%0 Unpublished work %T Programming with union, intersection, and negation types %+ Centre National de la Recherche Scientifique (CNRS) %+ Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)) %A Castagna, Giuseppe %8 2021-10-29 %D 2021 %Z 2111.03354 %K Type-theory %K Subtyping %K Union types %K Intersection types %K Negation types %K Polymorphism %K Overloading %K Semantic subtyping %Z Computer Science [cs]/Programming Languages [cs.PL]Preprints, Working Papers, ... %X 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 languageĆ  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. %G English %2 https://cnrs.hal.science/hal-03389659/document %2 https://cnrs.hal.science/hal-03389659/file/main.pdf %L hal-03389659 %U https://cnrs.hal.science/hal-03389659 %~ CNRS %~ UNIV-PARIS %~ UNIVERSITE-PARIS %~ UP-SCIENCES %~ TEST4-HALCNRS %~ IRIF