In order to illuminate the fundamental concepts involved in object-oriented programming languages, we describe the design of TOOPL, a paradigmatic, statically-typed, functional, object-oriented programming language which supports classes, objects, methods, hidden instance variables, subtypes, and inheritance. It has proven to be quite difficult to design such a language which has a secure type system. A particular problem with statically type checking object-oriented languages is designing type-checking rules which ensure that methods provided in a superclass will continue to be type correct when inherited in a subclass. The type-checking rules for TOOPL have this feature, enabling library suppliers to provide only the interfaces of classes with actual executable code, while still allowing users to safely create subclasses. In order to achieve greater expressibility while retaining type-safety, we choose to separate the inheritance and subtyping hierarchy in the language. The design of...

. This paper presents an untyped object calculus that reflects the capabilities of so-called delegation-based object-oriented languages. A type inference system allows static detection of errors, such as message not understood, while at the same time allowing the type of an inherited method to be specialized to the type of the inheriting object. The main advance over previous work is the provision for subtyping in the presence of delegation primatives. This is achieved by distinguishing a prototype, whose methods may be extended or replaced, from an object, which only responds to messages for which it already has methods. An advantage of this approach is that we have full subtyping without restricting the "runtime " use of inheritance. Type soundness is proved using operational semantics and an analysis of typing derivations. 1 Introduction There are two basic forms of object-oriented languages, the most common of which is class-based. In these languages, which include C [Str86, ES9...

We describe a general module language integrating abstract data types, specifications and object-oriented concepts. The framework is based on the Standard ML module system, with three main extensions: subtyping, a form of object derived from ML structures, and inheritance primitives. The language aims at supporting a range of programming styles, including mixtures of object-oriented programming and programs built around specified algebraic or higher-order abstract data types. We separate specification from implementation, and provide independent inheritance mechanisms for each. In order to support binary operations on objects within this framework, we introduce "internal interfaces" which govern the way that function components of one structure may access components of another. The language design has been tested by writing a number of program examples; an implementation is under development in the context of a larger project.

We extend a fragment of the programming language ML by incorporating a more general form of record pattern matching and providing for user-declared subtypes. Together, these two enhancements may be used to support a restricted object-oriented programming style. In keeping with the framework of ML, we present typing rules for the language, and develop a type inference aJgorithm. We prove that the algorithm is sound with respect to the typing rules, and that it infers a most general typing for every typable expression.

. This paper, which is partly tutorial in nature, summarizes some basic research goals in the study and development of typed objectoriented programming languages. These include both immediate repairs to problems with existing languages and the long-term development of more flexible and expressive, yet type-safe, approaches to program organization and design. We summarize and compare three object models used in the theoretical literature. We also consider approaches to a few technical problems, including changes in the type of a method (member function) from super (base) class to sub (derived) class and the use of types that give information about the implementations as well as the interfaces of objects. Such implementation types seem essential for adequate typing of binary operations on objects, for example. 1 Introduction A number of largely "theoretical" research efforts over the last five to ten years have developed and analyzed type systems for model object-oriented languages. Thi...

Object-oriented programming languages (oopl's) provide important support for today's large-scale software development projects. Unfortunately, the typing issues arising from the object-oriented features that provide this support are substantially different from those that arise in typing procedural languages. Attempts to adapt procedural type systems to object-oriented languages have resulted in languages like Simula, C++ , and Object Pascal, which have overly restrictive type systems. Among other things, the rigidity of these systems frequently force programmers to use type casts, which are a notorious source of hard-to-find bugs. These restrictive type systems also mean that many programming idioms common to untyped oopl's such as Smalltalk are not typeable. One source of this lack of flexibility is the conflation of subtyping and inheritance. Briefly, inheritance is an implementation technique in which new object definitions may be given as incremental modifications to existing defi...

This paper, which is partly tutorial in nature, summarizes some basic research goals in the study and development of typed object-oriented programming languages. These include both immediate repairs to problems with existing languages and the long-term development of more flexible and expressive, yet type-safe, approaches to program organization and design. The technical part of the paper is a summary and comparison of three object models from the literature. We conclude by discussing approaches to selected research problems, including changes in the type of a method from super class to sub class and the use of types that give information about the implementations as well as the interfaces of objects. Such implementation types seem essential for adequate typing of binary operations on objects, for example. 1 Introduction A number of largely "theoretical" research efforts over the last five to ten years have developed and analyzed type systems for model object-oriented languages. This ...

We study the complexity of type inference for programming languages with subtypes. There are three language variations that effect the problem: (i) basic functions may have polymorphic or more limited types, (ii) the subtype hierarchy may be fixed or vary as a result of subtype declarations within a program, and (iii) the subtype hierarchy may be an arbitrary partial order or may have a more restricted form, such as a tree or lattice. The naive algorithm for inferring a most general polymorphic type, under variable subtype hypotheses, requires deterministic exponential time. If we fix the subtype ordering, this upper bound grows to nondeterministic exponential time. We show that it is np-hard to decide whether a lambda term has a type with respect to a fixed subtype hierarchy (involving only atomic type names). This lower bound applies to monomorphic or polymorphic languages. We give pspace upper bounds for deciding polymorphic typability if the subtype hierarchy has a lattice structur...

Rapide is a programming language framework designed for the development of large, concurrent, real-time systems by prototyping. The framework consists of a type language and default executable, specification and architecture languages, along with associated programming tools. Interfaces are the central construct of the type system. This document describes Rapide interfaces, their expressiveness and their use as a typing construct. 1 Introduction Rapide is a programming language framework consisting of a types language, default executable and specification languages, and a set of tools. Although the languages, together, provide a complete programming language, Rapide is intended to accommodate additional implementation and specification languages. The constant of the framework is the type language, which is intended to be general enough to allow the types of relevant implementation languages to be expressed within it. The types language is a general interface definition language, expre...

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