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This paper describes a new abstract interpretation-based approach to verify temporal safety properties of recursive, higher-order programs. While prior works have provided theoretical impact and some automation, they have had limited scalability. We begin with a new automata-based abstract effect domain for summarizing context-sensitive dependent effects, capable of abstracting relations between the program environment and the automaton control state. Our analysis includes a new transformer for abstracting event prefixes to automatically computed context-sensitive effect summaries, and is instantiated in a type-and-effect system grounded in abstract interpretation. Since the analysis is parametric on the automaton, we next instantiate it to a broader class of history/register (or accumulator) automata, beyond finite state automata to express some context-free properties, input-dependency, event summation, resource usage, cost, equal event magnitude, etc. We implemented a prototype evDrift that computes dependent effect summaries (and validates assertions) for OCaml-like recursive higher-order programs. As a basis of comparison, we describe reductions to assertion checking for higher-order but effect-free programs, and demonstrate that our approach outperforms prior tools Drift, RCaml/Spacer, MoCHi, and ReTHFL. Overall, across a set of 23 benchmarks, Drift verified 12 benchmarks, RCaml/Spacer verified 6, MoCHi verified 11, ReTHFL verified 18, and evDrift verified 21; evDrift also achieved a 6.3x, 5.3x, 16.8x, and 6.4x speedup over Drift, RCaml/Spacer, MoCHi, and ReTHFL, respectively, on those benchmarks that both tools could solve. 

Commutativity of program code (the equivalence of two code fragments composed in alternate orders) is of ongoing interest in many settings such as program verification, scalable concurrency, and security analysis. While some recent works have explored static analysis for code commutativity, few have specifically catered to heap-manipulating programs. We introduce an abstract domain in which commutativity synthesis or verification techniques can safely be performed on abstract mathematical models and, from those results, one can directly obtain commutativity conditions for concrete heap programs. This approach offloads challenges of concrete heap reasoning into the simpler abstract space. We show this reasoning supports framing and composition, and conclude with commutativity analysis of programs operating on example heap data structures. Our work has been mechanized in Coq and is available in the supplement. 

There is an ongoing effort to provide programming abstractions that ease the burden of exploiting multicore hardware. Many programming abstractions (e.g., concurrent objects, transactional memory, etc.) simplify matters, but still involve intricate engineering. We argue that some difficulty of multicore programming can be meliorated through a declarative programming style in which programmers directly express the independence of fragments of sequential programs. In our proposed paradigm, programmers write programs in a familiar, sequential manner, with the added ability to explicitly express the conditions under which code fragments sequentially commute. Putting such commutativity conditions into source code offers a new entry point for a compiler to exploit the known connection between commutativity and parallelism. We give a semantics for the programmer’s sequential perspective and, under a correctness condition, find that a compiler-transformed parallel execution is equivalent to the sequential semantics. Serializability/linearizability are not the right fit for this condition, so we introduce scoped serializability and show how it can be enforced with lock synthesis techniques. We next describe a technique for automatically verifying and synthesizing commute conditions via a new reduction from our commute blocks to logical specifications, upon which symbolic commutativity reasoning can be performed. We implemented our work in a new language called Veracity, implemented in Multicore OCaml. We show that commutativity conditions can be automatically generated across a variety of new benchmark programs, confirm the expectation that concurrency speedups can be seen as the computation increases, and apply our work to a small in-memory filesystem and an adaptation of a crowdfund blockchain smart contract.