Formally Verified Space-Safety for Program Transformations

Existing work on compilers has often primarily concerned itself with preserving behavior, but programs have other facets besides their observable behavior. We expect that the performance of our code is preserved and bettered by the compiler, not made worse. Unfortunately, that\u27s exactly what sometimes occurs in modern optimizing compilers. Poor representations or incorrect optimizations may preserve the correct behavior, but push that program into a different complexity class entirely. We\u27ve seen such blowups like this occurring in practice, and many transformations have pitfalls which can cause issues. Even when a program is not dramatically worsened, it can cause the program to use more resources than expected, causing issues in resource-constrained environments, and increasing garbage-collection pauses. While several researchers have noticed potential issues, there have been a relative dearth of proofs for space-safety, and none at all concerning non-local optimizations. This work expands upon existing notions of space-safety, allowing them to be used to reason about long-running programs with both input and output, while ensuring that the program maintains some temporal locality of space costs. In addition, this work includes new proof techniques which can handle more dramatic shifts in the program and heap structure than existing methods, as well as more frequent garbage collection. The results are formalized in Coq, including a proof of space-safety for lifting data up in scope, which increases sharing and saves duplicate work, but may also catastrophically increase space usage, if done incorrectly

Automatic Time-Bound Analysis for High-Level Languages

Thesis (PhD) - Indiana University, Computer Sciences, 2006Analysis of program running time is important for reactive systems, interactive environments, compiler optimizations, performance evaluation, and many other computer applications. Automatic and efficient prediction of accurate time bounds is particularly important, and being able to do so for high-level languages is particularly desirable. This dissertation presents a general approach for automatic and accurate time-bound analysis for high-level languages, combining methods and techniques studied in theory, languages, and systems. The approach consists of transformations for building time-bound functions in the presence of partially known input structures, symbolic evaluation of the time-bound function based on input parameters, optimizations to make the analysis efficient as well as accurate, and measurements of primitive parameters, all at the source-language level. We describe analysis and transformation algorithms and explain how they work. We have implemented this approach and performed a large number of experiments analyzing Scheme programs. The measured worst-case times are closely bounded by the calculated bounds. We describe our prototype system, ALPA, as well as the analysis and measurement results

The weak call-by-value λ-calculus is reasonable for both time and space

We study the weak call-by-value -calculus as a model for computational complexity theory and establish the natural measures for time and space Ð the number of beta-reduction steps and the size of the largest term in a computation Ð as reasonable measures with respect to the invariance thesis of Slot and van Emde Boas from 1984. More precisely, we show that, using those measures, Turing machines and the weak call-by-value -calculus can simulate each other within a polynomial overhead in time and a constant factor overhead in space for all computations terminating in (encodings of) łtruež or łfalsež. The simulation yields that standard complexity classes like , NP, PSPACE, or EXP can be defined solely in terms of the -calculus, but does not cover sublinear time or space. Note that our measures still have the well-known size explosion property, where the space measure of a computation can be exponentially bigger than its time measure. However, our result implies that this exponential gap disappears once complexity classes are considered instead of concrete computations. We consider this result a first step towards a solution for the long-standing open problem of whether the natural measures for time and space of the -calculus are reasonable. Our proof for the weak call-by-value -calculus is the first proof of reasonability (including both time and space) for a functional language based on natural measures and enables the formal verification of complexity-theoretic proofs concerning complexity classes, both on paper and in proof assistants. The proof idea relies on a hybrid of two simulation strategies of reductions in the weak call-by-value -calculus by Turing machines, both of which are insufficient if taken alone. The first strategy is the most naive one in the sense that a reduction sequence is simulated precisely as given by the reduction rules; in particular, all substitutions are executed immediately. This simulation runs within a constant overhead in space, but the overhead in time might be exponential. The second strategy is heap-based and relies on structure sharing, similar to existing compilers of eager functional languages. This strategy only has a polynomial overhead in time, but the space consumption might require an additional factor of log, which is essentially due to the size of the pointers required for this strategy. Our main contribution is the construction and verification of a space-aware interleaving of the two strategies, which is shown to yield both a constant overhead in space and a polynomial overhead in time

Shared-Environment Call-by-Need

Call-by-need semantics formalize the wisdom that work should be done at most once. It frees programmers to focus more on the correctness of their code, and less on the operational details. Because of this property, programmers of lazy functional languages rely heavily on their compiler to both preserve correctness and generate high-performance code for high level abstractions. In this dissertation I present a novel technique for compiling call-by-need semantics by using shared environments to share results of computation. I show how the approach enables a compiler that generates high-performance code, while staying simple enough to lend itself to formal reasoning. The dissertation is divided into three main contributions. First, I present an abstract machine, the \ce machine, which formalizes the approach. Second, I show that it can be implemented as a native code compiler with encouraging performance results. Finally, I present a verified compiler, implemented in the Coq proof assistant, demonstrating how the simplicity of the approach enables formal verification

Dynamic Compilation for Functional Programs

Diese Arbeit behandelt die dynamische, zur Laufzeit stattfindende Übersetzung und Optimierung funktionaler Programme. Ziel der Optimierung ist die erhöhte Laufzeiteffizient der Programme, die durch die compilergesteuerte Eliminierung von Abstraktionen der Programmiersprache erreicht wird. Bei der Implementierung objekt-orientierter Programmiersprachen werden bereits seit mehreren Jahrzehnten Compiler-Techniken zur Laufzeit eingesetzt, um objekt-orientierte Programme effizient ausführen zu können. Spätestens seit der Einführung der Programmiersprache Java und ihres auf einer abstrakten Maschine basierenden Ausführungsmodells hat sich die Praktikabilität dieser Implementierungstechnik gezeigt. Viele Eigenschaften moderner Programmiersprachen konnten erst durch den Einsatz dynamischer Transformationstechniken effizient realisiert werden, wie zum Beispiel das dynamische Nachladen von Programmteilen (auch über Netzwerke), Reflection sowie verschiedene Sicherheitslösungen (z.B. Sandboxing). Ziel dieser Arbeit ist zu zeigen, dass rein funktionale Programmiersprachen auf ähnliche Weise effizient implementiert werden können, und sogar Vorteile gegenüber den allgemein eingesetzten objekt-orientierten Sprachen bieten, was die Effizienz, Sicherheit und Korrektheit von Programmen angeht. Um dieses Ziel zu erreichen, werden in dieser Arbeit Implementierungstechniken entworfen bzw. aus bestehenden Lösungen weiterentwickelt, welche die dynamische Kompilierung und Optimierung funktionaler Programme erlauben: zum einen präsentieren wir eine Programmzwischendarstellung (getypte dynamische Continuation-Passing-Style-Darstellung), welche sich zur dynamischen Kompilierung und Optimierung eignet. Basierend auf dieser Darstellung haben wir eine Erweiterung zur verzögerten und selektiven Codeerzeugung von Programmteilen entwickelt. Der wichtigste Beitrag dieser Arbeit ist die dynamische Spezialisierung zur Eliminierung polymorpher Funktionen und Datenstrukturen, welche die Effizienz funktionaler Programme deutlich steigern kann. Die präsentierten Ergebnisse experimenteller Messungen eines prototypischen Ausführungssystems belegen, dass funktionale Programme effizient dynamisch kompiliert werden können.This thesis is about dynamic translation and optimization of functional programs. The goal of the optimization is increased run-time efficiency, which is obtained by compiler-directed elimination of programming language abstractions. Object-oriented programming languages have been implemented for several decades using run-time compilation techniques. With the introduction of the Java programming language and its virtual machine-based execution model, the practicability of this implementation method for real-world applications has been proved. Many aspects of modern programming languages, such as dynamic loading and linking of code (even across networks), reflection and security solutions (e.g., sandboxing) can be realized efficiently only by using dynamic transformation techniques. The goal of this work is to show that functional programming languages can be efficiently implemented in a similar way, and that these languages even offer advantages when compared to more common object-oriented languages. Efficiency, security and correctness of programs is easier to ensure in the functional setting. Towards this goal, we design and develop implementation techniques to enable dynamic compilation and optimization of functional programming languages: we describe an intermediate representation for functional programs (typed dynamic continuation-passing style), which is well suited for dynamic compilation. Based on this representation, we have developed an extension for incremental and selective code generation. The main contribution of this work shows how dynamic specialization of polymorphic functions and data structures can increase the run-time efficiency of functional programs considerably. We present the results of experimental measurements for a prototypical implementation, which prove that functional programs can efficiently be dynamically compiled

GNU epsilon - an extensible programming language

Reductionism is a viable strategy for designing and implementing practical programming languages, leading to solutions which are easier to extend, experiment with and formally analyze. We formally specify and implement an extensible programming language, based on a minimalistic first-order imperative core language plus strong abstraction mechanisms, reflection and self-modification features. The language can be extended to very high levels: by using Lisp-style macros and code-to-code transforms which automatically rewrite high-level expressions into core forms, we define closures and first-class continuations on top of the core. Non-self-modifying programs can be analyzed and formally reasoned upon, thanks to the language simple semantics. We formally develop a static analysis and prove a soundness property with respect to the dynamic semantics. We develop a parallel garbage collector suitable to multi-core machines to permit efficient execution of parallel programs.Comment: 172 pages, PhD thesi

Lazy Evaluation: From natural semantics to a machine-checked compiler transformation

In order to solve a long-standing problem with list fusion, a new compiler transformation, \u27Call Arity\u27 is developed and implemented in the Haskell compiler GHC. It is formally proven to not degrade program performance; the proof is machine-checked using the interactive theorem prover Isabelle. To that end, a formalization of Launchbury`s Natural Semantics for Lazy Evaluation is modelled in Isabelle, including a correctness and adequacy proof

Scheme 2003: proceedings of the fourth workshop on scheme and functional programming

technical reportThis report contains the papers presented at the Fourth Workshop on Scheme and Functional Programming. The purpose of the Scheme Workshop is to discuss experience with and future developments of the Scheme programming language?including the future of Scheme standardization?as well as general aspects of computer science loosely centered on the general theme of Scheme

Compiling functional reactive macroprograms for sensor networks

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 77-79).Sensor networks present a number of novel programming challenges for application developers. Their inherent limitations of computational power, communication bandwidth, and energy demand new approaches to programming that shield the developer from low-level details of resource management, concurrency, and in-network processing. To answer this challenge, this thesis presents a functional macroprogramming language called Regiment. The essential data model in Regiment is based on regions, which represent spatially distributed, time-varying collections of state. The programmer uses regions to define and manipulate dynamic sets of sensor nodes. A first compiler for Regiment has been constructed, which implements the essential core of the language on the TinyOS platform. This thesis presents the compiler as well as an intermediate language developed to serve as a Regiment compilation target.by Ryan Rhodes Newton.S.M