Why Separation Logic Works

Abstract

One might poetically muse that computers have the essence both of logic and machines. Through the case of the history of Separation Logic, we explore how this assertion is more than idle poetry. Separation Logic works because it merges the software engineer's conceptual model of a program's manipulation of computer memory with the logical model that interprets what sentences in the logic are true, and because it has a proof theory which aids in the crucial problem of scaling the reasoning task. Scalability is a central problem, and some would even say the central problem, in applications of logic in computer science. Separation Logic is an interesting case because of its widespread success in verification tools. For these two senses of model-the engineering/conceptual and the logical-to merge in a genuine sense, each must maintain their norms of use from their home disciplines. When this occurs, both the logic and engineering benefit greatly. Seeking this intersection of two different senses of model provides a strategy for how computer scientists and logicians may be successful. Furthermore, the history of Separation Logic for analysing programs provides a novel case for philosophers of science of how software engineers and computer scientists develop models and the components of such models. We provide three contributions: an exploration of the extent of models merging that is necessary for success in computer science; an introduction to the technical details of Separation Logic, which can be used for reasoning about other exhaustible resources; and an introduction to (a subset of) the problems, process, and results of computer scientists for those outside the field.

Towards Scientific Incident Response

“…Automation is a clear prerequisite for any decisionsupport in a field like incident analysis, where data volumes are so large. At the same time, we have adapted logical tools that have demonstrated scalable reasoning in other contexts [16,22]. The design of our logic is not just tailored to incident analysis, but, insofar as is possible at this stage, tailored to a scalable automation of support for incident analysis.…”

“…This sense is quite far from a scientific model. However, as [22] argues, a logic will be most effective when its logic model aligns with the salient features of a scientific model of the represented phenomenon. Therefore, we develop logical tools with the purpose of incident analysis in mind at every step.…”

“…Separation Logic is a specific theory of BI for handling memory allocation-our direct starting point in this section. Readers may see [22] for an accessible introduction to Separation Logic.…”

The Inner and Outer Algebras of Unified Concurrency

“…Our goal for a UTP semantics was to obtain one that was not only compositional (denotational), but was also "local", in the sense that the semantics would only talk about the behaviour of the command under consideration, without being required to also explicitly mention all possible interference. This goal was inspired by the success of separation logic at being able to scale to automatically check very large codebases for pointer errors [21]. A key enabler of that success is that separation logic allows the reasoner to focus on the few pointers actually being manipulated by a program, rather than having to consider (or quantify over) all possible heaps.…”

A refinement to the general mechanistic account

“…The difficulty (or ease) of indexing components clearly lies beyond the scope of the present work. Rather, we wish to note merely that the apparent objection is an intuitive and direct way to establish the need for the indexing we propose.38 See Floridi (2011) for details.39 Pym et al (2018) describe a case where scientific and logic models are merged in computer science, specifically program verification. So it does appear to be possible to link a mechanistic and logical account of a phenomenon in computer science, but it is painstaking work to merge them.…”