Java has no module system. Its packages only subdivide the class name space, allowing only a very limited form of component-level information hiding and reuse. Two Java Community Processes have started addressing this problem: one describes the runtime system and has reached an early draft stage, while the other considers the developer's view and only has a straw-man proposal. Both are natural language documents, which inevitably contain ambiguities.
In this work we design and formalize a core module system for Java. Where the JCP documents are complete, we follow them closely; elsewhere we make reasonable choices. We define the syntax, the type system, and the operational semantics of an LJAM language, defining these rigorously in the Isabelle/HOL automated proof assistant. Using this formalization, we identify various issues with the module system. We highlight the underlying design decisions, and discuss several alternatives and their benefits. Our Isabelle/HOL definitions should provide a basis for further consideration of the design alternatives, for reference implementations, and for proofs of soundness.