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Inko's type checker, start at TypeChecker.check and work your way down the call stack. TypeChecker.check_type_ref is where most of the work is done.
TypeScript is actually an... interesting example because it depends on compiler settings. When noImplicitAny is ON, then the list is first inferred as implicit any[] (riddle me that!). It then gets narrowed (unified?) later to string[]. I have to imagine this is a special case in the compiler because it doesn't work on user-defined data types (see example link above). The TypeScript checker.ts code is a single 50k LOC file so I'm probably not going to be able to understand the implementation.