Proving correctness of actor systems using FIFO communication

Abstract

We are developing a hierarchy of theories to reason about actor systems, with the ability to reuse proofs formalized at an abstract level in reasoning about concrete actor programs. Several actor languages, e.g., the ABCL family of languages, implement First-In First-Out (FIFO) communication between actors. Furthermore, many practical systems require FIFO communication for correctness. In previous work, Musser and Varela formalized properties including monotonicity of actor local states, guaranteed message delivery, and general consequences of fairness. While the actor model requires fairness, it does not require FIFO communication.

We continue on to show an example of an actor system, based on the computation of the Sieve of Eratosthenes, that requires FIFO communication in order to be able to prove correctness of its computation.

The third new theory begins to prove the ordering of messages given an order of the sequence numbers. We use results from the first two theories to show that if two messages are about to be sent or received, then the order in which the messages are sent or received is dictated by the sequence numbers. We then use that result to show that two messages must be received in the same order in which they were sent.

We introduce three new theories into the actor model framework of Athena. All three of these theories are developed at the abstract level, enabling the use of them in many concrete programs. The first two of these theories introduce sequence numbers into the messages passed between actors, one for sending and one for receiving. We take advantage of the monotonicity of actor transitions to show that send sequence numbers and receive sequence numbers will only ever increase.

In this thesis, we extend the actor reasoning framework to enable proving correctness of systems which require FIFO communication. This is done by extending the actor framework within the Athena proof system, in which proofs are both human-readable and machine-checkable, taking advantage of its library of algebraic and relational theories.