Plan generation using a method of deductive program synthesis

In this paper we introduce a planning approach based on a method of deductive program synthesis. The program synthesis system we rely upon takes first-order specifications and from these derives recursive programs automatically. It uses a set of transformation rules whose applications are guided by an overall strategy. Additionally several heuristics are involved which considerably reduce the search space. We show by means of an example taken from the blocks world how even recursive plans can be obtained with this method. Some modifications of the synthesis strategy and heuristics are discussed, which are necessary to obtain a powerful and automatic planning system. Finally it is shown how subplans can be introduced and generated separately

Derived Preconditions and Their Use in Program Synthesis

In this paper we pose and begin to explore a deductive problem more general than that of finding a proof that a given goal formula logically follows from a given set of hypotheses. The problem is most simply stated in the propositional calculus: given a goal A and hypothesis H we wish to find a formula P, called a precondition, such that A logically follows from P A H. A precondition pro- vides any additional conditions under which A can be shown to follow from H. A slightly more complex definition of preconditions in a first-order theory is given and used throughout the paper. A formal system based on natural deduction is presented in which preconditions can be derived. A number of examples are then given which show how derived preconditions are used in a program synthesis method we are developing. These uses include theorem proving, formula simplification, simple code generation, the completion of partial specifications for a subalgorithm, and other tasks of a deductive nature.Foundation Research Program of the Naval Postgraduate SchoolChief of Naval ResearchApproved for public release; distribution is unlimited

Logic Program Synthesis via Proof Planning

We propose a novel approach to automating the synthesis of logic programs: Logic programs are synthesized as a by-product of the planning of a verification proof. The approach is a two-level one: At the object level, we prove program verification conjectures in a sorted, first-order theory. The conjectures are of the form $\forall \vec{args}. \; prog(\vec{args}) \leftrightarrow spec(\vec{args})$. At the meta-level, we plan the object-level verification with an unspecified program definition. The definition is represented with a (second-order) meta-level variable, which becomes instantiated in the course of the planning. This technique is an application of the Clam proof planning system. Clam is currently powerful enough to plan verification proofs for given programs. We show that, if Clam's use of middle-out reasoning is extended, it will also be able to synthesize programs

Research Perspectives for Logic and Deduction

The article is meant to be kind of the author's manifesto for the role of logic and deduction within Intellectics. Based on a brief analysis of this role the paper presents a number of proposals for future scientic research along the various di-mensions in the space of logical explorations. These dimensions include the range of possible applications including modelling intelligent behavior, the grounding of logic in some semantic context, the choice of an appropriate logic from the great variety of alternatives, then the choice of an appropriate formal system for repre-senting the chosen logic, and nally the issue of developing the most ecient search strategies. Among the proposals is a conjecture concerning the treatment of cuts in proof search. Often a key advance is a matter of applying a small change to a single formula. Ray Kurzweil [Kur05, p.5]

Genetic Improvement of Software: a Comprehensive Survey

Genetic improvement (GI) uses automated search to find improved versions of existing software. We present a comprehensive survey of this nascent field of research with a focus on the core papers in the area published between 1995 and 2015. We identified core publications including empirical studies, 96% of which use evolutionary algorithms (genetic programming in particular). Although we can trace the foundations of GI back to the origins of computer science itself, our analysis reveals a significant upsurge in activity since 2012. GI has resulted in dramatic performance improvements for a diverse set of properties such as execution time, energy and memory consumption, as well as results for fixing and extending existing system functionality. Moreover, we present examples of research work that lies on the boundary between GI and other areas, such as program transformation, approximate computing, and software repair, with the intention of encouraging further exchange of ideas between researchers in these fields

Genetic Improvement of Software: a Comprehensive Survey

Genetic improvement uses automated search to find improved versions of existing software. We present a comprehensive survey of this nascent field of research with a focus on the core papers in the area published between 1995 and 2015. We identified core publications including empirical studies, 96% of which use evolutionary algorithms (genetic programming in particular). Although we can trace the foundations of genetic improvement back to the origins of computer science itself, our analysis reveals a significant upsurge in activity since 2012. Genetic improvement has resulted in dramatic performance improvements for a diverse set of properties such as execution time, energy and memory consumption, as well as results for fixing and extending existing system functionality. Moreover, we present examples of research work that lies on the boundary between genetic improvement and other areas, such as program transformation, approximate computing, and software repair, with the intention of encouraging further exchange of ideas between researchers in these fields

Derivación deductiva de programas funcionales con patrones

Una de las dificultades principales en el desarrollo de software es la ausencia de un marco conceptual adecuado para su estudio. Una propuesta la constituye el modelo transformativo, que entiende el desarrollo de software como un proceso iterativo de transformación de especificaciones: se parte de una especificación inicial que va transformándose sucesivamente hasta obtener una especificación final que se toma como programa. Este modelo básico puede llevarse a la práctica de varias maneras. En concreto, la aproximación deductiva toma una sentencia lógica como especificación inicial y su proceso transformador consiste en la demostración de la sentencia; como producto secundario de la demostración se deriva un programa que satisface la especificación inicial. La tesis desarrolla un método deductivo para la derivación de programas funcionales con patrones, escritos en un lenguaje similar a Hope. El método utiliza una lógica multigénero, cuya relación con el lenguaje de programación es estudiada. También se identifican los esquemas de demostración necesarios para la derivación de funciones con patrones, basados en la demostración independiente de varias subsentencias. Cada subsentencia proporciona una subespecificación de una ecuación del futuro programa a derivar. Nuestro método deductivo está inspirado en uno previo de Zohar Manna y Richard Waldinger, conocido como el cuadro deductivo, que deriva programas en un lenguaje similar a Lisp. El nuevo método es una modificación del cuadro de estos autores, que incorpora géneros y permite demostrar una especificación mediante varios cuadros. Cada cuadro demuestra una subespecificación y por tanto deriva una ecuación del programa. Se prevén mecanismos para que los programas derivados puedan contener definiciones locales con patrones y variables anónimas y sinónimas y para que las funciones auxiliares derivadas no usen variables de las funciones principales. La tesis se completa con varios ejemplos de aplicación, un mecanismo que independentiza el método del lenguaje de programación y un prototipo de entorno interactivo de derivación deductiva. Categorías y descriptores de materia CR D.l.l [Técnicas de programación]: Programación funcional; D.2.10 [Ingeniería de software]: Diseño - métodos; F.3.1 [Lógica y significado de los programas]: Especificación, verificación y razonamiento sobre programas - lógica de programas; F.3.3 [Lógica y significado de los programas]: Estudios de construcciones de programas - construcciones funcionales; esquemas de programa y de recursion; 1.2.2 [Inteligencia artificial]: Programación automática - síntesis de programas; 1.2.3 [Inteligencia artificial]: Deducción y demostración de teoremas]: extracción de respuesta/razón; inducción matemática. Términos generales Programación funcional, síntesis de programas, demostración de teoremas. Otras palabras claves y expresiones Funciones con patrones, cuadro deductivo, especificación parcial, inducción estructural, teorema de descomposición.---ABSTRACT---One of the main difficulties in software development is the lack of an adequate conceptual framework of study. The transformational model is one such proposal that conceives software development as an iterative process of specifications transformation: an initial specification is developed and successively transformed until a final specification is obtained and taken as a program. This basic model can be implemented in several ways. The deductive approach takes a logical sentence as the initial specification and its proof constitutes the transformational process; as a byproduct of the proof, a program which satisfies the initial specification is derived. In the thesis, a deductive method for the derivation of Hope-like functional programs with patterns is developed. The method uses a many-sorted logic, whose relation to the programming language is studied. Also the proof schemes necessary for the derivation of functional programs with patterns, based on the independent proof of several subsentences, are identified. Each subsentence provides a subspecification of one equation of the future program to be derived. Our deductive method is inspired on a previous one by Zohar Manna and Richard Waldinger, known as the deductive tableau, which derives Lisp-like programs. The new method incorporates sorts in the tableau and allows to prove a sentence with several tableaux. Each tableau proves a subspecification and therefore derives an equation of the program. Mechanisms are included to allow the derived programs to contain local definitions with patterns and anonymous and synonymous variables; also, the derived auxiliary functions cannot reference parameters of their main functions. The thesis is completed with several application examples, i mechanism to make the method independent from the programming language and an interactive environment prototype for deductive derivation. CR categories and subject descriptors D.l.l [Programming techniques]: Functional programming; D.2.10 [Software engineering]: Design - methodologies; F.3.1 [Logics and meanings of programa]: Specifying and verifying and reasoning about programs - logics of programs; F.3.3 [Logics and meanings of programs]: Studies of program constructs - functional constructs; program and recursion schemes; 1.2.2 [Artificial intelligence]: Automatic programming - program synthesis; 1.2.3 [Artificial intelligence]: Deduction and theorem proving - answer/reason extraction; mathematical induction. General tenas Functional programming, program synthesis, theorem proving. Additional key words and phrases Functions with patterns, deductive tableau, structural induction, partial specification, descomposition theorem