A debugging model for functional logic programs

This paper presents a box-oriented debugging model for the functional logic language ALF. Due to the sophisticated operational semantics of ALF which is based on innermost basic narrowing with simplification, the debugger must reflect the application of the different computation rules during program execution. Hence our debugging model includes not only one box type as in Byrd's debugging model for logic programs but several different kinds of boxes corresponding to the various computation rules of the functional logic language (narrowing, simplification etc.). Moreover, additional box types are introduced in order to allow skips over (sometimes) uninteresting program parts like proofs of the condition in a conditional equation. Since ALF is a genuine amalgamation of functional and logic languages, our debugging model subsumes operational aspects of both kinds of languages. As a consequence, it can be also used for pure logic languages, pure functional languages with eager evaluation, or functional logic languages with a less sophisticated operational semantics like SLOG or eager BABEL

Narrowing strategies for arbitrary canonical rewrite systems

Narrowing is a universal unification procedure for equational theories defined by a canonical term rewriting system. In its original form it is extremely inefficient. Therefore, many optimizations have been proposed during the last years. In this paper, we present the narrowing strategies for arbitrary canonical systems in a uniform framework and introduce the new narrowing strategy LSE narrowing. LSE narrowing is complete and improves all other strategies which are complete for arbitrary canonical systems. It is optimal in the sense that two different LSE narrowing derivations cannot generate the same narrowing substitution. Moreover, LSE narrowing computes only normalized narrowing substitutions

Lazy unification with inductive simplification

Unification in the presence of an equational theory is an important problem in theorem-proving and in the integration of functional and logic programming languages. This paper presents an improvement of the proposed lazy unification methods by incorporating simplification with inductive axioms into the unification process. Inductive simplification reduces the search space so that in some case infinite search spaces are reduced to finite ones. Consequently, more efficient unification algorithms can be achieved. We prove soundness and completeness of our method for equational theories represented by ground confluent and terminating rewrite systems

Narrowing strategies for arbitrary canonical rewrite systems

Narrowing is a universal unification procedure for equational theories defined by a canonical term rewriting system. In its original form it is extremely inefficient. Therefore, many optimizations have been proposed during the last years. In this paper, we present the narrowing strategies for arbitrary canonical systems in a uniform framework and introduce the new narrowing strategy LSE narrowing. LSE narrowing is complete and improves all other strategies which are complete for arbitrary canonical systems. It is optimal in the sense that two different LSE narrowing derivations cannot generate the same narrowing substitution. Moreover, LSE narrowing computes only normalized narrowing substitutions

Rule-Based Software Verification and Correction

The increasing complexity of software systems has led to the development of sophisticated formal Methodologies for verifying and correcting data and programs. In general, establishing whether a program behaves correctly w.r.t. the original programmer s intention or checking the consistency and the correctness of a large set of data are not trivial tasks as witnessed by many case studies which occur in the literature. In this dissertation, we face two challenging problems of verification and correction. Specifically, verification and correction of declarative programs, and the verification and correction of Web sites (i.e. large collections of semistructured data). Firstly, we propose a general correction scheme for automatically correcting declarative, rule-based programs which exploits a combination of bottom-up as well as topdown inductive learning techniques. Our hybrid hodology is able to infer program corrections that are hard, or even impossible, to obtain with a simpler,automatic top-down or bottom-up learner. Moreover, the scheme will be also particularized to some well-known declarative programming paradigm: that is, the functional logic and the functional programming paradigm. Secondly, we formalize a framework for the automated verification of Web sites which can be used to specify integrity conditions for a given Web site, and then automatically check whether these conditions are fulfilled. We provide a rule-based, formal specification language which allows us to define syntactic as well as semantic properties of the Web site. Then, we formalize a verification technique which detects both incorrect/forbidden patterns as well as lack of information, that is, incomplete/missing Web pages. Useful information is gathered during the verification process which can be used to repair the Web site. So, after a verification phase, one can also infer semi-automatically some possible corrections in order to fix theWeb site. The methodology is based on a novel rewritBallis, D. (2005). Rule-Based Software Verification and Correction [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/194

Algebraic specification : syntax, semantics, structure

Algebraic specification is the technique of using algebras to model properties of a system and using axioms to characterize such algebras. Algebraic specification comprises two aspects: the underlying logic used in the axioms and algebras, and the use of a small, general set of operators to build specifications in a structured manner. We describe these two aspects using the unifying notion of institutions. An institution is an abstraction of a logical system, describing the vocabulary, the kinds of axioms, the kinds of algebras, and the relation between them. Using institutions, one can define general structuring operators which are independent of the underlying logic. In this paper, we survey the different kind of logics, syntax, semantics, and structuring operators that have been used in algebraic specification

Nondeterminism in algebraic specifications and algebraic programs

"Nondeterminism in Algebraic Specifications and Algebraic Programs" presents a mathematical theory for the integration of three concepts: non-determinism, axiomatic specification and term rewriting. For non-deterministic programs, an algebraic specification language is provided which admits the application of automated tools based on term rewriting techniques. This general framework is used to explore connections between logic programming and algebraic programming. Examples from various areas of computer science are given, including results of computer experiments with a prototypical implementation. This book should be of interest to readers working within several fields of theoretical computer science, from algebraic specification theory to formal descriptions of distributed systems

Improving the Usability of Static Analysis Tools Using Machine Learning

Static analysis can be useful for developers to detect critical security flaws and bugs in software. However, due to challenges such as scalability and undecidability, static analysis tools often have performance and precision issues that reduce their usability and thus limit their wide adoption. In this dissertation, we present machine learning-based approaches to improve the adoption of static analysis tools by addressing two usability challenges: false positive error reports and proper tool configuration. First, false positives are one of the main reasons developers give for not using static analysis tools. To address this issue, we developed a novel machine learning approach for learning directly from program code to classify the analysis results as true or false positives. The approach has two steps: (1) data preparation that transforms source code into certain input formats for processing by sophisticated machine learning techniques; and (2) using the sophisticated machine learning techniques to discover code structures that cause false positive error reports and to learn false positive classification models. To evaluate the effectiveness and efficiency of this approach, we conducted a systematic, comparative empirical study of four families of machine learning algorithms, namely hand-engineered features, bag of words, recurrent neural networks, and graph neural networks, for classifying false positives. In this study, we considered two application scenarios using multiple ground-truth program sets. Overall, the results suggest that recurrent neural networks outperformed the other algorithms, although interesting tradeoffs are present among all techniques. Our observations also provide insight into the future research needed to speed the adoption of machine learning approaches in practice. Second, many static program verification tools come with configuration options that present tradeoffs between performance, precision, and soundness to allow users to customize the tools for their needs. However, understanding the impact of these options and correctly tuning the configurations is a challenging task, requiring domain expertise and extensive experimentation. To address this issue, we developed an automatic approach, auto-tune, to configure verification tools for given target programs. The key idea of auto-tune is to leverage a meta-heuristic search algorithm to probabilistically scan the configuration space using machine learning models both as a fitness function and as an incorrect result filter. auto-tune is tool- and language-agnostic, making it applicable to any off-the-shelf configurable verification tool. To evaluate the effectiveness and efficiency of auto-tune, we applied it to four popular program verification tools for C and Java and conducted experiments under two use-case scenarios. Overall, the results suggest that running verification tools using auto-tune produces results that are comparable to configurations manually-tuned by experts, and in some cases improve upon them with reasonable precision

Test-sets und Termersetzungen für die Generierung rekursiv definierter Algorithmen aus Existenzaussagen

In dieser Arbeit wurde ein Verfahren vorgestellt, mit dem man rekursiv definierte Algorithmen aus Gueltigkeitsbeweisen von Existenzformeln extrahieren kann.Das Verfahren beschränkt sich auf einen einfachen Formalismus und basiert auf Test-sets und einem Vereinfachungsmechanismus.Termersetzungen und logische Simplifikationen bilden den Kern dieses Vereinfachungsmechanismus, waehrend Test-sets eine Beschreibung des initialen Modells einer Axiommenge darstellen.In this thesis we presented a method for extracting recursive defined algorithms from existentially quantified formulas, being based on a simple formalism, test sets and a simplification strategy.Term rewriting and logical simplification represent the core of that simplification strategy and test sets the description of the initial model of a set of axioms