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Computational LambdaCalculus and Monads
, 1988
"... The calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with terms. However, if one goes further and uses fijconversion to prove equivalence of programs, then a gross simplification 1 is introduced, that may jeopardise the ..."
Abstract

Cited by 439 (6 self)
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The calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with terms. However, if one goes further and uses fijconversion to prove equivalence of programs, then a gross simplification 1 is introduced, that may jeopardise the applicability of theoretical results to real situations. In this paper we introduce a new calculus based on a categorical semantics for computations. This calculus provides a correct basis for proving equivalence of programs, independent from any specific computational model. 1 Introduction This paper is about logics for reasoning about programs, in particular for proving equivalence of programs. Following a consolidated tradition in theoretical computer science we identify programs with the closed terms, possibly containing extra constants, corresponding to some features of the programming language under consideration. There are three approaches to proving equivalence of programs: ffl T...
NuPRLâ€™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 ..."
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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
A logical framework for software proof reuse
 Proceedings of the ACM SIGSOFT Symposium on Software Reusability
, 1995
"... We describe a logical framework PR for verification of reusable software components. Within our system, developers can employ the advantages traditionally associated with software reuse to reduce the cost of software verification by reusing abstract proofs and specifications. One can construct an ..."
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Cited by 4 (0 self)
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We describe a logical framework PR for verification of reusable software components. Within our system, developers can employ the advantages traditionally associated with software reuse to reduce the cost of software verification by reusing abstract proofs and specifications. One can construct an algorithm with parameters, a specification with parameters, and a proof that the algorithm satisfies the specification provided the parameters satisfy certain conditions, Proofs in PR will themselves contain parameters for subproofs concerning those conditions. In this framework, typing, type checking, and proof checking are decidable. 1