Programming with union, intersection, and negation types - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Programming with union, intersection, and negation types

Résumé

In this essay, I present the advantages and, I dare say, the beauty of programming in a language with set-theoretic types, that is, types that include union, intersection, and negation type connectives. I show by several examples how set-theoretic types are necessary to type some common programming patterns, but also how they play a key role in typing several language constructs-from branching and pattern matching to function overloading and type-cases-very precisely. I start by presenting the theory of types known as semantic subtyping and extend it to include polymorphic types. Next, I discuss the design of languages that use these types. I start by defining a theoretical framework that covers all the examples given in the first part of the presentation. Since the system of the framework cannot be effectively implemented, I then describe three effective restrictions of this system: (i) a polymorphic language with explicitly-typed functions, (ii) an implicitly-typed polymorphic languageà la Hindley-Milner, and (iii) a monomorphic language that, by implementing classic union-elimination, precisely reconstructs intersection types for functions and implements a very general form of occurrence typing. I conclude the presentation with a short overview of other aspects of these languages, such as pattern matching, gradual typing, and denotational semantics.
Fichier principal
Vignette du fichier
main.pdf (485.68 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03389659 , version 1 (29-10-2021)

Identifiants

Citer

Giuseppe Castagna. Programming with union, intersection, and negation types. 2021. ⟨hal-03389659⟩
25 Consultations
98 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More