In concurrent verification, separation logic provides a strong story for handling both resources that are owned exclusively and resources that are shared persistently (i.e., forever). However, the situation is more complicated for temporarily shared state, where state might be shared and then later reclaimed as exclusive. We believe that a framework for temporarily-shared state should meet two key goals not adequately met by existing techniques. One, it should allow and encourage users to verify new sharing strategies. Two, it should provide an abstraction where users manipulate shared state in a way agnostic to the means with which it is shared. We present Leaf, a library in the Iris separation logic which accomplishes both of these goals by introducing a novel operator, which we call guarding, that allows one proposition to represent a shared version of another. We demonstrate that Leaf meets these two goals through a modular case study: we verify a reader-writer lock that supports shared state, and a hash table built on top of it that uses shared state.

Ivy is a multi-modal verification tool for correct design and implementation of distributed protocols and algorithms, supporting modular specification, implementation and proof. Ivy supports proving safety and liveness properties of parameterized and infinite-state systems via three modes: deductive verification using an SMT solver, abstraction and model checking, and manual proofs using natural deduction. It supports light-weight formal methods via compositional specification-based testing and bounded model checking. Ivy can extract executable distributed programs by translation to efficient C++ code. It is designed to support decidable automated reasoning, to improve proof stability and to provide transparency in the case of proof failures. For this purpose, it presents concrete finite counterexamples, automatically audits proofs for decidability of verification conditions, and provides modular hiding of theories.

Formal verification of infinite-state systems, and distributed systems in particular, is a long standing research goal. In the deductive verification approach, the programmer provides inductive invariants and pre/post specifications of procedures, reducing the verification problem to checking validity of logical verification conditions. This check is often performed by automated theorem provers and SMT solvers, substantially increasing productivity in the verification of complex systems. However, the unpredictability of automated provers presents a major hurdle to usability of these tools. This problem is particularly acute in case of provers that handle undecidable logics, for example, first-order logic with quantifiers and theories such as arithmetic. The resulting extreme sensitivity to minor changes has a strong negative impact on the convergence of the overall proof effort.

This paper surveys the work to date on Ivy, a language and a tool for the formal specification and verification of distributed systems. Ivy supports deductive verification using automated provers, model checking, automated testing, manual theorem proving and generation of executable code. In order to achieve greater verification productivity, a key design goal for Ivy is to allow the engineer to apply automated provers in the realm in which their performance is relatively predictable, stable and transparent. In particular Ivy focuses on the use of decidable fragments of first-order logic. We consider the rationale or Ivy’s design, the various capabilities of the tool, as well as case studies and applications.

Despite several decades of research, the problem of formal verification of infinite-state systems has resisted effective automation. We describe a system — Ivy — for interactively verifying safety of infinite-state systems. Ivy’s key principle is that whenever verification fails, Ivy graphically displays a concrete counterexample to induction. The user then interactively guides generalization from this counterexample. This process continues until an inductive invariant is found. Ivy searches for universally quantified invariants, and uses a restricted modeling language. This ensures that all verification conditions can be checked algorithmically. All user interactions are performed using graphical models, easing the user’s task. We describe our initial experience with verifying several distributed protocols.

Induction is a successful approach for verification of hardware and software systems. A common practice is to model a system using logical formulas, and then use a decision procedure to verify that some logical formula is an inductive safety invariant for the system. A key ingredient in this approach is coming up with the inductive invariant, which is known as invariant inference. This is a major difficulty, and it is often left for humans or addressed by sound but incomplete abstract interpretation. This paper is motivated by the problem of inductive invariants in shape analysis and in distributed protocols. This paper approaches the general problem of inferring first-order inductive invariants by restricting the language L of candidate invariants. Notice that the problem of invariant inference in a restricted language L differs from the safety problem, since a system may be safe and still not have any inductive invariant in L that proves safety. Clearly, if L is finite (and if testing an inductive invariant is decidable), then inferring invariants in L is decidable. This paper presents some interesting cases when inferring inductive invariants in L is decidable even when L is an infinite language of universal formulas. Decidability is obtained by restricting L and defining a suitable well-quasi-order on the state space. We also present some undecidability results that show that our restrictions are necessary. We further present a framework for systematically constructing infinite languages while keeping the invariant inference problem decidable. We illustrate our approach by showing the decidability of inferring invariants for programs manipulating linked-lists, and for distributed protocols.