As model transformations have become an integral part of the automated software engineering lifecycle, reuse, modularisation, and composition of model transformations becomes important. One way to compose model transformations is to compose modules of transformation rules, and execute the composition as one transformation (internal composition). This kind of composition can provide richer semantics, as it is part of the transformation language. This paper aims to generalise two internal composition mechanisms for rule-based transformation languages, module import and rule inheritance, by providing executable semantics for the composition mechanisms within a virtual machine. The generality of the virtual machine is demonstrated for different rule-based transformation languages by compiling those languages to, and executing them on this virtual machine. We will discuss how ATL and graph transformations can be mapped to modules and rules inside the virtual machine.