CLP Scheme Research Articles

A declarative semantics for CLP with qualification and proximity

AbstractUncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause annotations based on uncertain truth values, qualification values as a generalization of uncertain truth values, and unification based on proximity relations. On the other hand, the CLP scheme has established itself as a powerful extension of LP that supports efficient computation over specialized domains while keeping a clean declarative semantics. In this paper we propose a new scheme SQCLP designed as an extension of CLP that supports qualification values and proximity relations. We show that several previous proposals can be viewed as particular cases of the new scheme, obtained by partial instantiation. We present a declarative semantics for SQCLP that is based on observables, providing fixpoint and proof-theoretical characterizations of least program models as well as an implementation-independent notion of goal solutions.

A Logical Framework for Debugging in Declarative Constraint Programming

We present a logical and semantic framework for diagnosing wrong computed answers in CFLP(D), a newly proposed generic scheme for lazy Constraint Functional Logic Programming which can be instantiated by any constraint domain D given as parameter, and supports a powerful combination of functional and constraint logic programming over D. Our approach extends and combines declarative debugging techniques previously developed for less expressive programming paradigms, namely the CLP(D) scheme and lazy functional logic languages. Debugging starts with the observation of a wrong computed answer which the user regards as incorrect w.r.t. an intended model that provides a declarative description of the program's semantics. Debugging proceeds by exploring an abridged proof tree that provides a purely declarative view of the computation, so that the user does not need to understand the complex underlying operational mechanisms. Debugging ends with the detection of a function rule in the program that is incorrect w.r.t. the intended model. We prove the logical correctness of the debugging method for any sound CFLP(D)-system whose computed answers are logical consequences of the program, and we describe a practical tool which implements the debugging method for the domain of arithmetic constraints over the real numbers.

Constraint Functional Logic Programming Revisited

In this paper we propose a new generic scheme CFLP(D), intended as a logical and semantic framework for lazy Constraint Functional Logic Programming over a parametrically given constraint domain D. As in the case of the well known CLP(D) scheme for Constraint Logic Programming, D is assumed to provide domain specific data values and constraints. CFLP(D) programs are presented as sets of constrained rewrite rules that define the behaviour of possibly higher order and/or non-deterministic lazy functions over D. As the main novelty w.r.t. previous related work, we present a Constraint Rewriting Logic CRWL(D) which provides a declarative semantics for CFLP(D) programs. This logic relies on a new formalization of constraint domains and program interpretations, which allows a flexible combination of domain specific data values and user defined data constructors, as well as a functional view of constraints.

Value Constraints in the CLP Scheme

We define value constraints, a method for incorporating constraint propagation into logic programming. It is a subscheme of the CLP scheme and is applicable wherever one has an efficient method for representing sets of possible values. As examples we present: small finite sets, sets of ground instances of a term, and intervals of reals with floating-point numbers as bounds. Value constraints are defined by distinguishing two storage management strategies in the CLP scheme. In value constraints the infer step of the CLP scheme is implemented by Waltz filtering. We give a semantics for value constraints in terms of set algebra that gives algebraic characterizations of local and global consistency. The existing extremal fixpoint characterization of chaotic iteration is shown to be applicable to prove convergence of Waltz filtering.

Generalized constraint propagation over the CLP scheme

Constraint logic programming is often described as logic programming with unification replaced by constraint solving over a computation domain. There is another, very different, CLP paradigm based on constraint satisfaction, where program-defined goals can be treated as constraints and handled using propagation. This paper proposes a generalization of propagation that enables it to be applied on arbitrary computation domains revealing that the two paradigms of CLP are orthogonal and can be freely combined. The main idea behind generalized propagation is to use whatever constraints are available over the computation domain to express restrictions on problem variables. Generalized propagation on a goal G requires that the system extracts a constraint approximating all the answers to G. This paper introduces a generic algorithm for generalized propagation called topological branch and bound, which avoids enumerating all the answers to G. Generalized propagation over the Herbrand universe has been implemented in a system called Propia, and we describe its behavior in some applications.

Computational complexity and constraint logic programming languages

We give a complexity analysis of a variety of languages across the spectrum of the CLP scheme. By varying the logic and memory management, the role of the constraints and the role of the logic can be measured. The analysis clarifies the relation between linear/integer programming and constraint logic programming. We also determine how the power of constraints can easily lead to undecidable queries in Datalog languages with constraints. This work is motivated in large part by the problems of efficient implementation of CLP languages and the concomitant need for low level constraint languages.