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NuPRL’s class theory and its applications
 Foundations of Secure Computation, NATO ASI Series, Series F: Computer & System Sciences
, 2000
"... This article presents a theory of classes and inheritance built on top of constructive type theory. Classes are defined using dependent and very dependent function types that are found in the Nuprl constructive type theory. Inheritance is defined in terms of a general subtyping relation over the und ..."
Abstract

Cited by 15 (7 self)
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This article presents a theory of classes and inheritance built on top of constructive type theory. Classes are defined using dependent and very dependent function types that are found in the Nuprl constructive type theory. Inheritance is defined in terms of a general subtyping relation over the underlying types. Among the basic types is the intersection type which plays a critical role in the applications because it provides a method of composing program components. The class theory is applied to defining algebraic structures such as monoids, groups, rings, etc. and relating them. It is also used to define communications protocols as infinite state automata. The article illustrates the role of these formal automata in defining the services of a distributed group communications system. In both applications the inheritance mechanisms allow reuse of proofs and the statement of general properties of system composition. 1
Naïve computational type theory
 Proof and SystemReliability, Proceedings of International Summer School Marktoberdorf, July 24 to August 5, 2001, volume 62 of NATO Science Series III
, 2002
"... ..."
Caltech
"... Abstract This article presents a theory of classes and inheritance built on top of constructive typetheory. Classes are defined using dependent and very dependent function types that are found in the Nuprl constructive type theory. Inheritance is defined in terms of a general subtypingrelation over ..."
Abstract
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Abstract This article presents a theory of classes and inheritance built on top of constructive typetheory. Classes are defined using dependent and very dependent function types that are found in the Nuprl constructive type theory. Inheritance is defined in terms of a general subtypingrelation over the underlying types. Among the basic types is the intersection type which plays a critical role in the applications because it provides a method of composing program components.The class theory is applied to defining algebraic structures such as monoids, groups, rings, etc. and relating them. It is also used to define communications protocols as infinite stateautomata. The article illustrates the role of these formal automata in defining the services of a distributed group communications system. In both applications the inheritance mechanismsallow reuse of proofs and the statement of general properties of system composition. 1 Introduction The results presented here were created as part of a broad effort to understand how to use computers to significantly automate the design and development of software systems. This is one of the main goals of the "PRL project " at Cornell1. One of the basic tenants of our approach to this task is that we should seek the most naturally expressive formal language in which to specify the services, characteristics and constraints that a software system must satisfy. If the formal expression of services is close to a natural one, then people can more readily use it. We also want to allow very compact notations for concepts used to describe systems, and this effect is also a consequence of expressive richness. We have discovered that it is frequently the case that the system we have built to implement one formal language will support an even richer one. So we have come to see our work as also progressively improving the reach of our tools.