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

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.

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

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

We present the problem of integrating functional languages and logic languages. We explain why the narrowing-based techniques have so far prevailed as operational mechanisms for the functional logic interpreters. We then discuss various strategies of narrowing. Finally we explain how to simulate these strategies of narrowing using the leftmost SLD-resolution rule of Prolog, and compare some experimental results with those obtained with direct narrowing implementations. 1. Introduction There has been a flurry of research on the integration of functional programming (FP) and logic programming (LP). A natural framework would be to consider the union of a set H of Horn clauses with a set E of conditional equations as a program. The declarative semantics of a program is then given by first-order logic with equality [26], that is, first-order logic extended with an equality symbol and the standard equality axioms. The operational semantics of a program is usually given by a system of infere...

This paper presents a new operational semantics for logic programs with external procedures, introduced in [BM88]. A new resolution procedure S-SLD-resolution is defined, in which each step of computation is characterized by a goal and a set of equational constraints, whose satisfiability cannot be decided with the information at hand. This approach improves the completeness of the resulting system, since further computation may result in the information needed to solve some earlier unsolved constraints. We also state a sufficient condition to distinguish a class of programs where no unsolved constraints will remain at the end of computation. 1 Introduction We will address the problem of defining an operational semantics for logic programs with external procedures, a formalism presented in [BM88, Bon89]. In this approach the external procedures, which can be written in any language, are regarded as "black boxes" that reduce ground terms. Under this assumption an external procedure imp...

Curry is a multi-paradigm declarative language aiming to amalgamate functional, logic, and concurrent programming paradigms. Curry combines in a seamless way features from functional programming and (concurrent) logic programming. Curry’s operational semantics is based on the combination of lazy reduction of expressions together with a possibly non-deterministic binding of free variables occurring in expressions. Moreover, (equational) constraints can be executed concurrently which provides for passive constraints and concurrent computation threads that are synchronized on logical variables. machine for executing Curry programs. The machine is designed to provide a link for compiling Curry programs into Java but it can also be a basis for implementations of Curry in other (object-oriented) languages. The main emphasis of the Java-based implementation is the exploitation of Java threads to implement the concurrent and nondeterministic features of Curry.

LIFE is an experimental programming language proposing to integrate logic programming, functional programming, and object-oriented programming. It replaces first-order terms with ψ-terms, data structures which allow computing with partial information. These are approximation structures denoting sets of values. LIFE further enriches the expressiveness of ψ-terms with functional dependency constraints. We must explain the meaning and use of functions in LIFE declaratively as solving partial information constraints. These constraints do not attempt to generate their solutions but behave as demons filtering out anything else.

We present a clean approach to integrating logic programs with functional procedures written in other programming languages. Many existing logic programming systems allow for use of such external procedures in logic programs. In these systems the integration is achieved on the level of implementation so that the integrated programs have no declarative semantics. Our integrated programs have a declarative semantics and a sound operational semantics. The declarative semantics is constructed by viewing the integrated programs as equational logic programs. To define the operational semantics a special kind of unification, called Sunification, is introduced. The operational semantics is based on an extension of SLD-resolution that employs S-unification and a concept of delay. The operational semantics is sound but incomplete with respect to the declarative semantics. The incompleteness is a consequence of our general assumptions about the nature of the external procedures. However, the oper...

This paper presents a new program analysis framework to approximate call patterns and their results in functional logic computations. We consider programs containing non-strict, nondeterministic operations in order to make the analysis applicable to modern functional logic languages like Curry or TOY. For this purpose, we present a new fixpoint characterization of functional logic computations w.r.t. a set of initial calls. We show how programs can be analyzed by approximating this fixpoint. The results of such an approximation have various applications, e.g., program optimization as well as verifying safety properties of programs. 1