Related papers: Intersection Subtyping with Constructors
One of the modern paradigms to develop a system is object oriented analysis and design. In this paradigm, there are several objects and each object plays some specific roles. After identifying objects, the various relationships among…
In this paper we consider a type system with a universal type $\omega$ where any term (whether open or closed, $\beta$-normalising or not) has type $\omega$. We provide this type system with a realisability semantics where an atomic type is…
We introduce some deformations of the biset category and prove a semisimplicity property. We also consider another group category, called the subgroup category, whose morphisms are subgroups of direct products, the composition being star…
We exploit the classical correspondence between finitely generated abelian groups and abelian complex algebraic reductive groups to study the intersection theory of translated subgroups in an abelian complex algebraic reductive group, with…
In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these…
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…
The rapid emergence of single-cell data has facilitated the study of many different biological conditions at the cellular level. Cluster analysis has been widely applied to identify cell types, capturing the essential patterns of the…
The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…
Linear and substructural types are powerful tools, but adding them to standard functional programming languages often means introducing extra annotations and typing machinery. We propose a lightweight substructural type system design that…
Given a suitable functor T:C -> D between model categories, we define a long exact sequence relating the homotopy groups of any X in C with those of TX, and use this to describe an obstruction theory for lifting an object G in D to C.…
Given an ordered structure, we study a natural way to extend the order to preorders on type spaces. For definably complete, linearly ordered structures, we give a characterisation of the preorder on the space of 1-types. We apply these…
Interaction nets are a form of restricted graph rewrite system that can serve as a graphical or textual programming language. As such, benefits include one-step confluence, ease of parallelism and explicit garbage collection. However, some…
Union and intersection types are a staple of gradually typed language such as TypeScript. While it's long been recognized that union and intersection types are difficult to verify statically, it may appear at first that the dynamic part of…
We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is naturally interpreted in a class of structured…
There is a well-documented research programme on graph operators which addresses questions such as `Which graphs appear as images of graphs?'; `Which graphs are fixed under the operator?'; `What happens if the operator is iterated?' In this…
We introduce two-sided type systems, which are sequent calculi for typing formulas. Two-sided type systems allow for hypothetical reasoning over the typing of compound program expressions, and the refutation of typing formulas. By…
We investigate how the concepts of intersection and sums of subobjects carry to exact categories. We obtain a new characterisation of quasi-abelian categories in terms of admitting admissible intersections in the sense of Hassoun and Roy.…
Many type systems have been presented in the literature for variants of the pi-calculus, but none of them are able to handle composite subjects such as those found in the language epi, which features polyadic synchronisation. The purpose of…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
We present intersection type systems in the style of sequent calculus, modifying the systems that Valentini introduced to prove normalisation properties without using the reducibility method. Our systems are more natural than Valentini's…