An extended Theory of Primitive Objects: First order system

Journal of Functional Programming, 1994

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 typechecking 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. To achieve greater expressibility while retaining type-safety, we choose to separate the inheritance and subtyping hierarchy in the language. The design of TOOPL has been guided by an analysis of the semantics of the language, which is given in terms of a model of the F-bounded second-order lambda calculus with fixed points at both the element and type level. This semantics supports the language design by providing a means to prove that the type-checking rules are sound, thus guaranteeing that the language is type-safe. While the semantics of our language is rather complex, involving fixed points at both the element and type level, we believe that this reflects the inherent complexity of the basic features of object-oriented programming languages. Particularly complex features include the implicit recursion inherent in the use of the keyword, self, to refer to the current object, and its corresponding type, MyType. The notions of subclass and inheritance introduce the greatest semantic complexities, whereas the notion of subtype is more straightforward to deal with. Our semantic investigations lead us to recommend caution in the use of inheritance, since small changes to method definitions in subclasses can result in major changes to the meanings of the other methods of the class.

Lecture Notes in Computer Science, 1998

This paper presents an imperative object calculus designed to support class-based programming via a combination of extensible objects and encapsulation. This calculus simpli es the language presented in 17] in that, like C++ and Java, it chooses to support an imperative semantics instead of method specialization. We show how Java-style classes and \mixins" may be coded in this calculus, prove a type soundness theorem (via a subject reduction property), and give a sound and complete typing algorithm.

Lecture Notes in Computer Science, 1993

This paper proposes an extension of the notion of method as it is currently used in most objectoriented languages. We define polymethods as methods that we can attach directly to types, as opposed to classes and that we can describe with a second-order type. Two benefits result from this extension; first, the expressive power of the language is improved with better modeling abilities. Next, secondorder types yield a more powerful (precise) type inference, which extends the range of static type checking in a truly extensible object-oriented language. We first show that extensible object-oriented languages present many difficulties for static type-checking and that second-order types are necessary to get stronger type-checking. We illustrate how to combine polymethods through type inheritance and propose a technique based on abstract interpretation to derive a second-order type for new polymethods.

Theoretical Computer Science, 1995

In [3] we defined the)`&-calculus, a simple extension of the typed),-calculus to model typed object-oriented languages. To develop a formal study of type systems for object-oriented languages we define, in this paper, a metalanguage based on)`& and we show by a practical example how to use it to prove properties of a language. To this purpose we define a toy object-oriented language and its type-checking algorithm; then we translate this toy language into our metalanguage. The translation gives the semantics of the toy language and a theorem on the translation of well-typed programs proves the correction of the type-checker of the toy language. As an aside we also illustrate the expressivity of the)`&-based model by showing how to translate existing features like multiple inheritance and multiple dispatch, but also by integrating in the toy language new features directly suggested by the model, such as first-class messages, a generalization of the use of super and the use of explicit coercions.

ACM Transactions on Computational Logic, 2002

Finding typed encodings of object-oriented into procedural or functional programming sheds light on the theoretical foundations of object-oriented languages and their specific typing constructs and techniques. This article describes a type preserving and computationally adequate interpretation of a full-fledged object calculus that supports message passing and constructs for object update and extension. The target theory is a higher-order λ-calculus with records and recursive folds/unfolds, polymorphic and recursive types, and subtyping. The interpretation specializes to calculi of nonextensible objects, and validates the expected subtypin

Our objective is to understand the notion of type in programming languages, present a model of typed, polymorphic programming languages that reflects recent research in type theory, and examine the relevance of recent research to the design of practical programming languages. Object-oriented languages provide both a framework and a motivation for exploring the interaction among the concepts of type, data abstraction, and polymorphism, since they extend the notion of type to data abstraction and since type inheritance is an important form of polymorphism. We develop a X-calculus-based model for type systems that allows us to explore these interactions in a simple setting, unencumbered by complexities of production programming languages. The evolution of languages from untyped universes to monomorphic and then polymorphic type systems is reviewed. Mechanisms for polymorphism such as overloading, coercion, subtyping, and parameterization are examined. A unifying framework for polymorphic type systems is developed in terms of the typed A-calculus augmented to include binding of types by quantification as well as binding of values by abstraction. The typed X-calculus is augmented by universal quantification to model generic functions with type parameters, existential quantification and packaging (information hiding) to model abstract data types, and bounded quantification to model subtypes and type inheritance. In this way we obtain a simple and precise characterization of a powerful type system that includes abstract data types, parametric polymorphism, and multiple inheritance in a single consistent framework. The mechanisms for type checking for the augmented X-calculus are discussed. The augmented typed X-calculus is used as a programming language for a variety of illustrative examples. We christen this language Fun because fun instead of X is the functional abstraction keyword and because it is pleasant to deal with. Fun is mathematically simple and can serve as a basis for the design and implementation of real programming languages with type facilities that are more powerful and expressive than those of existing programming languages. In particular, it provides a basis for the design of strongly typed object-oriented languages.

Theoretical Computer Science, 2006

This article presents a mathematical characterization of object-oriented concepts by defining an observation-oriented semantics for a relational objectoriented language with a rich variety of features including subtypes, visibility, inheritance, type casting, dynamic binding and polymorphism. The language is expressive enough for the specification of object-oriented designs and programs. We also propose a calculus based on this model to support both structural and behavioral refinement of object-oriented designs. We take the approach of the development of the design calculus based on the standard predicate logic in Hoare and He's Unifying Theories of Programming (UTP). We also consider object reference in terms of object identity as values and mutually dependent methods.

2008

We introduce basic concepts from object-oriented programming into dependent type theory based on the idea of modelling objects as interactive programs. We consider methods, interfaces, and the interaction between a fixed number of objects, including self-referential method calls. We introduce a monad like syntax for developing objects in dependent type theory.

Lecture Notes, December, 1998

In this document we hope to explore the foundations of object-oriented programming languages by providing a way of understanding these languages via a translation to an extended typed lambda calculus. We will start with a quite simple encoding of objects and classes, and then see that support for such features as subclasses and parametric polymorphism will push us into more complex encodings. Moreover these encodings will suggest the addition of new extensions (eg, MyType) to object-oriented programming ...