Proofs-as-Model-Transformations

• Published in: Theory and Practice of Model Transformations Vol. 5063; pp. 214 - 228
• Main Author: Poernomo, Iman
• Format: Book Chapter
• Language: English
• Published: Germany Springer Berlin / Heidelberg 2008; Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• ISBN: 3540699260; 9783540699262
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-540-69927-9_15

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.