Related papers: Higher category models of the pi-calculus

This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck…

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…

We propose a method to adapt functional logic programming to deal with reasoning on coinductively interpreted programs as well as on inductively interpreted programs. In order to do so, we consider a class of objects interesting for this…

Psi-calculi are a parametric framework for nominal calculi, where standard calculi are found as instances, like the pi-calculus, or the cryptographic spi-calculus and applied-pi. Psi-calculi have an interleaving operational semantics, with…

Using attention weights to identify information that is important for models' decision-making is a popular approach to interpret attention-based neural networks. This is commonly realized in practice through the generation of a heat-map for…

We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

This paper shows how internal models for polymorphic lambda calculi arise in any 2-category with a notion of discreteness. We generalise to a 2-categorical setting the famous theorem of Peter Freyd saying that there are no sufficiently…

Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in…

The Curry-Howard Correspondence has a long history, and still is a topic of active research. Though there are extensive investigations into the subject, there doesn't seem to be a definitive formulation of this result in the level of…

We present a symbolic transition system and bisimulation equivalence for psi-calculi, and show that it is fully abstract with respect to bisimulation congruence in the non-symbolic semantics. A psi-calculus is an extension of the…

Linear logic (LL) has inspired the design of many computational systems, offering reasoning techniques built on top of its meta-theory. Since its inception, several connections between concurrent systems and LL have emerged from different…

This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…

We deliver here second new $\textit{H(x)}-binomials'$ recurrence formula, were $H(x)-binomials' $ array is appointed by $Ward-Horadam$ sequence of functions which in predominantly considered cases where chosen to be polynomials . Secondly,…

Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…

This paper studies the design of programming languages with handlers of higher-order effectful operations -- effectful operations that may take in computations as arguments or return computations as output. We present and analyse a core…

Here are considered some categorical aspects of "Differential calculus" archetype of local approximation of arbitrary morphisms by "linear" ones.

We study concrete sheaf models for a call-by-value higher-order language with recursion. Our family of sheaf models is a generalization of many examples from the literature, such as models for probabilistic and differentiable programming,…

This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…

Guided by consideration of problems in 2 and 3 dimensional lattice model computation, we are led to define a number of new categories, and functors between these categories and the partition category, culminating in the introduction of two…