POSIX is a standard for operating systems, with a substantial part devoted to specifying file-system operations. File-system operations exhibit complex concurrent behaviour, comprising multiple actions affecting different parts of the state: typically, multiple atomic reads followed by an atomic update. However, the standard's description of concurrent behaviour is unsatisfactory: it is fragmented; contains ambiguities; and is generally under-specified. We provide a formal concurrent specification of POSIX file systems and demonstrate scalable reasoning for clients. Our specification is based on a concurrent specification language, which uses a modern concurrent separation logic for reasoning about abstract atomic operations, and an associated refinement calculus. Our reasoning about clients highlights an important difference between reasoning about modules built over a heap, where the interference on the shared state is restricted to the operations of the module, and modules built over a file system, where the interference cannot be restricted as the file system is a public namespace. We introduce specifications conditional on context invariants used to restrict the interference, and apply our reasoning to the example of lock files.

We introduce a program logic for specifying a core sequential subset of the POSIX file system and for reasoning abstractly about client programs working with the file system. The challenge is to reason about the combination of local directory update and global pathname traversal (including '..' and symbolic links) which may overlap the directories being updated. Existing reasoning techniques are either based on first-order logic and do not scale, or on separation logic and can only handle linear pathnames (no '..' or symbolic links). We introduce fusion logic for reasoning about local update and global pathname traversal, introducing a novel effect frame rule to propagate the effect of a local update on overlapping pathnames. We apply our reasoning to the standard recursive remove utility (rm -r), discovering bugs in well-known implementations.