arXiv subjects

Eric Campbell

Publications and source records attributed to Eric Campbell.

3 recordsLinked to original sources

arXiv2021

Injecting Finiteness to Prove Completeness for Finite Linear Temporal Logic

Temporal logics over finite traces are not the same as temporal logics over potentially infinite traces. Ro\c{s}u first proved completeness for linear temporal logic on finite traces (LTLf) with a novel coinductive axiom. We offer a different proof, with fewer, more conventional axioms. Our proof is a direct adaptation of Kr\"{o}ger and Merz's Henkin-Hasenjaeger-style proof. The essence of our adaption is that we "inject" finiteness: that is, we alter the proof structure to ensure that models are finite. We aim to present a thorough, accessible proof.

cs.LO↗

arXiv2019

How to Avoid Making a Billion-Dollar Mistake: Type-Safe Data Plane Programming with SafeP4

The P4 programming language offers high-level, declarative abstractions that bring the flexibility of software to the domain of networking. Unfortunately, the main abstraction used to represent packet data in P4, namely header types, lacks basic safety guarantees. Over the last few years, experience with an increasing number of programs has shown the risks of the unsafe approach, which often leads to subtle software bugs. This paper proposes SafeP4, a domain-specific language for programmable data planes in which all packet data is guaranteed to have a well-defined meaning and satisfy essential safety guarantees. We equip SafeP4 with a formal semantics and a static type system that statically guarantees header validity---a common source of safety bugs according to our analysis of real-world P4 programs. Statically ensuring header validity is challenging because the set of valid headers can be modified at runtime, making it a dynamic program property. Our type system achieves static safety by using a form of path-sensitive reasoning that tracks dynamic information from conditional statements, routing tables, and the control plane. Our evaluation shows that SafeP4's type system can effectively eliminate common failures in many real-world programs.

cs.PL↗

arXiv2017

Kleene Algebra Modulo Theories

Kleene algebras with tests (KATs) offer sound, complete, and decidable equational reasoning about regularly structured programs. Interest in KATs has increased greatly since NetKAT demonstrated how well extensions of KATs with domain-specific primitives and extra axioms apply to computer networks. Unfortunately, extending a KAT to a new domain by adding custom primitives, proving its equational theory sound and complete, and coming up with an efficient implementation is still an expert's task. Abstruse metatheory is holding back KAT's potential. We offer a fast path to a "minimum viable model" of a KAT, formally or in code through our framework, Kleene algebra modulo theories (KMT). Given primitives and a notion of state, we can automatically derive a corresponding KAT's semantics, prove its equational theory sound and complete with respect to a tracing semantics (programs are denoted as traces of states), and derive a normalization-based decision procedure for equivalence checking. Our framework is based on pushback, a generalization of weakest preconditions that specifies how predicates and actions interact. We offer several case studies, showing tracing variants of theories from the literature (bitvectors, NetKAT) along with novel compositional theories (products, temporal logic, and sets). We derive new results over unbounded state, reasoning about monotonically increasing, unbounded natural numbers. Our OCaml implementation closely matches the theory: users define and compose KATs with the module system.

cs.PL↗