Related papers: Towards a Java Subtyping Operad

Due to supporting variance annotations, such as wildcard types, the subtyping relation in Java and other generic nominally-typed OO programming languages is both interesting and intricate. In these languages, the subtyping relation between…

While developing their software, professional object-oriented (OO) software developers keep in their minds an image of the subtyping relation between types in their software. The goal of this paper is to present an observation about the…

Of the complex features of generic nominally-typed OO type systems, wildcard types and variance annotations are probably the hardest to fully grasp. As demonstrated when adding closures (a.k.a., lambdas) and when extending type inference in…

Generics have been added to Java so as to increase the expressiveness of its type system. Generics in Java, however, include some features---such as Java wildcards, $F$-bounded generics, and Java erasure---that have been hard to analyze and…

An outline and summary of four new potential applications of category theory to OOP research are presented. These include (1) the use of operads to model Java subtyping, (2) the use of Yoneda's lemma and representable functors in the…

Extending a given language with new dedicated features is a general and quite used approach to make the programming language more adapted to problems. Being closer to the application, this leads to less programming flaws and easier…

The mathematical modeling of generics in Java and other similar nominally-typed object-oriented programming languages is a challenge. In this short paper we present the outline of a novel order-theoretic approach to modeling generics, in…

Modeling generics in object-oriented programming languages such as Java and C# is a challenge. Recently we proposed a new order-theoretic approach to modeling generics. Given the strong relation between order theory and category theory, in…

The construction of GNOOP as a domain-theoretic model of generic nominally-typed OOP is currently underway. This extended abstract presents the concepts of `nominal intervals' and `full generication' that are likely to help in building…

This paper considers an example of Object-Oriented Programming (OOP) leading to subtle errors that break separation of interface and implementations. A comprehensive principle that guards against such errors is undecidable. The paper…

Many programming languages in the OO tradition now support pattern matching in some form. Historical examples include Scala and Ceylon, with the more recent additions of Java, Kotlin, TypeScript, and Flow. But pattern matching on generic…

Mainstream object-oriented programming languages such as Java, C#, C++ and Scala are all almost entirely nominally-typed. NOOP is a recently developed domain-theoretic model of OOP that was designed to include full nominal information found…

We generalize the construction of multitildes in the aim to provide multitilde operators for regular languages. We show that the underliying algebraic structure involves the action of some operads. An operad is an algebraic structure that…

While generalized abstract datatypes (GADT) are now considered well-understood, adding them to a language with a notion of subtyping comes with a few surprises. What does it mean for a GADT parameter to be covariant? The answer turns out to…

Interfaces are widely used as central design elements of Java applications. Although interfaces are abstract types similar to abstract classes, the usage of interfaces in Java applications may considerably differ from the usage of abstract…

Design patterns are distilled from many real systems to catalog common programming practice. However, some object-oriented design patterns are distorted or overly complicated because of the lack of supporting programming language constructs…

Semantic subtyping is an approach to define subtyping relations for type systems featuring union and intersection type connectives. It has been studied only for strict languages, and it is unsound for non-strict semantics. In this work, we…

NOOP is a mathematical model of nominally-typed OOP that proves the identification of inheritance and subtyping in mainstream nominally-typed OO programming languages and the validity of this identification. This report gives an overview of…

The majority of industrial-strength object-oriented (OO) software is written using nominally-typed OO programming languages. Extant domain-theoretic models of OOP developed to analyze OO type systems miss, however, a crucial feature of…

While generalized algebraic datatypes (\GADTs) are now considered well-understood, adding them to a language with a notion of subtyping comes with a few surprises. What does it mean for a \GADT parameter to be covariant? The answer turns…