Transformations over assembly code are common in many compilers. These transformations are also some of the most bug-dense compiler components. Such bugs could be elim- inated by formally verifying the compiler, but state-of-the- art formally verified compilers like CompCert do not sup- port assembly-level program transformations. This paper presents Peek, a framework for expressing, verifying, and running meaning-preserving assembly-level program trans- formations in CompCert. Peek contributes four new com- ponents: a lower level semantics for CompCert x86 syntax, a liveness analysis, a library for expressing and verifying peephole optimizations, and a verified peephole optimiza- tion pass built into CompCert. Each of these is accompanied by a correctness proof in Coq against realistic assumptions about the calling convention and the system memory alloca- tor. Verifying peephole optimizations in Peek requires prov- ing only a set of local properties, which we have proved are sufficient to ensure global transformation correctness. We have proven these local properties for 28 peephole transfor- mations from the literature. We discuss the development of our new assembly semantics, liveness analysis, representa- tion of program transformations, and execution engine; de- scribe the verification challenges of each component; and detail techniques we applied to mitigate the proof burden.

Translation validation is a technique for checking that, after an optimization has run, the input and output of the optimization are equivalent. Traditionally, translation validation has been used to prove concrete, fully specified programs equivalent. In this paper we present Parameterized Equivalence Checking (PEC), a generalization of translation validation that can prove the equivalence of parameterized programs. A parameterized program is a partially specified program that can represent multiple concrete programs. For example, a parameterized program may contain a section of code whose only known property is that it does not modify certain variables. By proving parameterized programs equivalent, PEC can prove the correctness of transformation rules that represent complex optimizations once and for all, before they are ever run. We implemented our PEC technique in a tool that can establish the equivalence of two parameterized programs. To highlight the power of PEC, we designed a language for implementing complex optimizations using many-to-many rewrite rules, and used this language to implement a variety of optimizations including software pipelining, loop unrolling, loop unswitching, loop interchange, and loop fusion. Finally, to demonstrate the effectiveness of PEC, we used our PEC implementation to verify that all the optimizations we implemented in our language preserve program behavior.

Large software systems are typically composed of multiple layers, written in different languages and loosely coupled using a string-based interface. For example, in modern webapplications, a server written in Java communicates with a database back-end by passing in query strings. This widely prevalent approach is unsafe as the analyses developed for the individual layers are oblivious to the semantics of the dynamically constructed strings, making it impossible to statically reason about the correctness of the interaction. Further, even simple refactoring in such systems is daunting and error prone as the changes must also be applied to isolated string fragments scattered across the code base.We present techniques for deep typechecking and refactoring for systems that combine Java code with a database back-end using the Java Persistence API [10]. Deep typechecking ensures that the queries that are constructed dynamically are type safe and that the values returned from the queries are used safely by the program. Deep refactoring builds upon typechecking to allow programmers to safely and automatically propagate code refactorings through the query string fragments.Our algorithms are implemented in a tool called QUAIL. We present experiments evaluating the effectiveness of QUAIL on several benchmarks ranging from 3,369 to 82,907 lines of code. We show that QUAIL is able to verify that 84% of query strings in our benchmarks are type safe. Finally, we * Supported in part by the NSF grants CCF-0427202, CNS-0541606, and CCF-0546170.Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. show that QUAIL reduces the number of places in the code that a programmer must look at in order to perform a refactoring by several orders of magnitude.

Floating-point arithmetic plays a central role in science, engineering, and finance by enabling developers to approximate real arithmetic. To address numerical issues in large floating-point applications, developers must identify root causes, which is difficult because floating-point errors are generally non-local, non-compositional, and non-uniform. This paper presents Herbgrind, a tool to help developers identify and address root causes in numerical code written in low-level languages like C/C++ and Fortran. Herbgrind dynamically tracks dependencies between operations and program outputs to avoid false positives and abstracts erroneous computations to simplified program fragments whose improvement can reduce output error. We perform several case studies applying Herbgrind to large, expert-crafted numerical programs and show that it scales to applications spanning hundreds of thousands of lines, correctly handling the low-level details of modern floating point hardware and mathematical libraries and tracking error across function boundaries and through the heap.

Implementing systems in proof assistants like Coq and proving their correctness in full formal detail has consistently demonstrated promise for making extremely strong guarantees about critical software, ranging from compilers and operating systems to databases and web browsers. Unfortunately, these verifications demand such heroic manual proof effort, even for a single system, that the approach has not been widely adopted.We demonstrate a technique to eliminate the manual proof burden for verifying many properties within an entire class of applications, in our case reactive systems, while only expending effort comparable to the manual verification of a single system. A crucial insight of our approach is simultaneously designing both (1) a domain-specific language (DSL) for expressing reactive systems and their correctness properties and (2) proof automation which exploits the constrained language of both programs and properties to enable fully automatic, pushbutton verification. We apply this insight in a deeply embedded Coq DSL, dubbed REFLEX, and illustrate REFLEX's expressiveness by implementing and automatically verifying realistic systems including a modern web browser, an SSH server, and a web server. Using REFLEX radically reduced the proof burden: in previous, similar versions of our benchmarks written in Coq by experts, proofs accounted for over 80% of the code base; our versions require no manual proofs.