Matching Logic

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain (the set of values that match it), in contrast to FOL where functions and predicates map into a regular domain. Matching logic uniformly generalizes several logical frameworks important for program analysis, such as: propositional logic, algebraic specification, FOL with equality, modal logic, and separation logic. Patterns can specify separation requirements at any level in any program configuration, not only in the heaps or stores, without any special logical constructs for that: the very nature of pattern matching is that if two structures are matched as part of a pattern, then they can only be spatially separated. Like FOL, matching logic can also be translated into pure predicate logic with equality, at the same time admitting its own sound and complete proof system. A practical aspect of matching logic is that FOL reasoning with equality remains sound, so off-the-shelf provers and SMT solvers can be used for matching logic reasoning. Matching logic is particularly well-suited for reasoning about programs in programming languages that have an operational semantics, but it is not limited to this

Symbolic and analytic techniques for resource analysis of Java bytecode

Recent work in resource analysis has translated the idea of amortised resource analysis to imperative languages using a program logic that allows mixing of assertions about heap shapes, in the tradition of separation logic, and assertions about consumable resources. Separately, polyhedral methods have been used to calculate bounds on numbers of iterations in loop-based programs. We are attempting to combine these ideas to deal with Java programs involving both data structures and loops, focusing on the bytecode level rather than on source code

Automatic parallelization with separation logic

Separation logic is a recent approach to the analysis of pointer programs in which resource separation is expressed with a logical connective in assertions that describe the state at any given point in the program. We extend this approach to express properties of memory separation between different points in the program, and present an algorithm for determining independences between program statements which can be used for parallelization

Principles of Security and Trust: 7th International Conference, POST 2018, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018, Thessaloniki, Greece, April 14-20, 2018, Proceedings

authentication; computer science; computer software selection and evaluation; cryptography; data privacy; formal logic; formal methods; formal specification; internet; privacy; program compilers; programming languages; security analysis; security systems; semantics; separation logic; software engineering; specifications; verification; world wide we

Local reasoning about the presence of bugs: Incorrectness Separation Logic

There has been a large body of work on local reasoning for proving the absence of bugs, but none for proving their presence. We present a new formal framework for local reasoning about the presence of bugs, building on two complementary foundations: 1) separation logic and 2) incorrectness logic. We explore the theory of this new incorrectness separation logic (ISL), and use it to derive a begin-anywhere, intra-procedural symbolic execution analysis that has no false positives by construction. In so doing, we take a step towards transferring modular, scalable techniques from the world of program verification to bug catching

Resource-sensitive synchronization inference by abduction

We present an analysis which takes as its input a sequential program, augmented with annotations indicating potential parallelization opportunities, and a sequential proof, written in separation logic, and produces a correctly-synchronized parallelized program and proof of that program. Unlike previous work, ours is not an independence analysis; we insert synchronization constructs to preserve relevant dependencies found in the sequential program that may otherwise be violated by a naive translation. Separation logic allows us to parallelize fine-grained patterns of resource-usage, moving beyond straightforward points-to analysis. Our analysis works by using the sequential proof to discover dependencies between different parts of the program. It leverages these discovered dependencies to guide the insertion of synchronization primitives into the parallelized program, and to ensure that the resulting parallelized program satisfies the same specification as the original sequential program, and exhibits the same sequential behaviour. Our analysis is built using frame inference and abduction, two techniques supported by an increasing number of separation logic tools