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45
The Integration of Functions into Logic Programming: From Theory to Practice
 Journal of Logic Programming
, 1994
"... Abstract. Functional logic programming languages combine the most important declarative programming paradigms, and attempts to combine these paradigms have a long history. The declarative multiparadigm language Curry is influenced by recent advances in the foundations and implementation of function ..."
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Cited by 334 (52 self)
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Abstract. Functional logic programming languages combine the most important declarative programming paradigms, and attempts to combine these paradigms have a long history. The declarative multiparadigm language Curry is influenced by recent advances in the foundations and implementation of functional logic languages. The development of Curry is an international initiative intended to provide a common platform for the research, teaching, and application of integrated functional logic languages. This paper surveys the foundations of functional logic programming that are relevant for Curry, the main features of Curry, and extensions and applications of Curry and functional logic programming. 1
An Implementation of Narrowing Strategies
 Journal of the ACM
, 2001
"... This paper describes an implementation of narrowing, an essential component of implementations of modern functional logic languages. These implementations rely on narrowing, in particular on some optimal narrowing strategies, to execute functional logic programs. We translate functional logic progra ..."
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Cited by 291 (121 self)
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This paper describes an implementation of narrowing, an essential component of implementations of modern functional logic languages. These implementations rely on narrowing, in particular on some optimal narrowing strategies, to execute functional logic programs. We translate functional logic programs into imperative (Java) programs without an intermediate abstract machine. A central idea of our approach is the explicit representation and processing of narrowing computations as data objects. This enables the implementation of operationally complete strategies (i.e., without backtracking) or techniques for search control (e.g., encapsulated search). Thanks to the use of an intermediate and portable representation of programs, our implementation is general enough to be used as a common back end for a wide variety of functional logic languages.
A unified computation model for functional and logic programming
 IN PROC. OF THE 24TH ACM SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES (PARIS
, 1997
"... We propose a new computation model which combines the operational principles of functional languages (reduction), logic languages (nondeterministic search for solutions), and integrated functional logic languages (residuation and narrowing). This computation model combines efficient evaluation prin ..."
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Cited by 141 (68 self)
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We propose a new computation model which combines the operational principles of functional languages (reduction), logic languages (nondeterministic search for solutions), and integrated functional logic languages (residuation and narrowing). This computation model combines efficient evaluation principles of functional languages with the problemsolving capabilities of logic programming. Since the model allows the delay of function calls which are not sufficiently instantiated, it also supports a concurrent style of programming. We provide soundness and completeness results and show that known evaluation principles of functional logic languages are particular instances of this model. Thus, our model is a suitable basis for future declarative programming languages.
Curry: A Truly Functional Logic Language
, 1995
"... Functional and logic programming are the most important declarative programming paradigms, and interest in combining them has grown over the last decade. However, integrated functional logic languages are currently not widely used. This is due to the fact that the operational principles are not w ..."
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Cited by 53 (5 self)
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Functional and logic programming are the most important declarative programming paradigms, and interest in combining them has grown over the last decade. However, integrated functional logic languages are currently not widely used. This is due to the fact that the operational principles are not well understood and many different evaluation strategies have been proposed which resulted in many different functional logic languages. To overcome this situation, we propose the functional logic language Curry which can deal as a standard language in this area. It includes important ideas of existing functional logic languages and recent developments, and combines the most important features of functional and logic languages. Thus, Curry can be the basis to combine the currently separated research efforts of the functional and logic programming communities and to boost declarative programming in general. Moreover, since functions provide for more efficient evaluation strategies and ...
Parallel Evaluation Strategies for Functional Logic Languages
 In Proc. of the Fourteenth International Conference on Logic Programming (ICLP’97
, 1997
"... We introduce novel, sound, complete, and locally optimal evaluation strategies for functional logic programming languages. Our strategies combine, in a nontrivial way, two landmark techniques in this area: the computation of unifiers performed by needed narrowing in inductively sequential rewrite s ..."
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Cited by 46 (25 self)
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We introduce novel, sound, complete, and locally optimal evaluation strategies for functional logic programming languages. Our strategies combine, in a nontrivial way, two landmark techniques in this area: the computation of unifiers performed by needed narrowing in inductively sequential rewrite systems and the simultaneous reduction of a necessary set of redexes performed by rewriting in weakly orthogonal, constructorbased rewrite systems. First, we define a sequential strategy similar in scope to other narrowing strategies used in modern lazy functional logic languages. Then, based on the sequential strategy, we define a parallel narrowing strategy that has several noteworthy characteristics: it is the first complete narrowing strategy which evaluates ground expressions in a fully deterministic, optimal way; it computes shortest derivations and minimal sets of solutions on inductively sequential rewrite systems; and when combined with term simplification, it subsumes and improves all r...
Completeness Results for Basic Narrowing
, 1994
"... In this paper we analyze completeness results for basic narrowing. We show that basic narrowing is not complete with respect to normalizable solutions for equational theories defined by confluent term rewriting systems, contrary to what has been conjectured. By imposing syntactic restrictions on the ..."
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Cited by 44 (2 self)
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In this paper we analyze completeness results for basic narrowing. We show that basic narrowing is not complete with respect to normalizable solutions for equational theories defined by confluent term rewriting systems, contrary to what has been conjectured. By imposing syntactic restrictions on the rewrite rules we recover completeness. We refute a result of Holldobler which states the completeness of basic conditional narrowing for complete (i.e. confluent and terminating) conditional term rewriting systems without extra variables in the conditions of the rewrite rules. In the last part of the paper we extend the completeness result of Giovannetti and Moiso for levelconfluent and terminating conditional systems with extra variables in the conditions to systems that may also have extra variables in the righthand sides of the rules. 1985 Mathematics Subject Classification: 68Q50 1987 CR Categories: F.4.1, F.4.2 Key Words and Phrases: narrowing, basic narrowing, conditional narrowin...
The Integration of Functions into Logic Programming: A Survey
, 1994
"... Functional and logic programming are the most important declarative programming paradigms, and interest in combining them has grown over the last decade. Early research concentrated on the definition and improvement of execution principles for such integrated languages, while more recently efficient ..."
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Cited by 35 (0 self)
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Functional and logic programming are the most important declarative programming paradigms, and interest in combining them has grown over the last decade. Early research concentrated on the definition and improvement of execution principles for such integrated languages, while more recently efficient implementations of these execution principles have been developed so that these languages became relevant for practical applications. In this paper we survey the development of the operational semantics as well as
Specialization of Lazy Functional Logic Programs
 IN PROC. OF THE ACM SIGPLAN CONF. ON PARTIAL EVALUATION AND SEMANTICSBASED PROGRAM MANIPULATION, PEPM'97, VOLUME 32, 12 OF SIGPLAN NOTICES
, 1997
"... 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 socalled static/dynamic distinction is hard ..."
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Cited by 35 (21 self)
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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 socalled 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 twophase specialization method for a nonstrict, 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 postprocessing renaming scheme (second phase) is necessary which we describe and illustrate on the wellknown matching example. This phase is essential also for other nonlazy 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.
Efficient Translation of Lazy Functional Logic Programs into Prolog
 In Proc. Fifth International Workshop on Logic Program Synthesis and Transformation
, 1995
"... Abstract. In this paper, we present a highlevel implementation of lazy functional logic programs by transforming them into Prolog programs. The transformation is controlled by generalized definitional trees which specify the narrowing strategy to be implemented. Since we consider a sophisticated na ..."
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Cited by 30 (13 self)
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Abstract. In this paper, we present a highlevel implementation of lazy functional logic programs by transforming them into Prolog programs. The transformation is controlled by generalized definitional trees which specify the narrowing strategy to be implemented. Since we consider a sophisticated narrowing strategy, a direct mapping of functions into predicates is not possible. Therefore, we present new techniques to reduce the interpretational overhead of the generated Prolog code. This leads to a portable and efficient implementation of functional logic programs. 1 Introduction In recent years, a lot of proposals have been made to amalgamate functional and logic programming languages [15]. Functional logic languages with a sound and complete operational semantics are based on narrowing, a combination of the reduction principle of functional languages and the resolution principle of logic languages. Narrowing, originally introduced in automated theorem proving [26], is used to solve equations by finding appropriate values for variables occurring in arguments of functions. A narrowing step instantiates some variables in a goal and applies a reduction step to a redex of the instantiated goal. The instantiation of goal variables is usually computed by unifying a subterm of the goal with the lefthand side of some rule. Example 1. Consider the following rules defining the addition and comparison of natural numbers which are represented by terms built from 0 and s:
Categorybased Semantics for Equational and Constraint Logic Programming
, 1994
"... This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equation ..."
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Cited by 24 (10 self)
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This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfying certain natural conditions; completeness is proved under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and regards valuations as model morphisms rather than functions. This is used as a basis for a model theoretic categorybased approach to a paramodulationbased operational semantics for equational logic programming languages. Categorybased equational logic in conjunction with the theory of institutions is used to give mathematical foundations for modularisation in equational logic programming. We study the soundness and completeness problem for module imports i...