All-Path Reachability Logic

Abstract

This paper presents a language-independent proof system for reachability properties of programs written in non-deterministic (e.g., concurrent) languages, referred to as all-path reachability logic. It derives partial-correctness properties with all-path semantics (a state satisfying a given precondition reaches states satisfying a given postcondition on all terminating execution paths). The proof system takes as axioms any unconditional operational semantics, and is sound (partially correct) and (relatively) complete, independent of the object language. The soundness has also been mechanized in Coq. This approach is implemented in a tool for semantics-based verification as part of the K framework

Executing and verifying higher-order functional-imperative programs in Maude

“…Several versions of Reachability Logic have been proposed in the last few years [3,4,5,6]. Moreover, rl is built on top of Matching Logic (ml), which also exists in several versions [38,39,40].…”

“…(The situation is somewhat similar to the relationship between rewriting logic and the equational logics underneath it.) We adopt the recent all-paths interpretation of rl [6], and build it upon a minimal ml that is enough to express typical practically-relevant language semantics and properties of programs, and moreover is amenable to symbolic execution by rewriting.…”

“…We now recall Reachability-Logic (rl) formulas, the transition systems that they induce, and their all-paths semantics [6] that we use in this paper.…”

“…This property is called weak well-definedness in [6] and is shown there to be a necessary condition for obtaining a sound proof system for rl. The second condition says that the left and right-hand sides of rules cannot share instances; this is quite natural since rules are meant to describe progress in a computation.…”

“…We illustrate the resulting language with simple imperative-functional programs. We show how programs can be: executed with concrete and symbolic data; formally verified with respect to properties expressed in Reachability Logic [3,4,5,6], a language-independent generalisation of Hoare logic; and formally proved equivalent. The soundness of symbolic execution, program verification and program-equivalence verification is formally proved.…”