Incremental and Modular Context-sensitive Analysis

Context-sensitive global analysis of large code bases can be expensive, which can make its use impractical during software development. However, there are many situations in which modifications are small and isolated within a few components, and it is desirable to reuse as much as possible previous analysis results. This has been achieved to date through incremental global analysis fixpoint algorithms that achieve cost reductions at fine levels of granularity, such as changes in program lines. However, these fine-grained techniques are not directly applicable to modular programs, nor are they designed to take advantage of modular structures. This paper describes, implements, and evaluates an algorithm that performs efficient context-sensitive analysis incrementally on modular partitions of programs. The experimental results show that the proposed modular algorithm shows significant improvements, in both time and memory consumption, when compared to existing non-modular, fine-grain incremental analysis techniques. Furthermore, thanks to the proposed inter-modular propagation of analysis information, our algorithm also outperforms traditional modular analysis even when analyzing from scratch.Comment: 56 pages, 27 figures. To be published in Theory and Practice of Logic Programming. v3 corresponds to the extended version of the ICLP2018 Technical Communication. v4 is the revised version submitted to Theory and Practice of Logic Programming. v5 (this one) is the final author version to be published in TPL

Static analysis of energy consumption for LLVM IR programs

Energy models can be constructed by characterizing the energy consumed by executing each instruction in a processor's instruction set. This can be used to determine how much energy is required to execute a sequence of assembly instructions, without the need to instrument or measure hardware. However, statically analyzing low-level program structures is hard, and the gap between the high-level program structure and the low-level energy models needs to be bridged. We have developed techniques for performing a static analysis on the intermediate compiler representations of a program. Specifically, we target LLVM IR, a representation used by modern compilers, including Clang. Using these techniques we can automatically infer an estimate of the energy consumed when running a function under different platforms, using different compilers. One of the challenges in doing so is that of determining an energy cost of executing LLVM IR program segments, for which we have developed two different approaches. When this information is used in conjunction with our analysis, we are able to infer energy formulae that characterize the energy consumption for a particular program. This approach can be applied to any languages targeting the LLVM toolchain, including C and XC or architectures such as ARM Cortex-M or XMOS xCORE, with a focus towards embedded platforms. Our techniques are validated on these platforms by comparing the static analysis results to the physical measurements taken from the hardware. Static energy consumption estimation enables energy-aware software development, without requiring hardware knowledge

Repairing and mechanising the JavaScript relaxed memory model

© 2020 ACM. Modern JavaScript includes the SharedArrayBuffer feature, which provides access to true shared memory concurrency. SharedArrayBuffers are simple linear buffers of bytes, and the JavaScript specification defines an axiomatic relaxed memory model to describe their behaviour. While this model is heavily based on the C/C++11 model, it diverges in some key areas. JavaScript chooses to give a well-defined semantics to data-races, unlike the "undefined behaviour" of C/C++11. Moreover, the JavaScript model is mixed-size. This means that its accesses are not to discrete locations, but to (possibly overlapping) ranges of bytes. We show that the model, in violation of the design intention, does not support a compilation scheme to ARMv8 which is used in practice. We propose a correction, which also incorporates a previously proposed fix for a failure of the model to provide Sequential Consistency of Data-Race-Free programs (SC-DRF), an important correctness condition. We use model checking, in Alloy, to generate small counter-examples for these deficiencies, and investigate our correction. To accomplish this, we also develop a mixed-size extension to the existing ARMv8 axiomatic model. Guided by our Alloy experimentation, we mechanise (in Coq) the JavaScript model (corrected and uncorrected), our ARMv8 model, and, for the corrected JavaScript model, a "model-internal" SC-DRF proof and a compilation scheme correctness proof to ARMv8. In addition, we investigate a non-mixed-size subset of the corrected JavaScript model, and give proofs of compilation correctness for this subset to x86-TSO, Power, RISC-V, ARMv7, and (again) ARMv8, via the Intermediate Memory Model (IMM). As a result of our work, the JavaScript standards body (ECMA TC39) will include fixes for both issues in an upcoming edition of the specification

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

A Relational Logic for Higher-Order Programs

Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for reasoning about a broad range of properties, including equivalence and refinement, and specialized notions such as continuity, information flow security or relative cost. In a higher-order setting, relational program verification can be achieved using relational refinement type systems, a form of refinement types where assertions have a relational interpretation. Relational refinement type systems excel at relating structurally equivalent terms but provide limited support for relating terms with very different structures. We present a logic, called Relational Higher Order Logic (RHOL), for proving relational properties of a simply typed $\lambda$-calculus with inductive types and recursive definitions. RHOL retains the type-directed flavour of relational refinement type systems but achieves greater expressivity through rules which simultaneously reason about the two terms as well as rules which only contemplate one of the two terms. We show that RHOL has strong foundations, by proving an equivalence with higher-order logic (HOL), and leverage this equivalence to derive key meta-theoretical properties: subject reduction, admissibility of a transitivity rule and set-theoretical soundness. Moreover, we define sound embeddings for several existing relational type systems such as relational refinement types and type systems for dependency analysis and relative cost, and we verify examples that were out of reach of prior work.Comment: Submitted to ICFP 201

PerSeVerE: persistency semantics for verification under ext4.

Although ubiquitous, modern filesystems have rather complex behaviours that are hardly understood by programmers and lead to severe software bugs such as data corruption. As a first step to ensure correctness of software performing file I/O, we formalize the semantics of the Linux ext4 filesystem, which we integrate with the weak memory consistency semantics of C/C++. We further develop an effective model checking approach for verifying programs that use the filesystem. In doing so, we discover and report bugs in commonly-used text editors such as vim, emacs and nano