Related papers: Higher category models of the pi-calculus
In this short paper, we consider a form of higher-order rewriting with a call-by-value evaluation strategy so as to model call-by-value programs. We briefly present a cost-size semantics to call-by-value rewriting: a class of algebraic…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
We give simple upper bounds for rational sectional category and use them to compute invariants of the type of Farber's topological complexity of rational spaces. In particular we show that the sectional category of formal morphisms reaches…
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…
The Curry-Howard correspondence is often described as relating proofs (in intutionistic natural deduction) to programs (terms in simply-typed lambda calculus). However this narrative is hardly a perfect fit, due to the computational content…
Rewriting systems on words are very useful in the study of monoids. In good cases, they give finite presentations of the monoids, allowing their manipulation by a computer. Even better, when the presentation is confluent and terminating,…
Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…
This is the fourth in a series of papers extending Martin-L\"of's meaning explanation of dependent type theory to higher-dimensional types. In this installment, we show how to define cubical type systems supporting a general schema of…
While computer programs and logical theories begin by declaring the concepts of interest, be it as data types or as predicates, network computation does not allow such global declarations, and requires *concept mining* and *concept…
We propose a new definition of higher-order DisCoCat (categorical compositional distributional) models where the meaning of a word is not a diagram, but a diagram-valued higher-order function. Our models can be seen as a variant of Montague…
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the…
The goal of this thesis is threefold: first, to provide a general semantic setting for reasoning about incremental computation. Second, to establish and clarify the connection between derivatives in the incremental sense and derivatives in…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
In this paper I will develop a lambda-term calculus, lambda-2Int, for a bi-intuitionistic logic and discuss its implications for the notions of sense and denotation of derivations in a bilateralist setting. Thus, I will use the Curry-Howard…
In this paper we outline an approach to calculus over quasitriangular Hopf algebras. We study differential operators in the framework of monoidal categories equipped with a braiding or symmetry. To be more concrete, we choose as an example…
In this paper we present $2$-category theory from the perspective of Gray-categories using the graphical calculus of separated surface diagrams. As an extended example we consider cones and limits of $2$-functors. Then we use the canonical…
In this note we give explicit isomorphisms of 2-categories between various versions of the categorified quantum group associated to a simply-laced Kac-Moody algebra. These isomorphisms are convenient when working with the categorified…
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…
We treat the problem of lifting bicategories into double categories through categories of vertical morphisms. We consider structures on decorated 2-categories allowing us to formally implement arguments of sliding certain squares along…