The specialization problem and the completeness of unfolding

We discuss the problem of specializing a definite program with respect to sets of positive and negative examples, following Bostrom and Idestam-Almquist. This problem is very relevant in the field of inductive learning. First we show that there exist sets of examples that have no correct program, i.e., no program which implies all positive and no negative examples. Hence it only makes sense to talk about specialization problems for which a solution (a correct program) exists. To solve such problems, we first introduce UD1-specialization, based upon the transformation rule unfolding. We show UD1-specialization is incomplete - some solvable specialization problems do not have a UD1-specialization as solution - and generalize it to the stronger UD2-specialization. UD2 also turns out to be incomplete. An analysis of program specialization, using the subsumption theorem for SLD-resolution, shows the reason for this incompleteness. Based on that analysis, we then define UDS-specialization (a generalization of UD2-specialization), and prove that any specialization problem has a UDS-specialization as a solution. We also discuss the relationship between this specialization technique, and the generalization technique based on inverse resolution. Finally, we go into several more implementational matters, which outline an interesting topic for future research

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