Publication

A Nominal Theory of Objects with Dependent Types

Martin Odersky, Matthias Zenger
2002
Reports

Abstract

We design and study newObj, a calculus and dependent type system forobjects and classes which can have types as members. Type members canbe aliases, abstract types, or new types. The type system can modelthe essential concepts of Java's inner classes as well as virtual typesand family polymorphism found in BETA or gbeta. It can also model mostconcepts of SML-style module systems, including sharing constraintsand higher-order functors, but excluding applicative functors.The type system can thus be used as a basis for unifying conceptsthat so far existed in parallel in advanced object systems and inmodule systems. The technical report presents results on confluenceof the calculus, soundness of the type system, and undecidability oftype checking.

Official source

https://infoscience.epfl.ch/entities/publication/d4c26f14-3842-4b6d-8edf-3e829b29635e

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Martin Odersky, Matthias Zenger
2002
Reports

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/d4c26f14-3842-4b6d-8edf-3e829b29635e

About this result

Related concepts (24)

Type theory

In mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general, type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that were proposed as foundations are Alonzo Church's typed λ-calculus and Per Martin-Löf's intuitionistic type theory. Most computerized proof-writing systems use a type theory for their foundation, a common one is Thierry Coquand's Calculus of Inductive Constructions.

Type system

In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type (for example, integer, floating point, string) to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term.

Dependent type

In computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems. In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists". In functional programming languages like Agda, ATS, Coq, F*, Epigram, and Idris, dependent types help reduce bugs by enabling the programmer to assign types that further restrain the set of possible implementations.

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