Declarative Paradigm Research Articles

Formal Properties of Needed Narrowing with Similarity Relations

The integration of declarative paradigms such as functional-logic and fuzzy-logic programming seems to be an interesting challenge in the design of highly expressive declarative languages where mathematical functions cohabit with fuzzy logic features. Starting with two representative languages from both settings, namely Curry and Likelog, we have recently proposed an hybrid dialect where a set of (Curry) rewrite rules together with a set of (Likelog) similarity equations can be safely executed by means of a fuzzy variant of needed narrowing. This paper is devoted to show some important properties enjoyed by the new narrowing strategy. Firstly, we prove the termination of the process which determines the set of tuples that enable new narrowing steps for a given term. Termination in the fuzzy context is not trivial since, apart that it is required to compute the transitive closure of the initial set of similarity equations, it is also mandatory to ensure the finiteness of the set of recursive calls performed by the narrowing strategy, as well as that each call never falls into an infinite loop. From here, we prove two important (somehow complementary) properties, that we call crispness and fuzziness, respectively. The first one implies that the new strategy is (at least) conservative with respect to the original one of needed narrowing, in the sense that each tuple obtained in the crisp case, is also replicated (with the maximum truth degree) in the fuzzy case. On the other hand, fuzziness means the maximality of the new strategy when exploiting (as much as possible) the similarity relations collected in a given program.

Uniform Lazy Narrowing

Needed narrowing is a complete and optimal operational principle for modern declarative languages which integrate the best features of lazy functional and logic programming. We investigate the formal relation between needed narrowing and another (not so lazy) narrowing strategy which is the basis for popular implementa- tions of lazy functional logic languages. We demonstrate that needed narrowing and lazy narrowing are computationally equivalent over the class of uniform programs introduced in (16,17). We also introduce a complete refinement of lazy narrowing, called uniform lazy narrowing, which is still equivalent to needed narrowing over the aforementioned class. Since actual implementations of functional logic languages are based on the transformation of the original program into a uniform one—which is then executed using a lazy narrowing strategy—our results can be thought of as a formal basis for the correctness of these implementations. Functional logic programming (11) allows us to integrate some of the best features of the classical declarative paradigms, namely functional and logic programming. The operational semantics of the integrated languages is usually based on narrowing, an evaluation mecha- nism which combines the reduction principle of functional languages with the instantiation of unbound variables used in logic programming. Lazy evaluation is a significant feature of functional (logic) programming languages since it avoids unnecessary computations and al- lows programs to deal with infinite data structures. Due to its optimality properties, needed narrowing (5) is currently considered the best lazy narrowing strategy. It generalizes Huet and Levy's (15) call-by-need reduction in order to deal with logical variables and unification. This work investigates and clarifies the formal relation between needed narrowing and another (not so lazy) narrowing strategy which was introduced in (22)—where it is called lazy narrowing—and is the basis for the implementation of several lazy functional logic languages like, e.g., (12,16,22). Our main contributions are the following:

Approximate reasoning by similarity-based SLD resolution

In (Gerla and Sessa, Fuzzy Logic and Soft Computing, Kluwer, Norwell, 1999, pp. 19–31) a methodology that allows to manage uncertain and imprecise information in the frame of the declarative paradigm of Logic Programming has been proposed. With this aim, a Similarity relation R between function and predicate symbols in the language of a logic program is considered. Approximate inferences are then possible since similarity relation allows us to manage alternative instances of entities that can be considered “equal” with a given degree. The declarative semantics of the proposed transformation technique of logic programs is analyzed. The notion of fuzzy least Herbrand model is also introduced. In this paper the corresponding operational semantics is provided by introducing a modified version of SLD resolution. This top-down refutation procedure overcomes failure situations in the unification process by using the similarity relation. A generalized notion of most general unifier provides a numeric value which gives a measure of the exploited approximation. In this way, the SLD resolution is enhanced since it is possible both to handle uncertain or imprecise information, and to compute approximate answer substitutions, with an associated approximation-degree, when failures of the exact inference process occur. It can lead to the implementation of a more general PROLOG interpreter, without detracting from the elegance of the language.

Modeling Concurrent systems specified in a Temporal Concurrent Constraint language-I

In this paper we present an approach to model concurrent systems specified in a temporal concurrent constraint language. Our goal is to construct a framework in which it is possible to apply the Model Checking technique to programs specified in such language.This work is the first step to the framework construction. We present a formalism to transform a specification into a tcc Structure. This structure is a graph representation of the program behavior.Our basic tool is the Timed Concurrent Constraint Programming (tcc) framework defined by Saraswat et al. to describe reactive systems. With this language we take advantage of both the natural properties of the declarative paradigm and of the fact that the notion of time is built into the semantics of the programming language. In fact, on this ground it becomes reasonable to introduce the idea of applying the technique of Model Checking to a finite time interval (introduced by the user). With this restriction we naturally force the space representing the behavior of the program to be finite and hence Model Checking algorithms to be applicable. The graph construction is a completely automatic process that takes as input the tcc specification.

Declarative paradigm of test coverage

Two facts about declarative programming prevent the application of conventional testing methods. First, the classical test coverage measures such as statement, branch or path coverage, cannot be used, since in declarative programs no control flow notion exists. Second, there is no widely accepted language available for formal specification, since predicate logic, which is the most common formalism for declarative programming, is already a very high-level abstract language. This paper presents a new approach exending previous work by the authors on test input generation for declarative programs. For this purpose, the existing program instrumentation notion is extended and a new logic coverage measure is introduced. The approach is mathematically formalized and the goal of achieving 100% program logic coverage controls the automatic test input generation. The method is depicted by means of logic programming; the results are, however, generally applicable. Finally, the concepts introduced have been used practically within a test environment. © 1998 John Wiley & Sons, Ltd.

Automatic spatial layout planning system using a second-generation constraint logic programming language

Spatial layout planning generates two-dimensional layouts consisting of a configuration of rectangles. Our new method represents the rectangles as inconsistent sets of linear constraints. We then select the consistent sets from them by using a second-generation Constraint Logic Programming (CLP) language that employs a new search mechanism to handle disjunction efficiently. Because this is an NP-Complete class problem we introduce (1) domain knowledge to obtain feasible results, (2) some global constraints such as qualitative relation and capacity, and (3) a new mechanism that handles multiple disjunctions at the same time. Our approach is now being effectively applied to the layout of homes. In this paper, we use this example to explain our approach and describe our floor planning system, TG-FP/ 2, which can assist the customer by providing feasible plans. We also point out the advantages of our approach using a second-generation CLP language such as a declarative paradigm for easy description and efficiency for avoiding combinatorial explosion.

A look at clp: Theory and application

Constraint logic programming CLP is a relatively new programming paradigm. During its 10 years of existence the theory of CLP has been increasingly understood and the two differ ent approaches domain technology and incremental linear solving have been implemented in various CLP systems. Meanwhile the commercial attractivity of CLP has been growing. Since 1989 a couple of commercial CLP systems appeared on the software market and have been successfully used in many real life applications. The power of CLP stems from its ability to solve hard combinatorial problems such as planning scheduling resource allocation and many others. How CLP originated from two declarative paradigms - constraint solving and logic programming - is informally explained and the relationship between the different ap proaches in CLP is presented. The main part of the article presents a real life scheduling appli cation for the largest Slovak metallurgy company using the CLP system ECL PS.

Integration of declarative paradigms

We discuss the benefits of integrating the most important declarative programming paradigms namely functional and logic programming. Although many problems need to be solved to provide a true amalgamation of these paradigms, such an integration seems to be possible and has positive effects on teaching, research and application of declarative languages.

Integration of declarative paradigms

We discuss the benefits of integrating the most important declarative programming paradigms namely functional and logic programming. Although many problems need to be solved to provide a true amalgamation of these paradigms, such an integration seems to be possible and has positive effects on teaching, research and application of declarative languages.

I+: A multiparadigm language for object-oriented declarative programming

This paper presents a multiparadigm language I + which is an integration of the three major programming paradigms: object-oriented, logic and functional. I + has an object-oriented framework in which the notions of classes, objects, methods, inheritance and message passing are supported. Methods may be specified as clauses or functions, thus the two declarative paradigms are incorporated at the method level of the object-oriented paradigm. In addition, two levels of parallelism may be exploited in I + programming. Therefore I + is a multiparadigm language for object-oriented declarative programming as well as parallel programming.

Workshop on Integration of Declarative Paradigms

An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

Constraint logic programming: a survey

Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.

Constraint Violation and Conflict from the Perspective of Declarative Phonology

In phonology, constraints are finally coming into their own. There is no real consensus, however, about how constraints behave, and specifically how they interact with other aspects of the phonology and with each other. Theories of Declarative Phonology (DP) approach this “Interaction Problem” (Scobbie 1991a) in a radical way. In DP everything is a constraint — generalizations and lexical entries alike constrain the form of the intended phonological representation (“surface structure”). Moreover, constraints are mutually compatible, indefeasible and are declared non-procedurally. Declarative Phonology is therefore an extremely simple and restrictive type of constraint-based phonology, eschewing constraint conflict, violation and destructive repair. For details of various declarative theories as well as phonological and computational motivation for the declarative paradigm, see Scobbie (1991a) and the other papers in that volume, Bird et al (1993), Bird (1990), Broe (1993), Coleman (1992), Russell (1992), Scobbie (1991b) and Wheeler (1988).