Program Improvement by Automatic Redistribution of Intermediate Results

This paper was originally a Ph.D. thesis proposal.The problem of automatically improving the performance of computer programs has many facets. A common source of program inefficiency is the use of abstraction techniques in program design: general tools used in a specific context often do unnecessary or redundant work. Examples include needless copy operations, redundant subexpressions, multiple traversals of the same datastructure and maintenance of overly complex data invariants. I propose to focus on one broadly applicable way of improving a program's performance: redistributing intermediate results so that computation can be avoided. I hope to demonstrate that this is a basic principle of optimization from which many of the current approaches to optimization may be derived. I propose to implement a system that automatically finds and exploits opportunities for redistribution in a given program. In addition to the program source, the system will accept an explanation of correctness and purpose of the code. Beyond the specific task of program improvement, I anticipate that the research will contribute to our understanding of the design and explanatory structure of programs. Major results will include (1) definition and manipulation of representation of correctness and purpose of a program's implementation, and (2) definition, construction, and use of a representation of a program's dynamic behavior.MIT Artificial Intelligence Laborator

Program transformations using temporal logic side conditions

This paper describes an approach to program optimisation based on transformations, where temporal logic is used to specify side conditions, and strategies are created which expand the repertoire of transformations and provide a suitable level of abstraction. We demonstrate the power of this approach by developing a set of optimisations using our transformation language and showing how the transformations can be converted into a form which makes it easier to apply them, while maintaining trust in the resulting optimising steps. The approach is illustrated through a transformational case study where we apply several optimisations to a small program

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

Verification of the Schorr-Waite Algorithm - From Trees to Graphs

16 pagesInternational audienceThis article proposes a method for proving the correctness of graph algorithms by manipulating their spanning trees enriched with additional references. We illustrate this concept with a proof of the correctness of a (pseudo-)imperative version of the Schorr-Waite algorithm by re finement of a functional one working on trees. It is composed of two orthogonal steps of re finement -- functional to imperative and tree to graph -- fi nally merged to obtain the result. Our imperative speci fications use monadic constructs and syntax sugar, making them close to common imperative languages. This work has been realized within the Isabelle/HOL proof assistant

PROSET — A Language for Prototyping with Sets

We discuss the prototyping language PROSET(Prototyping with Sets) as a language for experimental and evolutionary prototyping, focusing its attention on algorithm design. Some of PROSET’s features include generative communication, flexible exception handling and the integration of persistence. A discussion of some issues pertaining to the compiler and the programming environment conclude the pape

A computer algebra user interface manifesto

Many computer algebra systems have more than 1000 built-in functions, making expertise difficult. Using mock dialog boxes, this article describes a proposed interactive general-purpose wizard for organizing optional transformations and allowing easy fine grain control over the form of the result even by amateurs. This wizard integrates ideas including: * flexible subexpression selection; * complete control over the ordering of variables and commutative operands, with well-chosen defaults; * interleaving the choice of successively less main variables with applicable function choices to provide detailed control without incurring a combinatorial number of applicable alternatives at any one level; * quick applicability tests to reduce the listing of inapplicable transformations; * using an organizing principle to order the alternatives in a helpful manner; * labeling quickly-computed alternatives in dialog boxes with a preview of their results, * using ellipsis elisions if necessary or helpful; * allowing the user to retreat from a sequence of choices to explore other branches of the tree of alternatives or to return quickly to branches already visited; * allowing the user to accumulate more than one of the alternative forms; * integrating direct manipulation into the wizard; and * supporting not only the usual input-result pair mode, but also the useful alternative derivational and in situ replacement modes in a unified window.Comment: 38 pages, 12 figures, to be published in Communications in Computer Algebr

Combining type checking with model checking for system verification

Type checking is widely used in mainstream programming languages to detect programming errors at compile time. Model checking is gaining popularity as an automated technique for systematically analyzing behaviors of systems. My research focuses on combining these two software verification techniques synergically into one platform for the creation of correct models for software designs. This thesis describes two modeling languages ATS/PML and ATS/Veri that inherit the advanced type system from an existing programming language ATS, in which both dependent types of Dependent ML style and linear types are supported. A detailed discussion is given for the usage of advanced types to detect modeling errors at the stage of model construction. Going further, various modeling primitives with well-designed types are introduced into my modeling languages to facilitate a synergic combination of type checking with model checking. The semantics of ATS/PML is designed to be directly rooted in a well-known modeling language PROMELA. Rules for translation from ATS/PML to PROMELA are designed and a compiler is developed accordingly so that the SPIN model checker can be readily employed to perform checking on models constructed in ATS/PML. ATS/Veri is designed to be a modeling language, which allows a programmer to construct models for real-world multi-threaded software applications in the same way as writing a functional program with support for synchronization, communication, and scheduling among threads. Semantics of ATS/Veri is formally defined for the development of corresponding model checkers and a compiler is built to translate ATS/Veri into CSP# and exploit the state-of-the-art verification platform PAT for model checking ATS/Veri models. The correctness of such a transformational approach is illustrated based on the semantics of ATS/Veri and CSP#. In summary, the primary contribution of this thesis lies in the creation of a family of modeling languages with highly expressive types for modeling concurrent software systems as well as the related platform supporting verification via model checking. As such, we can combine type checking and model checking synergically to ensure software correctness with high confidence

Derivation of data intensive algorithms by formal transformation: the Schorr-Waite graph marking algorithm

Dated September 19, 1996In this paper we consider a particular class of algorithms which present certain difficulties to formal verification. These are algorithms which use a single data structure for two or more purposes, which combine program control information with other data structures or which are developed as a combination of a basic idea with an implementation technique. Our approach is based on applying proven semantics-preserving transformation rules in a wide spectrum language. Starting with a set theoretical specification of “reachability” we are able to derive iterative and recursive graph marking algorithms using the “pointer switching” idea of Schorr and Waite. There have been several proofs of correctness of the Schorr-Waite algorithm, and a small number of transformational developments of the algorithm. The great advantage of our approach is that we can derive the algorithm from its specification using only general-purpose transformational rules: without the need for complicated induction arguments. Our approach applies equally well to several more complex algorithms which make use of the pointer switching strategy, including a hybrid algorithm which uses a fixed length stack, switching to the pointer switching strategy when the stack runs out

A Transactional Model and Platform for Designing and Implementing Reactive Systems

A reactive program is one that has ongoing interactions with its environment. Reactive programs include those for embedded systems, operating systems, network clients and servers, databases, and smart phone apps. Reactive programs are already a core part of our computational and physical infrastructure and will continue to proliferate within our society as new form factors, e.g. wireless sensors, and inexpensive (wireless) networking are applied to new problems. Asynchronous concurrency is a fundamental characteristic of reactive systems that makes them difficult to develop. Threads are commonly used for implementing reactive systems, but they may magnify problems associated with asynchronous concurrency, as there is a gap between the semantics of thread-based computation and the semantics of reactive systems: reactive software developed with threads often has subtle timing bugs and tends to be brittle and non-reusable as a holistic understanding of the software becomes necessary to avoid concurrency hazards such as data races, deadlock, and livelock. Based on these problems with the state of the art, we believe a new model for developing and implementing reactive systems is necessary. This dissertation makes four contributions to the state of the art in reactive systems. First, we propose a formal yet practical model for (asynchronous) reactive systems called reactive components. A reactive component is a set of state variables and atomic transitions that can be composed with other reactive components to yield another reactive component. The transitions in a system of reactive components are executed by a scheduler. The reactive component model is based on concepts from temporal logic and models like UNITY and I/O Automata. The major contribution of the reactive component model is a formal method for principled composition, which ensures that 1) the result of composition is always another reactive component, for consistency of reasoning; 2) systems may be decomposed to an arbitrary degree and depth, to foster divide-and-conquer approaches when designing and re-use when implementing; 3)~the behavior of a reactive component can be stated in terms of its interface, which is necessary for abstraction; and 4) properties of reactive components that are derived from transitions protected by encapsulation are preserved through composition and can never be violated, which permits assume-guarantee reasoning. Second, we develop a prototypical programming language for reactive components called rcgo that is based on the syntax and semantics of the Go programming language. The semantics of the rcgo language enforce various aspects of the reactive component model, e.g., the isolation of state between components and safety of concurrency properties, while permitting a number of useful programming techniques, e.g., reference and move semantics for efficient communication among reactive components. For tractability, we assume that each system contains a fixed set of components in a fixed configuration. Third, we provide an interpreter for the rcgo language to test the practicality of the assumptions upon which the reactive component model are founded. The interpreter contains an algorithm that checks for composition hazards like recursively defined transitions and non-deterministic transitions. Transitions are executed using a novel calling convention that can be implemented efficiently on existing architectures. The run-time system also contains two schedulers that use the results of composition analysis to execute non-interfering transitions concurrently. Fourth, we compare the performance of each scheduler in the interpreter to the performance of a custom compiled multi-threaded program, for two reactive systems. For one system, the combination of the implementation and hardware biases it toward an event-based solution, which was confirmed when the reactive component implementation outperformed the custom implementation due to reduced context switching. For the other system, the custom implementation is not prone to excessive context switches and outperformed the reactive component implementations. These results demonstrate that reactive components may be a viable alternative to threads in practice, but that additional work is necessary to generalize this claim