1. Using Alcoa to Specify a UNIX File System Specification of some structures and operations in a File System

2. Alcoa Predicate logic to specify a system of objects. (quantifiers, subsets, relations) Can only describe a two state relationship. Missing a sequential composition operator. currentnext time0time1time2 OK NO

3. Alcoa

4. Alcoa Tool Finds an instance which satisfies the specification. –Finds contradictions. –See an example of the specification. Preservation of some logical statement through an operation.

5. currentnext operation Invariant holds here. Does invariant hold here? Alcoa will check this and give counterexamples if not true. a & b | c is trueIs a’ & b’ | c’ true?

6. File System Basics Inode Directory Entry

7. File System Basics Inode Directory Entry 2 1

8. File System Basics Inode Directory Entry 2 1 Datablocks

9. Atomic Actions Ordering Imagine the system crashing while making changes to the file system. How should the atomic actions be ordered such that the file system can be recovered?

10. Atomic Actions Ordering Inode a Directory Entry rename a b

11. Atomic Actions Ordering Inode a Directory Entry rename a b Lost inode if system crashes here.

12. Atomic Actions Ordering Inode a Directory Entry rename a b

13. Atomic Actions Ordering Inode a Directory Entry rename a b b

14. Atomic Actions Ordering Inode a Directory Entry rename a b b

15. Atomic Actions Ordering From “Metadata Update Performance in File Systems” by G. Ganger, Y. Patt Operations –Link removal –Link addition –Block allocation –Block de-allocation

16. Link Addition 1. Link count in inode incremented. 2. Pointer to inode added to the list of directory entries. Inode DirEntry 1 Link Count

17. Link Addition 1. Link count in inode incremented. 2. Pointer to inode added to the list of directory entries. Inode DirEntry 2 Link Count

18. Link Addition 1. Link count in inode incremented. 2. Pointer to inode added to the list of directory entries. Inode DirEntry 2 Link Count DirEntry

19. Link Deletion 1. Directory Entry is removed first. 2. Link Count is decremented. Inode DirEntry 2 Link Count DirEntry

20. Link Deletion 1. Directory Entry is removed first. 2. Link Count is decremented. Inode DirEntry 2 Link Count

21. Link Deletion 1. Directory Entry is removed first. 2. Link Count is decremented. Inode DirEntry 1 Link Count

22. The Problem –Finding preserved invariant was not easy. “No lost inodes. All allocated inodes are pointed to by a directory entry.” is not an invariant. –Reverse engineering the invariant. –Tool helped determine which invariants are wrong.

23. Discovered Invariants “If an inode’s link count is zero, there are no directory entries pointing to the inode.” “At all times, an inode’s link count is higher than the number of directory entries pointing to an inode.”

24. Discovered Invariants “If an inode’s link count is zero, there are no directory entries pointing to the inode.” –Important when recovering after a crash so that an inode is not accidently deallocated.

25. Using the Invariants Weakened the precondition of the operations to see if the invariants are preserved. Some interesting configurations –Link count much higher than the actual number of directory entries.

26. Other Issues Relations in Alcoa can be –A function, surjective, partial/total, injective Abstraction design decision –Choosing relation type forces specification writer to be careful and specific.

27. Other Issues Alcoa does not have numbers. –Link Count was tricky to model. Inverse relations. –Alcoa allows this and inadvertently used. Many invariants do not hold because of the intermediate stages. –Tricky specifying an invariant.

28. Other Issues Must clearly specify the precondition and postcondition of an operation. –Hoare Triple Instance finding useful for careless errors such as typos. –b in UsedB –b not in UsedB’