Abstract. Functional logic programming languages combine the most important declarative programming paradigms, and attempts to combine these paradigms have a long history. The declarative multi-paradigm 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

We propose a new computation model which combines the operational principles of functional languages (reduction), logic languages (non-deterministic search for solutions), and integrated functional logic languages (residuation and narrowing). This computation model combines efficient evaluation principles of functional languages with the problem-solving 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.

Functional logic languages with a sound and complete operational semantics are mainly based on narrowing. Due to the huge search space of simple narrowing, steadily improved narrowing strategies have been developed in the past. Needed narrowing is currently the best narrowing strategy for first-order functional logic programs due to its optimality properties w.r.t. the length of derivations and the number of computed solutions. In this paper, we extend the needed narrowing strategy to higher-order functions and λ-terms as data structures. By the use of definitional trees, our strategy computes only incomparable solutions. Thus, it is the first calculus for higher-order functional logic programming which provides for such an optimality result. Since we allow higher-order logical variables denoting λ-terms, applications go beyond current functional and logic programming languages.

We introduce novel, sound, complete, and locally optimal evaluation strategies for functional logic programming languages. Our strategies combine, in a non-trivial 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, constructor-based 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...

We define a transformation from a left-linear constructor-based conditional rewrite system into an overlapping inductively sequential rewrite system. This transformation is sound and complete for the computations in the source system. Since there exists a sound and complete narrowing strategy for the target system, the combination of these results offers the first procedure for provably sound and complete narrowing computations for the whole class of the leftlinear constructor-based conditional rewrite systems. We address the differences between demand driven and lazy strategies and between narrowing strategies and narrowing calculi. In this context, we analyze the efficiency and practicality of using our transformation for the implementation of functional logic programming languages. The results of this paper complement, extend, and occasionally rectify, previously published results in this area. Categories and Subject Descriptors D.1.1 [Programming Techniques]: Applicative (Functional) Programming; D.1.6 [Programming Techniques]: Logic Programming; D.3.3 [Programming Languages]: Language Constructs and Features---Control structures; D.3.4 [Programming Languages ]: Processors---Optimization; F.4.2 [Mathematical Logic and Formal Languages]: Grammars and Other Rewriting Systems; I.1.1 [Algebraic Manipulation]: Expressions and Their Representation ---Simplification of expressions; I.2.2 [Automatic Programming ]: Program transformation General Terms Algorithms, Languages, Performance, Theory Keywords Functional Logic Programming Languages, Rewrite Systems, Narrowing Strategies, Call-By-Need This work has been supported in part by the National Science Foundation grant INT-9981317. 1.

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 ...

Context-sensitive rewriting is a simple restriction of rewriting which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is (explicitly or automatically) specified on the arguments of symbols of the signature and inductively extended to arbitrary positions of terms built from those symbols. Termination is not only preserved but usually improved and several methods have been developed to formally prove it. In this paper, we investigate the definition, properties, and use of context-sensitive rewriting strategies, i.e., particular, fixed sequences of context-sensitive rewriting steps. We study how to define them in order to obtain efficient computations and to ensure that context-sensitive computations terminate whenever possible. We give conditions enabling the use of these strategies for root-normalization, normalization, and infinitary normalization. We show that this theory is suitable for formalizing ...

Partial evaluation is a semantics-based program optimization technique which has been investigated within di#erent programming paradigms and applied to a wide variety of languages. Recently, a partial evaluation framework for functional logic programs has been proposed.

Abstract not found

1 Introduction Michael Hanus Salvador Lucas Aart Middeldorp Strongly sequential and inductively sequential term rewriting systems hanus@informatik.rwth-aachen.de slucas@dsic.upv.es ami@score.is.tsukuba.ac.jp first(0,x) [] first(s(x),y::z) y::first(x,z) first x 1 0 s(x) x 2 first x 1 x 2 first 0 x 2 first s x x 2 [] first s x y z y first x z first inductively sequential outermost-needed strategy needed rewriting needed Definitional trees inductively sequential inductively sequential index trees forward-branching index trees matching dags outermost-needed strategy index reduction Informatik II, RWTH Aachen, D-52056 Aachen, Germany, . Work partially supported by DFG (under grant Ha 2457/1-1) and Acci'on Integrada. DSIC, U.P. de Valencia, Camino de la Vera s/n, Apdo. 22012, E-46071 Valencia, Spain, . Work partially supported by EEC-HCM grant ERBCHRXCT940624, Bancaixa (Bancaja-Europa grant), Acci'on Integrada (HA19970073) and CICYT (under grant TIC 95-0433-C03-03). Institute of Informa...