Related papers: A Simple Categorical Calculus of Interacting Proce…
Refinement calculus is a powerful and expressive tool for reasoning about sequential programs in a compositional manner. In this paper we present an extension of refinement calculus for reactive systems. Refinement calculus is based on…
The category of double categories and double functors is equipped with a symmetric closed monoidal structure. For any double category $\mathbb A$, the corresponding internal hom functor $|[ \mathbb A,-]|$ sends a double category $\mathbb B$…
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…
We establish a correspondence between modules and spans of algebras within a general monoidal 2-category $\mathfrak{C}$. Specifically, for an algebra $A$ in $\mathfrak{C}$, we construct a normalized lax 3-functor from the 2-category of…
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…
Intensional computation derives concrete outputs from abstract function definitions; extensional computation defines functions through explicit input-output pairs. In formal semantics: intensional computation interprets expressions as…
We develop a symmetric monoidal closed category of games, incorporating sums and products, to model quantum computation at higher types. This model is expressive, capable of representing all unitary operators at base types. It is compatible…
We study coinductive invertibility of cells in weak $\omega$-categories. We use the inductive presentation of weak $\omega$-categories via an adjunction with the category of computads, and show that invertible cells are closed under all…
We extend intersection types to a computational $\lambda$-calculus with algebraic operations \`a la Plotkin and Power. We achieve this by considering monadic intersections, whereby computational effects appear not only in the operational…
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…
We give a construction that identifies the collection of pure processes (i.e. those which are deterministic, or without randomness) within a theory containing both pure and mixed processes. Working in the framework of symmetric monoidal…
Our aim is to detect mechanistic interaction between the effects of two causal factors on a binary response, as an aid to identifying situations where the effects are mediated by a common mechanism. We propose a formalization of mechanistic…
We present a categorical formulation of the cognitive frameworks of Predictive Processing and Active Inference, expressed in terms of string diagrams interpreted in a monoidal category with copying and discarding. This includes diagrammatic…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
We consider the transfer functions describing the input-output relation for a class of linear open quantum systems involving feedback with nonzero time delays. We show how such transfer functions can be factorized into a product of terms…
In this article, we introduce a reference model for interaction semantics among communicating discrete systems to guide the discourse on interoperability. The necessary set of unifying concepts is small and comprises essentially the notion…
Closure conversion is a program transformation at work in compilers for functional languages to turn inner functions into global ones, by building closures pairing the transformed functions with the environment of their free variables.…
We introduce a formalism based on a combinatorial notion of cell complex subject to an inclusion-reversing duality operation. Our main goal is to open the way for a functorial definition of field theories in a context where no manifold or…