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 l-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 l-calculus augmented to include binding of types by quantification as well as binding of values by abstraction.The typed l-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 l-calculus are discussed.The augmented typed l-calculus is used as a programming language for a variety of illustrative examples. We christen this language Fun because fun instead of l 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.

/pdf/on-understanding-types-data-abstraction-and-polymorphism-1a53y4aipq.pdf

On understanding types, data abstraction, and polymorphism

The use of hierarchy is an important component of object-oriented design. Hierarchy allows the use of type families, in which higher level supertypes capture the behavior that all of their subtypes have in common. For this methodology to be effective, it is necessary to have a clear understanding of how subtypes and supertypes are related. This paper takes the position that the relationship should ensure that any property proved about supertype objects also holds for its subtype objects. It presents two ways of defining the subtype relation, each of which meets this criterion, and each of which is easy for programmers to use. The subtype relation is based on the specifications of the sub- and supertypes; the paper presents a way of specifying types that makes it convenient to define the subtype relation. The paper also discusses the ramifications of this notion of subtyping on the design of type families.

A behavioral notion of subtyping

This article provides a detailed description of the automatic theorem prover Simplify, which is the proof engine of the Extended Static Checkers ESC/Java and ESC/Modula-3. Simplify uses the Nelson--Oppen method to combine decision procedures for several important theories, and also employs a matcher to reason about quantifiers. Instead of conventional matching in a term DAG, Simplify matches up to equivalence in an E-graph, which detects many relevant pattern instances that would be missed by the conventional approach. The article describes two techniques, error context reporting and error localization, for helping the user to determine the reason that a false conjecture is false. The article includes detailed performance figures on conjectures derived from realistic program-checking problems.

https://www.hpl.hp.com/techreports/2003/HPL-2003-148.pdf

Simplify: a theorem prover for program checking

Emerald is an object-based language and system designed for the construction of distributed programs. An explicit goal of Emerald is support for object mobility; objects in Emerald can freely move within the system to take advantage of distribution and dynamically changing environments. We say that Emerald has fine-grained mobility because Emerald objects can be small data objects as well as process objects. Fine-grained mobility allows us to apply mobility in new ways but presents implementation problems as well. This paper discusses the benefits of tine-grained mobility, the Emerald language and run-time mechanisms that support mobility, and techniques for implementing mobility that do not degrade the performance of local operations. Performance measurements of the current implementation are included.

Fine-grained mobility in the Emerald system

This paper presents an overview of an integrated programming language and system designed to support the construction and maintenance of distributed programs: programs in which modules reside and execute at communicating, but geographically distinct, nodes. The language is intended to support a class of applications in which the manipulation and preservation of long-lived, on-line, distributed data is important. The language addresses the writing of robust programs that survive hardware failures without loss of distributed information and that provide highly concurrent access to that information while preserving its consistency. Several new linguistic constructs are provided; among them are atomic actions, and modules called guardians that survive node failures.

Guardians and Actions: Linguistic Support for Robust, Distributed Programs

This document serves both as an introduction to CLU and as a language reference manual. Sections 1 through 4 present an overview of the language. These sections highlight the essential features of CLU, and discuss how CLU differs from other, more conventional, languages. Sections 5 though 13 form the reference manual proper. These sections describe each aspect of CLU in detail, and discuss the proper use of various features. Appendices 1 though III provide concise summaries of CLU''s syntax, data types, and I/O facilities. Appendix IV contains example programs.

E Moss

Papers

CLU: Reference Manual