Model management is essential for coping with the complexity introduced by the increasing number and varied nature of artifacts involved in model-driven engineering-based projects. Global model management (GMM) addresses this issue by enabling the representation of artifacts, particularly transformation composition and execution, within a model called a megamodel. Type information about artifacts can be used for preventing type errors during execution. Built on our previous work, in this paper we present the core elements of a type system for GMM that improves its original typing approach and enables both typechecking and type inference on artifacts within a megamodel. This type system is able to deal with non-trivial situations such as the use of higher order transformations. We also present a prototypical implementation of such a type system.