Data representation synthesis

We consider the problem of specifying combinations of data structures with complex sharing in a manner that is both declarative and results in provably correct code. In our approach, abstract data types are specified using relational algebra and functional dependencies. We describe a language of decompositions that permit the user to specify different concrete representations for relations, and show that operations on concrete representations soundly implement their relational specification. It is easy to incorporate data representations synthesized by our compiler into existing systems, leading to code that is simpler, correct by construction, and comparable in performance to the code it replaces

Concurrent data representation synthesis

We describe an approach for synthesizing data representations for concurrent programs. Our compiler takes as input a program written using concurrent relations and synthesizes a representation of the relations as sets of cooperating data structures as well as the placement and acquisition of locks to synchronize concurrent access to those data structures. The resulting code is correct by construction: individual relational operations are implemented correctly and the aggregate set of operations is serializable and deadlock free. The relational specification also permits a high-level optimizer to choose the best performing of many possible legal data representations and locking strategies, which we demonstrate with an experiment autotuning a graph benchmark

Rapid software prototyping

Rapid Prototyping is an approach to software development which emphasizes quick implementation of a working program. This dissertation makes two principal contributions. First, it provides concepts, techniques, and a philosophy of Rapid Software Prototyping and characterizes the benefits and limitations of its use. Second, it makes a contribution to programming environments which support Rapid Prototyping. An experimental language, Castor, is described which was implemented to validate this approach in the prototyping of Ada programs*. The following summarize the main results of this research:..

Software maintenance by program transformation in a wide spectrum language

This thesis addresses the software maintenance problem of extracting high-level designs from code. The investigated solution is to use a mathematically-based formal program transformation system. The resulting tool, the Maintainer's Assistant, is based on Ward's [177] WSL (wide spectrum language) and method of proving program equivalence. The problems addressed include: how to reverse engineer from code alone (the only reliable source of information about a program [158]), how to express program transformations within the system, what kinds of transformations should be incorporated, how to make the tool simple to use, how to perform abstraction and how to create a tool suitable for use with large programs. Using the Maintainer's Assistant, the program code is automatically translated into WSL and the transformations, although tested for valid applicability by the system, are interactively applied by the user. Notable features include a mathematical simplifier, a large flexible transformation catalogue and, significantly, the use of an extension of WSL, A4etaWSL, for representing the transformations. MetaWSL expands WSL by incorporating a variety of extensions, including: program editing statements, pattern matching and template filling functions, symbolic mathematics and logic functions, statements for moving within the program’s syntax tree and statements for repeating an operation at each node of the tree. Using MetaWSL, 80% of the 601 transformations can be expressed in less than 20 program statements. The Maintainer's Assistant has been used on a wide variety of examples of up to several thousand lines, including commercial software written in IBM 370 assembler. It has been possible to transform initially unstructured programs into a hierarchy of procedures, facilitating subsequent design recovery. These results show that program transformation is a viable method of renovating old (370 assembler) code in a cost elective way, and that MetaWSL provides an effective basis for clearly and concisely expressing the required transformations

On Sets with Cardinality Constraints in Satisfiability Modulo Theories

Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that can express constraints on sets of elements and their cardinalities. Problems from verification of complex properties of software often contain fragments that belong to quantifier-free BAPA (QFBAPA). Deciding the satisfiability of QFBAPA formulas has been shown to be NP-complete using an eager reduction to quantifier-free Presburger arithmetic that exploits a sparse-solution property. In contrast to many other NP-complete problems (such as quantifier-free first-order logic or linear arithmetic), the applications of QFBAPA to a broader set of problems has so far been hindered by the lack of an efficient implementation that can be used alongside other efficient decision procedures. We overcome these limitations by extending the efficient SMT solver Z3 with the ability to reason about cardinality constraints. Our implementation uses the DPLL(T) mechanism of Z3 to reason about the top-level propositional structure of a QFBAPA formula, improving the efficiency compared to previous implementations. Moreover, we present a new algorithm for automated decomposition of QFBAPA formulas. Our algorithm alleviates the exponential explosion of considering all Venn regions, significantly improving the tractability of formulas with many set variables. Because it is implemented as a theory plugin, our implementation enables Z3 to prove formulas that use QFBAPA constructs alongside constructs from other theories that Z3 supports (e.g. linear arithmetic, uninterpreted function symbols, algebraic data types), as well as in formulas with quantifiers. We have applied our implementation to verification of functional programs; we show it can automatically prove formulas that no automated approach was reported to be able to prove before

Evolving Parallel Programs

This report describes research conducted at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for this research was provided in part by the Office of Naval Research of the Department of Defense under Contract N00014-75-C-0522.Message passing is directed toward the production of programs that are intended to execute efficiently in a computing environment with a large number of processors. The paradigm attempts to address the computational issues of state change and communication directly with appropriate primitives. Efficient programs are evolved for fast factorial and path existence determination in a directed graph. This paper is a contribution to the continuing debate on programming methodology. It advocates that simple initial implementations of programs should be constructed and then the implementations should be evolved to meet their partial specifications where it is anticipated that the partial specifications will themselves evolve with time. The programming methodology used in this paper is intended for use with an actor machine which consists of a large number of processors connected by a high bandwidth network. We evolve implementations for factorial and for the path existence problem that execute in the logarithm of the amount of time required on a conventional machine. The implementation (with no redundant exploration) of the path existence problem evolved in this paper is more efficient than any implementation that can be programmed in a dialect of pure LISP that allows the arguments to a function to be evaluated in parallel. This is evidence that applicative programming in languages like pure LISP is apparently less efficient in some practical applications. The efficiency of such applicative languages is important because many computer scientists are proposing to use them on future generation parallel machines whose architectures exploit ultra large scale integration.MIT Artificial Intelligence Laboratory Department of Defense Advanced Research Projects Agenc

The distributed computer system

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University

Programming with Specifications

This thesis explores the use of specifications for the construction of correct programs. We go beyond their standard use as run-time assertions, and present algorithms, techniques and implementations for the tasks of 1) program verification, 2) declarative programming and 3) software synthesis. These results are made possible by our advances in the domains of decision procedure design and implementation. In the first part of this thesis, we present a decidability result for a class of logics that support user-defined recursive function definitions. Constraints in this class can encode expressive properties of recursive data structures, such as sortedness of a list, or balancing of a search tree. As a result, complex verification conditions can be stated concisely and solved entirely automatically. We also present a new decision procedure for a logic to reason about sets and constraints over their cardinalities. The key insight lies in a technique to decompose con- straints according to mutual dependencies. Compared to previous techniques, our algorithm brings significant improvements in running times, and for the first time integrates reasoning about cardinalities within the popular DPLL(T ) setting. We integrated our algorithmic ad- vances into Leon, a static analyzer for functional programs. Leon can reason about constraints involving arbitrary recursive function definitions, and has the desirable theoretical property that it will always find counter-examples to assertions that do not hold. We illustrate the flexibility and efficiency of Leon through experimental evaluation, where we used it to prove detailed correctness properties of data structure implementations. We then illustrate how program specifications can be used as a high-level programming construct ; we present Kaplan, an extension of Scala with first-class logical constraints. Kaplan allows programmers to create, manipulate and combine constraints as they would any other data structure. Our implementation of Kaplan illustrates how declarative programming can be incorporated into an existing mainstream programming language. Moreover, we examine techniques to transform, at compile-time, program specifications into efficient executable code. This approach of software synthesis combines the correctness benefits of declarative programming with the efficiency of imperative or functional programming