Hofmann and Jost have presented a heap space analysis [1] that finds linear space bounds for many functional programs. It uses an amortised analysis: assigning hypothetical amounts of free space (called potential) to data structures in proportion to their sizes using type annotations. Constraints on these annotations in the type system ensure that the total potential assigned to the input is an upper bound on the total memory required to satisfy all allocations.

We describe a related system for bounding the stack space requirements which uses the depth of data structures, by expressing potential in terms of maxima as well as sums. This is achieved by adding extra structure to typing contexts (inspired by O'Hearn's bunched typing [2]) to describe the form of the bounds. We will also present the extra steps that must be taken to construct a typing during the analysis.

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Amortised Memory Analysis Using the Depth of Data Structures

Traditionally, the full verification of a program's functional correctness has been obtained with pen and paper or with interactive proof assistants, whereas only reduced verification tasks, such as extended static checking, have enjoyed the automation offered by satisfiability-modulo-theories (SMT) solvers. More recently, powerful SMT solvers and well-designed program verifiers are starting to break that tradition, thus reducing the effort involved in doing full verification.

This paper gives a tour of the language and verifier Dafny, which has been used to verify the functional correctness of a number of challenging pointer-based programs. The paper describes the features incorporated in Dafny, illustrating their use by small examples and giving a taste of how they are coded for an SMT solver. As a larger case study, the paper shows the full functional specification of the Schorr-Waite algorithm in Dafny.

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Dafny: an automatic program verifier for functional correctness

VCC is an industrial-strength verification environment for low-level concurrent system code written in C. VCC takes a program (annotated with function contracts, state assertions, and type invariants) and attempts to prove the correctness of these annotations. It includes tools for monitoring proof attempts and constructing partial counterexample executions for failed proofs. This paper motivates VCC, describes our verification methodology, describes the architecture of VCC, and reports on our experience using VCC to verify the Microsoft Hyper-V hypervisor.

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VCC: A Practical System for Verifying Concurrent C

This article describes Apron , a freely available library dedicated to the static analysis of the numerical variables of programs by abstract interpretation. Its goal is threefold: provide analysis implementers with ready-to-use numerical abstractions under a unified API, encourage the research in numerical abstract domains by providing a platform for integration and comparison, and provide teaching and demonstration tools to disseminate knowledge on abstract interpretation.

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Apron: A Library of Numerical Abstract Domains for Static Analysis

JavaScript is the main scripting language for Web browsers, and it is essential to modern Web applications. Programmers have started using it for writing complex applications, but there is still little tool support available during development.

We present a static program analysis infrastructure that can infer detailed and sound type information for JavaScript programs using abstract interpretation. The analysis is designed to support the full language as defined in the ECMAScript standard, including its peculiar object model and all built-in functions. The analysis results can be used to detect common programming errors --- or rather, prove their absence, and for producing type information for program comprehension.

Preliminary experiments conducted on real-life JavaScript code indicate that the approach is promising regarding analysis precision on small and medium size programs, which constitute the majority of JavaScript applications. With potential for further improvement, we propose the analysis as a foundation for building tools that can aid JavaScript programmers.

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Type Analysis for JavaScript

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Robert Bruce Findler

Papers

Programming Languages and Systems