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

Abstract. Declarative programming languages advocate a programming style expressing the properties of problems and their solutions rather than how to compute individual solutions. Depending on the underlying formalism to express such properties, one can distinguish different classes of declarative languages, like functional, logic, or constraint programming languages. This paper surveys approaches to combine these different classes into a single programming language. 1

Abstract. Functional logic languages extend purely functional languages with two features: operations defined by overlapping rules and logic variables in both defining rules and expressions to evaluate. In this paper, we show that only one of these features is sufficient in a core language. On the one hand, overlapping rules can be eliminated by introducing logic variables in rules. On the other hand, logic variables can be eliminated by introducing operations defined by overlapping rules. The proposed transformations between different classes of programs not only give a better understanding of the features of functional logic programs but also may simplify implementations of functional logic languages. 1

Abstract. We propose an extension of functional logic languages that allows the definition of operations with patterns containing other defined operation symbols. Such “function patterns ” have many advantages over traditional constructor patterns. They allow a direct representation of specifications as declarative programs, provide better abstractions of patterns as first-class objects, and support the highlevel programming of queries and transformation of complex structures. Moreover, they avoid known problems that occur in traditional programs using strict equality. We define their semantics via a transformation into standard functional logic programs. Since this transformation might introduce an infinite number of rules, we suggest an implementation that can be easily integrated with existing functional logic programming systems. 1

We present a generic scheme for the declarative debugging of functional logic programs which is valid for eager as well as lazy programs. In particular we show that the framework extends naturally some previous work and applies to the most modern lazy strategies, such as needed narrowing. First we associate to our pro- grams a semantics based on a (continuous) immediate consequence operator, which models computed answers. We show that, given the intended specification of a program 7, it is possible to check the correctness of 7 by a single step of Tn. We consider then a more effective methodology which is based on abstract interpretation: by approximating the intended specification of the success set we derive a finitely terminating diagnosis method, which can be used statically and is parametric w.r.t. to the chosen approximation. In order to correct the bugs, we sketch a preliminary deductive approach which uses example-guided unfolding. We specialize the incorrect rules w.r.t. sets of positive and negative examples which are gathered (bottom-up) during the diagnosis process, so that all refutations of nega- tive examples and no refutation of positive examples are excluded. Our debugging framework does not require the user to either provide error symptoms in advance or answer diicult questions concerning program correctness. We extend an implementation of our system to the case of needed narrowing and illustrate it through some examples which demonstrate the practicality of our approach.

Ωmega is an experimental system that combines features of both a programming language and a logical reasoning system. Ωmega is a language with an infinite hierarchy of computational levels. Terms at one level are classified (or typed) by terms at the next higher level. In this paper we report on using two different computational mechanisms. At the value level, computation is performed by reduction, and is largely unconstrained. At all higher levels, computation is performed by narrowing.

Abstract. We describe the architecture of a virtual machine for executing functional logic programming languages. A distinguishing feature of our machine is that it preserves the operational completeness of non-deterministic programs by concurrently executing a pool of independent computations. Each computation executes only root-needed sequential narrowing steps. We describe the machine’s architecture and instruction set, and show how to compile overlapping inductively sequential programs to sequences of machine instructions. The machine has been implemented in Java and in Standard ML. 1

We define a rewrite strategy for a class of non-confluent constructor-based term graph rewriting systems and prove its correctness. Our strategy and its extension to narrowing are intended for the implementation of non-strict non-deterministic functional logic programming languages. Our strategy is based on a graph transformation, called bubbling, that avoids the construction of large contexts of redexes with distinct replacements, an expensive and frequently wasteful operation executed by competitive complete techniques.

The evolution of programming languages is the stepwise introduction of abstractions hiding the underlying computer hardware and the details of program execution. Assembly languages introduce mnemonic instructions and symbolic

Abstract. Bubbling, a recently introduced graph transformation for functional logic computations, is well-suited for the reduction of redexes with distinct replacements. Unlike backtracking, bubbling preserves operational completeness; unlike copying, it avoids the up-front construction of large contexts of redexes, an expensive and frequently wasteful operation. We recall the notion of bubbling and offer the first proof of its completeness and soundness with respect to rewriting. 1 Introduction Non-determinism is one of the most appealing features of functional logic pro-graming. A program is non-deterministic when its execution may evaluate some expression that has multiple results. To better understand this concept, considera program to color a map of the Pacific Northwest so that no pair of adjacent states shares a color. The following declarations, in Curry [15], define the well-known topology of the problem: data State = WA | OR | ID | BC states = [WA,OR,ID,BC] adjacent = [(WA,OR),(WA,ID),(WA,BC),(OR,ID),(ID,BC)] (1)