A Semantic Approach to Automatic Program Improvement

The programs that are easiest to write and understand are often not the most efficient. This thesis gives methods of converting programs of the former type to those of the latter type; this involves converting definitions of algorithms given as recursion equations using high level primitives into lower level flow chart programs. The main activities involved are recursion removal (c.f. Strong), loop elimination, and the overwriting of shared structures. We have concentrated on the semantics, rather than the syntax, of the programs we are transforming and we have used techniques developed in work done on proving the correctness of programs. The transformations are done in a hierarchical manner and can be regarded as compiling a program defined in a structured manner (Dijkstra) to produce an efficient low level program that simulates it. We describe the implementation of a system that allows the user to specify algorithms in a simple set language and converts them to flow chart programs in either a bitstring or list processing language. Both of these lower languages allow the sharing of structures. The principles are applicable to other domains and we describe how our system can be applied more generally

Recursive Program Optimization Through Inductive Synthesis Proof Transformation

The research described in this paper involved developing transformation techniques which increase the efficiency of the noriginal program, the source, by transforming its synthesis proof into one, the target, which yields a computationally more efficient algorithm. We describe a working proof transformation system which, by exploiting the duality between mathematical induction and recursion, employs the novel strategy of optimizing recursive programs by transforming inductive proofs. We compare and contrast this approach with the more traditional approaches to program transformation, and highlight the benefits of proof transformation with regards to search, correctness, automatability and generality

Transformation of logic programs: Foundations and techniques

AbstractWe present an overview of some techniques which have been proposed for the transformation of logic programs. We consider the so-called “rules + strategies” approach, and we address the following two issues: the correctness of some basic transformation rules w.r.t. a given semantics and the use of strategies for guiding the application of the rules and improving efficiency. We will also show through some examples the use and the power of the transformational approach, and we will briefly illustrate its relationship to other methodologies for program development

Rule-based Methodologies for the Specification and Analysis of Complex Computing Systems

Desde los orígenes del hardware y el software hasta la época actual, la complejidad de los sistemas de cálculo ha supuesto un problema al cual informáticos, ingenieros y programadores han tenido que enfrentarse. Como resultado de este esfuerzo han surgido y madurado importantes áreas de investigación. En esta disertación abordamos algunas de las líneas de investigación actuales relacionada con el análisis y la verificación de sistemas de computación complejos utilizando métodos formales y lenguajes de dominio específico. En esta tesis nos centramos en los sistemas distribuidos, con un especial interés por los sistemas Web y los sistemas biológicos. La primera parte de la tesis está dedicada a aspectos de seguridad y técnicas relacionadas, concretamente la certificación del software. En primer lugar estudiamos sistemas de control de acceso a recursos y proponemos un lenguaje para especificar políticas de control de acceso que están fuertemente asociadas a bases de conocimiento y que proporcionan una descripción sensible a la semántica de los recursos o elementos a los que se accede. También hemos desarrollado un marco novedoso de trabajo para la Code-Carrying Theory, una metodología para la certificación del software cuyo objetivo es asegurar el envío seguro de código en un entorno distribuido. Nuestro marco de trabajo está basado en un sistema de transformación de teorías de reescritura mediante operaciones de plegado/desplegado. La segunda parte de esta tesis se concentra en el análisis y la verificación de sistemas Web y sistemas biológicos. Proponemos un lenguaje para el filtrado de información que permite la recuperación de informaciones en grandes almacenes de datos. Dicho lenguaje utiliza información semántica obtenida a partir de ontologías remotas para re nar el proceso de filtrado. También estudiamos métodos de validación para comprobar la consistencia de contenidos web con respecto a propiedades sintácticas y semánticas. Otra de nuestras contribuciones es la propuesta de un lenguaje que permite definir y comprobar automáticamente restricciones semánticas y sintácticas en el contenido estático de un sistema Web. Finalmente, también consideramos los sistemas biológicos y nos centramos en un formalismo basado en lógica de reescritura para el modelado y el análisis de aspectos cuantitativos de los procesos biológicos. Para evaluar la efectividad de todas las metodologías propuestas, hemos prestado especial atención al desarrollo de prototipos que se han implementado utilizando lenguajes basados en reglas.Baggi ., M. (2010). Rule-based Methodologies for the Specification and Analysis of Complex Computing Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8964Palanci

Interactive program verification using virtual programs

This thesis is concerned with ways of proving the correctness of computer programs. The first part of the thesis presents a new method for doing this. The method, called continuation induction, is based on the ideas of symbolic execution, the description of a given program by a virtual program, and the demonstration that these two programs are equivalent whenever the given program terminates. The main advantage of continuation induction over other methods is that it enables programs using a wide variety of programming constructs such as recursion, iteration, non-determinism, procedures with side-effects and jumps out of blocks to be handled in a natural and uniform way. In the second part of the thesis a program verifier which uses both this method and Floyd's inductive assertion method is described. The significance of this verifier is that it is designed to be extensible, and to this end the user can declare new functions and predicates to be used in giving a natural description of the program's intention. Rules describing these new functions can then be used when verifying the program. To actually prove the verification conditions, the system employs automatic simplification, a relatively clever matcher, a simple natural deduction system and, most importantly, the user's advice. A large number of commands are provided for the user in guiding the system to a proof of the program's correctness. The system has been used to verify various programs including two sorting programs and a program to invert a permutation 'in place' the proofs of the sorting programs included a proof of the fact that the final array was a permutation of the original one. Finally, some observations and suggestions are made concerning the continued development of such interactive verification systems

Computational Logic: Structure sharing and proof of program properties

Centre for Intelligent Systems and their ApplicationsThis thesis describes the results of two studies in computational logic. The first concerns a very efficient method of implementing resolution theorem provers. The second concerns a non-resolution program which automatically proves many theorems about LISP functions, using structural induction. In Part 1, a method of representing clauses, called 'structure sharing'is presented. In this representation, terms are instantiated by binding their variables on a stack, or in a dictionary, and derived clauses are represented in terms of their parents. This allows the structure representing a clause to be used in different contexts without renaming its variables or copying it in any way. The amount of space required for a clause is (2 + n) 36-bit words, where n is the number of components in the unifying substitution made for the resolution or factor. This is independant of the number of literals in the clause and the depth of function nesting. Several ways of making the unification algorithm more efficient are presented. These include a method od preprocessing the input terms so that the unifying substitution for derived terms can be discovered by a recursive look-up proceedure. Techniques for naturally mixing computation and deduction are presented. The structure sharing implementation of SL-resolution is described in detail. The relationship between structure sharing and programming language implementations is discussed. Part 1 concludes with the presentation of a programming language, based on predicate calculus, with structure sharing as the natural implementation. Part 2 of this thesis describes a program which automatically proves a wide variety of theorems about functions written in a subset of pre LISP. Features of this program include: The program is fully automatic, requiring no information from the user except the LISP definitions of the functions involved and the statement of the theorem to be proved. No inductive assertions are required for the user. The program uses structural induction when required, automatically generating its own induction formulas. All relationships in the theorem are expressed in terms of user defined LISP functions, rather than a secong logical language. The system employs no built-in information about any non-primitive function. All properties required of any function involved in a proof are derived and established automatically. The progeam is capable of generalizing some theorems in order to prove them; in doing so, it often generates interesting lemmas. The program can write new, recursive LISP functions automatically in attempting to generalize a theorem. Finally, the program is very fast by theorem proving standards, requiring around 10 seconds per proof