Introducing Constraint Functional Logic Programming

This paper presents a theoretical framework for the integration of the cooperative constraint solving of several algebraic domains into higher-order functional and logic programming on λ-abstractions, using an instance of a generic Constraint Functional Logic Programming (CFLP) scheme over a so-called higher-order coordination domain. We provide this framework as a powerful computational model for the higherorder cooperation of algebraic constraint domains over real numbers and integers, which has been useful in practical applications involving the hybrid combination of its components, so that more declarative and efficient solutions can be promoted. Our proposal of computational model has been proved sound and complete with respect to the declarative semantics provided by the CFLP scheme, and enriched with new mechanisms for modeling the intended cooperation among the algebraic domains and a novel higher-order constraint domain equipped with a sound and complete constraint solver for solving higher-order equations. We argue the applicability of our approach describing a prototype implementation on top of the constraint functional logic system TOY

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).

In functional logic programs, rules are applicable independently of textual order, i.e., any rule can potentially be used to evaluate an expression. This is similar to logic languages and contrary to functional languages, e.g., Haskell enforces a strict sequential interpretation of rules. However, in some situations it is convenient to express alternatives by means of compact default rules. Although default rules are often used in functional programs, the non-deterministic nature of functional logic programs does not allow to directly transfer this concept from functional to functional logic languages in a meaningful way. In this paper we propose a new concept of default rules for Curry that supports a programming style similar to functional programming while preserving the core properties of functional logic programming, i.e., completeness, non-determinism, and logic-oriented uses of functions. We discuss the basic concept and sketch an initial implementation of it which exploits advanced features of functional logic languages.

In functional logic programs, rules are applicable independently of textual order, i.e., any rule can potentially be used to evaluate an expression. This is similar to logic languages and contrary to functional languages, e.g., Haskell enforces a strict sequential interpretation of rules. However, in some situations it is convenient to express alternatives by means of compact default rules. Although default rules are often used in functional programs, the non-deterministic nature of functional logic programs does not allow to directly transfer this concept from functional to functional logic languages in a meaningful way. In this paper, we propose a new concept of default rules for Curry that supports a programming style similar to functional programming while preserving the core properties of functional logic programming, i.e., completeness, non-determinism, and logic-oriented use of functions. We discuss the basic concept and propose an implementation which exploits advanced features of functional logic languages.

Debugging tools are a practical need for diagnosing the causes of erroneous computations. Declarative programming paradigms involving complex operational details, such as constraint solving and lazy evaluation, do not fit well to traditional debugging techniques relying on the inspection of low-level computation traces. As a solution to this problem, declarative diagnosis uses Computation Trees (shortly, CTs) in place of traces. CTs are built a posteriori to represent the structure of a computation whose top level outcome is regarded as an error symptom by the user. Each node in a CT represents the computation of some observable result, depending on the results of its children nodes. Declarative diagnosis explores a CT looking for a so-called buggy node which computes an incorrect result from children whose results are correct; such a node must point to an incorrect program fragment. The search for a buggy node can be implemented with the help of an external oracle (usually the user with some semiautomatic support) who has a reliable declarative knowledge of the expected program semantics, the so-called intended interpretation.

In [1] we presented the language TOY(FD) that integrates the best features of existing functional and logic languages, as well as finite domain (FD) constraint solving. We believe that TOY(FD) is more flexible and expressive than the existing approaches of constraint logic programming on finite domain (CLP(FD)) as it integrates FD constraint solving, lazy evaluation, higher order applications of functions and constraints, polymorphism, type checking, composition of functions (and, in particular, constraints), combination of relational and functional notation, and a number of other characteristics. These features allow to write more concise programs, therefore increasing the expressivity level.

Constraint Logic Programming (CLP) languages extend logic programming by allowing the use of constraints from different domains such as real numbers or Boolean functions. They have proved to be ideal for expressing problems that require interactive mathematical modeling and complex combinatorial optimization problems. However, CLP languages have mainly been considered as research systems, useful for rapid prototyping, by not really competitive with more conventional programming languages where efficiency is a more important consideration. One promising approach to improving the performance of CLP systems is the use of powerful program optimizations to reduce the cost of constraint solving. We extend work in this area by describing a new optimizing compiler for the CLP language CLP(ℛ). The compiler implements six powerful optimizations: reordering of constraints, removal of redundant variables, and specialization of constraints which cannot fail. Each program optimization is designed to remove the overhead of constraint solving when possible and keep the number of constraints in the store as small as possible. We systematically evaluate the effectiveness of each optimization in isolation and in combination. Our empirical evaluation of the compiler verifies that optimizing compilation can be made efficient enough to allow compilation of real-world programs and that it is worth performing such compilation because it gives significant time and space performance improvements.

In recent years, several constraintdbased temporal reasoning frameworks have been proposed. They consider temporal points or intervals as domain elements linked by temporal constraints. Temporal reasoning in these systems is based on constraint propagation. In this paper, we argue that a language based on constraint propagation can be a suitable tool for expressing and reasoning about temporal problems. We concentrate on Constraint Logic Programming (CLP) which is a powerful programming paradigm combining the advantages of Logic Programming and the efficiency of constraint solving. However, CLP presents some limitations in dealing with temporal reasoning. First, it uses an “arc consistency” propagation algorithm which is embedded in the inference engine, cannot be changed by the user, and is too weak in many temporal frameworks. Second, CLP is not able to deal with qualitative temporal constraints. We present a general meta CLP architecture which maintains the advantages of CLP, but overcomes these two main limitations. Each architectural level is a finite domain constraint solver (CLP(FD)) that reasons about constraints of the underlying level. Based on this conceptual architecture, we extend the CLP(FD) language and we specialize the extension proposed on Vilain and Kautz’s Point Algebra, on Allen’s Interval Algebra and on the STP framework by Dechter, Meiri and Pearl. In particular, we show that we can cope effectively with disjunctive constraints even in an intervaldbased framework.

Preface: Volume 59, Issue 4

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.

In object-oriented representation, inheritance determines the attributes of a given object, given its type. Conversely, recognition determines the type of an object, given its attributes. The author addresses the more general problem of recognition from constraints; arguing that it can be seen as a special case of the classical abduction process and that it can be implemented as an abduction operation on constraints. Abductive reasoning is common in most fields of artificial intelligence. Constraint logic programming (CLP) generalizes logic programming by replacing unification with constraint solving. He first explores the relationship between abduction and CLP and shows that CLP is a special case of abduction. A class of problems is then identified for which the usual unrestricted forms of abduction are unsuitable. Within the CLP framework a restricted form of abduction is formulated which is applicable to the whole class of problems, in which object-oriented recognition can be considered as a special case. >

This document presents a new compiler for the Functional Logic programming language Curry based on a novel pull-tabbing evaluation strategy called the Fair Scheme. A simple version of the Fair Scheme is proven sound, complete, and optimal. An elaborated version is also developed, which supports narrowing computations and other features of Curry, such as constraint programming, equational constraints, and set functions. The Fair Scheme is used to develop a new Curry system called Sprite, a high-quality, performant implementation whose aims are to promote practical uses of Curry and to serve as a laboratory for further research. An important aspect of Sprite is its integration with the popular imperative language Python. This combination allows one to write hybrid programs in which the programmer may move between declarative and non-declarative styles with relative ease. Benchmarking data show Sprite to be more complete than other Curry systems and competitive in terms of execution time, particularly for non-deterministic programs.

The basics of logic programming, as embodied by Prolog, are generally well-known in the programming language community. However, more advanced techniques, such as tabling, answer subsumption and probabilistic logic programming fail to attract the attention of a larger audience. The cause for the community's seemingly limited interest lies with the presentation of these features: the literature frequently focuses on implementations and examples that do little to aid the understanding of non-experts in the field. The key point is that many of these advanced logic programming features can be characterised in more generally known, more accessible terms. In my research I try to reconcile these advanced concepts from logic programming (Tabling, Answer subsumption and probabilistic programming) with concepts from functional programming (effects, monads and applicative functors).

The generic programming approach is popular in functional languages (for example, OCaml, Haskell). In essence, it is a compile-time generation of code that performs transformations of user-defined data types. The generated code can carry out various kinds of transformations of the values. Usually, transformations are represented as functions that implement algorithms of transformation. New transformations could be built from these transformation functions and user-defined ones. The representation based on functions has a downside: functions behave as final representations, and hence it is not possible to modify the behavior of the already built function. If the current set of transformations does not suit well, software developers are obliged to write a completely distinct transformation, even in the case when the new transformation is almost identical to the existing one. This work proposes to build transformations that are extensible after construction. The object-oriented programming paradigm will be followed, transformations will be represented not as functions but as objects. Instead of calling a transformation function, one of the object’s methods will be called. The transformation itself will be split into methods. The extensibility is supported by adding new methods and overriding existing ones. In this paper, the authors propose an approach to represent transformations as objects in the OCaml functional programming language. Every alternative in data type definition has a corresponding object method. This design allows the construction of many distinct transformations. The cases where too many methods are not desirable are also discussed. The method is applicable to represent extensible transformations for polymorphic variant data types in OCaml when other methods fail to do it. The method is not bound to any particular domain. It allows the creation of extensible transformations in OCaml. It could be ported to other functional languages supporting object-oriented programming.

The incorporation of global program analysis into recent compilers for Constraint Logic Programming (CLP) languages has greatly improved the efficiency of compiled programs. We present a global analyser based on abstract interpretation. Unlike traditional optimizers, whose designs tend to be ad hoc, the analyser has been designed with flexibility in mind. The analyser is incremental, allowing substantial program transformations by a compiler without requiring redundant re-computation of analysis data. The analyser is also generic in that it can perform a large number of different program analyses. Furthermore, the analyser has an object-oriented design, enabling it to be adapted to different applications easily and allowing it to be used with various CLP languages with simple modifications. As an example of this generality, we sketch the use of the analyser in two different applications involving two distinct CLP languages: an optimizing compiler for CLP(R) programs and an application for detecting occur-check problems in Prolog programs. © 1998 John Wiley & Sons Ltd.