Cyclic Abduction of Inductively Defined Safety and Termination Preconditions

We describe a new method, called cyclic abduction, for automatically inferring safety and/or termination preconditions for heap-manipulating while programs, expressed as inductive definitions in separation logic. Cyclic abduction essentially works by searching for a cyclic proof of memory safety and/or termination, abducing definitional clauses of the precondition as necessary in order to advance the proof search process. This is achieved via a suite of heuristically guided automatic tactics. We have implemented our cyclic abduction procedure as an automatic tool, Caber, that automatically infers the correct safety and termination preconditions for a range of common small programs manipulating lists and trees, and can also abduce the definitions of more exotic data structures such as cyclic or segmented lists, or trees of linked lists. To our knowledge, cyclic abduction is the first technique for automatically abducing such inductive definitions from