María Alpuente

Partial evaluation of functional logic programs

Languages that integrate functional and logic programming with a complete operational semantics are based on narrowing, a unification-based goal-solving mechanism which subsumes the reduction principle of functional languages and the resolution principle of logic languages. In this article, we present a partial evaluation scheme for functional logic languages based on an automatic unfolding algorithm which builds narrowing trees. The method is formalized within the theoretical framework established by Lloyd and Shepherdson for the partial deduction of logic programs, which we have generalized for dealing with functional computations. A generic specialization algorithm is proposed which does not depend on the eager or lazy nature of the narrower being used. To the best of our knowledge, this is the first generic algorithm for the specialization of functional logic programs. We also discuss the relation to work on partial evaluation in functional programming, term-rewriting systems, and logic programming. Finally, we present some experimental results with an implementation of the algorithm which show in practice that the narrowing-driven partial evaluator effectively combines the propagation of partial data structures (by means of logical variables and unification) with better opportunities for optimization (thanks to the functional dimension).

Specialization of lazy functional logic programs

Partial evaluation is a method for program specialization based on fold/unfold transformations [8, 25]. Partial evaluation of pure functional programs uses mainly static values of given data to specialize the program [15, 44]. In logic programming, the so-called static/dynamic distinction is hardly present, whereas considerations of determinacy and choice points are far more important for control [12]. We discuss these issues in the context of a (lazy) functional logic language. We formalize a two-phase specialization method for a non-strict, first order, integrated language which makes use of lazy narrowing to specialize the program w.r. t. a goal. The basic algorithm (first phase) is formalized as an instance of the framework for the partial evaluation of functional logic programs of [2, 3], using lazy narrowing. However, the results inherited by [2, 3] mainly regard the termination of the PE method, while the (strong) soundness and completeness results must be restated for the lazy strategy. A post-processing renaming scheme (second phase) is necessary which we describe and illustrate on the well-known matching example. This phase is essential also for other non-lazy narrowing strategies, like innermost narrowing, and our method can be easily extended to these strategies. We show that our method preserves the lazy narrowing semantics and that the inclusion of simplification steps in narrowing derivations can improve control during specialization.

Abstract Diagnosis of Functional Programs

We present a generic scheme for the declarative debugging of functional programs modeled as term rewriting systems. We associate to our programs a semantics based on a (continuous) immediate consequence operator, \( T_\mathcal{R} \), which models the (values/normal forms) semantics of \( \mathcal{R} \) . Then, we develop an effective debugging methodology which is based on abstract interpretation: by approximating the intended specification of the semantics of \( \mathcal{R} \) we derive a finitely terminating bottom-up diagnosis method, which can be used statically. Our debugging framework does not require the user to either provide error symptoms in advance or answer questions concerning program correctness. We have made available a prototypical implementation in Haskell and have tested it on some non trivial examples.

Narrowing-Driven Partial Evaluation of Functional Logic Programs

Languages that integrate functional and logic programming with a complete operational semantics are based on narrowing, a unification-based goal-solving mechanism which subsumes the reduction principle of functional languages and the resolution principle of logic languages. Formal methods of transformation of functional logic programs can be based on this well-established operational semantics. In this paper, we present a partial evaluation scheme for functional logic languages based on an automatic unfolding algorithm which builds narrowing trees. We study the semantic properties of the transformation and the conditions under which the technique terminates, is sound and complete, and is also generally applicable to a wide class of programs. We illustrate our method with several examples and discuss the relation with Supercompilation and Partial Evaluation. To the best of our knowledge, this is the first formal approach to partial evaluation of functional logic programs.

A Rewriting-based Framework for Web Sites Verification

In this paper, we develop 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. First, we provide a rewriting-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 obtains the requirements not fulfilled by the Web site, and helps to repair the errors by finding out incomplete information and/or missing pages. Our methodology is based on a novel rewriting-based technique, called partial rewriting, in which the traditional pattern matching mechanism is replaced by tree simulation, a suitable technique for recognizing patterns inside semistructured documents. The framework has been implemented in the prototype Web verification system Verdi which is publicly available.

Specialization of inductively sequential functional logic programs

Functional logic languages combine the operational principles of the most important declarative programming paradigms, namely functional and logic programming. Inductively sequential programs admit the definition of optimal computation strategies and are the basis of several recent (lazy) functional logic languages. In this paper, we define a partial evaluator for inductively sequential functional logic programs. We prove strong correctness of this partial evaluator and show that the nice properties of inductively sequential programs carry over to the specialization process and the specialized programs. In particular, the structure of the programs is preserved by the specialization process. This is in contrast to other partial evaluation methods for functional logic programs which can destroy the original program structure. Finally, we present some experiments which highlight the practical advantages of our approach.

Rules + strategies for transforming lazy functional logic programs

This work introduces a transformation methodology for functional logic programs based on needed narrowing, the optimal and complete operational principle for modern declarative languages which integrate the best features of functional and logic programming. We provide correctness results for the transformation system w.r.t, the set of computed values and answer substitutions and show that the prominent properties of needed narrowing--namely, the optimality w.r.t, the length of derivations and the number of computed solutions--carry over to the transformation process and the transformed programs. We illustrate the power of the system by taking on in our setting two well-known transformation strategies (composition and tupling). We also provide an implementation of the transformation system which, by means of some experimental results, highlights the potentiality of our approach.

A Transformation System for Lazy Functional Logic Programs

Needed narrowing is a complete operational principle for modern declarative languages which integrate the best features of (lazy) functional and logic programming. We define a transformation methodology for functional logic programs based on needed narrowing. We provide (strong) correctness results for the transformation system w.r.t. the set of computed values and answer substitutions and show that the prominent properties of needed narrowing -namely, the optimality w.r.t. the length of derivations and the number of computed solutions- carry over to the transformation process and the transformed programs. We illustrate the power of the system by taking on in our setting two well-known transformation strategies (composition and tupling). We also provide an implementation of the transformation system which, by means of some experimental results, highlights the benefits of our approach.

Backward trace slicing for rewriting logic theories

Trace slicing is a widely used technique for execution trace analysis that is effectively used in program debugging, analysis and comprehension. In this paper, we present a backward trace slicing technique that can be used for the analysis of Rewriting Logic theories. Our trace slicing technique allows us to systematically trace back rewrite sequences modulo equational axioms (such as associativity and commutativity) by means of an algorithm that dynamically simplifies the traces by detecting control and data dependencies, and dropping useless data that do not influence the final result. Our methodology is particularly suitable for analyzing complex, textually-large system computations such as those delivered as counter-example traces by Maude model-checkers.

Rule-based verification of Web sites

In this paper, we develop 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. First, we provide a rewriting-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 inside the Web site. Useful information is gathered during the verification process which can be used to repair the Web site. Our methodology is based on a novel rewriting-based technique, called partial rewriting, in which the traditional pattern matching mechanism is replaced by tree simulation, a suitable technique for recognizing patterns inside semistructured documents. The framework has been implemented in the prototype GVerdi, which is publicly available.