Compilers that can type check compilation units in parallel can make more efficient use of multi-core architectures, which are nowadays widespread. Developing parallel type checker implementations is complicated by the need to handle concurrency and synchronization between checking of compilation units. Dependencies between compilation units are induced by name resolution, and a parallel type checker needs to ensure that units have defined all relevant names before other units do a lookup. Mutually recursive references and implicitly discovered dependencies between compilation units preclude determining a static compilation order for many programming languages.

In this paper, we present a new framework for implementing hierarchical type checkers that provides implicit parallel execution in the presence of dynamic, mutually recursive, dependencies between compilation units. The resulting type checkers can be written without explicit handling of communication or synchronization with different compilation units. We achieve this by providing type checkers with an API for name resolution based on scope graphs, a language-independent formalism that supports a wide range of binding patterns. We introduce the notion of \emph{scope state} to ensure safe name resolution. Scope state tracks the completeness of a scope, and is used to decide whether a scope graph query between compilation units must be delayed. Our framework is implemented in Java using the actor paradigm. We evaluated our approach by parallelizing the solver for Statix, a meta-language for type checkers based on scope graphs, using our framework. This parallelizes every Statix-based type checker, provided its specification follows a split declaration-type style. Benchmarks show that the approach results in speedups up to approximately $3x$ on $6$ cores for the parallel Statix solver for larger projects.