Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Adapting Proofs-as-Programs: The Curry-Howard Protocol (Monographs in Computer Science)
Adapting Proofs-as-Programs: The Curry-Howard Protocol (Monographs in Computer Science)
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Electronic Notes in Theoretical Computer Science (ENTCS)
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This paper provides an overview of how to develop model transformations that are "provably correct" with respect to a given functional specification. The approach is based in a mathematical formalism called Constructive Type Theory (CTT) and a related synthesis formal method known as proofs-as-programs. We outline how CTT can be used to provide a uniform formal foundation for representing models, metamodels and model transformations as understood within the Object Management Group's Meta-Object Facility (MOF 2.0) and Model Driven Architecture (MDA) suite of standards [6, 8]. CTT was originally developed to provide a unifying foundation for logic, data and programs. It is higher-order, in the sense that it permits representation and reasoning about programs, types of programs and types of types. We argue that this higher-order aspect affords a natural formal definition of metamodel/model/model instantiation relationships within the MOF. We develop formal notions of models, metamodels and model transformation specifications by utilizing the logic that is built into CTT. In proofs-as-programs, a functional program specification is represented as a special kind of type. A program is provably correct with respect to a given specification if it can be typed by that specification. We develop an analogous approach, defining model transformation specifications as types and provably correct transformations as inhabitants of specification types.