Model transformation has become an established field, and it is important to improve the quality of specifications written in transformation languages. Different transformation patterns have been introduced in the model-driven engineering (MDE) community to improve the quality of transformation specifications. However, due to the different definitions of pattern concepts by different authors, it is difficult for practitioners to understand how to apply patterns in practice. Therefore, there is a need to unify transformation pattern concepts by presenting a generic metamodel and formalizing patterns in terms of this metamodel, to define the meaning of pattern application. In this research a general metamodel for definition of different design patterns in model transformation is provided. The metamodel presents clear description of common aspects of transformation patterns, which facilitates the application of patterns on model transformations by validating the application against the underlying formalism. Additionally, a unified and precise terminology for the application and verification of model transformation patterns by using a formal model of model transformation patterns in the Z notation is presented. To show the applicability of the proposed formalism, four well-known model transformation patterns are specified. K E Y W O R D S model-driven development (MDD), model transformation, design pattern, formal model 1 | INTRODUCTION Model transformations (MTs) have become more and more complex in recent years, as a result of their application to substantial problem cases in both academia and industry. Enhancing the quality of model transformations to provide a result in an efficient and modular way is a crucial task for the model-driven community. Design patterns for model transformations have been identified as an important solution to potentially improve the quality of model transformations. 1-3To obtain the benefit and utilize the productivity accompanied by the pattern application in MDE, model transformation patterns must first be formalized, which paves the way for automating the MT-based software development and verification. [3][4][5] Exploring the literature reveals some formal models for model transformations. [6][7][8] However, to the best of our knowledge, there is not any formalism for model transformation patterns in the literature. Having a unified formalism regarding model transformation patterns will provide a foundation to support the pattern application and verification features easily in the current model transformation tools. 9,10 As a result, this research aims to present a new formalism for defining model transformation patterns and expressing the semantics of pattern application.To provide a conceptual view which serves as the informal basics of the proposed formalism of the MT patterns, an abstract architecture representing the underlying concepts such as model and metamodel is presented first. In this research, we use the Z specification language to formalize the MT design patterns. In a...