas interpretation, by establishing a correspondence between specific sequent calculus derivations and computation trees in…
The class of type-two basic feasible functionals ($\mathtt{BFF}_2$) is the analogue of $\mathtt{FP}$ (polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments.…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
The concept of category from mathematics happens to be useful to computer programmers in many ways. Unfortunately, all "good" explanations of categories so far have been designed by mathematicians, or at least theoreticians with a strong…
In this paper, we show that theory of processes can be reduced to the theory of spatial logic. Firstly, we propose a spatial logic SL for higher order pi-calculus, and give an inference system of SL. The soundness and incompleteness of SL…
We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.
The complexity of large-scale distributed systems, particularly when deployed in physical space, calls for new mechanisms to address composability and reusability of collective adaptive behaviour. Computational fields have been proposed as…
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
We show that an intuitionistic version of counting propositional logic corresponds, in the sense of Curry and Howard, to an expressive type system for the probabilistic event lambda-calculus, a vehicle calculus in which both call-by-name…
We consider the 3-category $2\mathfrak{C}at$ whose objects are 2-categories, 1-morphisms are lax functors, 2-morphisms are lax transformations and 3-morphisms are modifications. The aim is to show that it carries interesting…
Psi-calculi is a parametric framework for extensions of the pi-calculus with data terms and arbitrary logics. In this framework there is no direct way to represent action priorities, where an action can execute only if all other enabled…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…
We present a proof system for a multimodal logic, based on our previous work on a multimodal Martin-Loef type theory. The specification of modes, modalities, and implications between them is given as a mode theory, i.e. a small 2-category.…
Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
Type systems as a way to control or analyze programs have been largely studied in the context of functional programming languages. Some of those work allow to extract from a typing derivation for a program a complexity bound on this…
We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem,…
The pi-calculus is a widely used process calculus, which models communications between processes and allows the passing of communication links. Various operational semantics of the pi-calculus have been proposed, which can be classified…
In this paper, we establish the foundations of a novel logical framework for the {\pi}-calculus, based on the deduction-as-computation paradigm. Following the standard proof-theoretic interpretation of logic programming, we represent…
Proof theory provides a foundation for studying and reasoning about programming languages, most directly based on the well-known Curry-Howard isomorphism between intuitionistic logic and the typed lambda-calculus. More recently, a…