Refactoring tools are commonly used for remodularization tasks. Basic refactoring operations are combined to perform complex program transformations, but the resulting composed operations are rarely reused, even partially, because popular tools have few support for composition. In this paper, we recast two calculus for static composition of refactorings in a type system framework and we discuss their use for inferring useful properties. We illustrate the value of support for static composition in refactoring tools with a complex remodularization use case: a round-trip transformation between programs conforming to the Composite and Visitor patterns.