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.

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In this paper we develop methods for analyzing key management and authentication protocols using techniques developed for the solutions of equations in a term rewriting system. In particular, we describe a model of a class of protocols and possible attacks on those protocols as term rewriting systems, and we also describe a software tool based on a narrowing algorithm that can be used in the analysis of such protocols. We formally model a protocol and describe the results of using these techniques to analyze security properties. We show how a security flaw was found, and we also describe the verification of a corrected scheme using these techniques. 1 Introduction It is difficult to be certain whether or not a cryptographic protocol satisfies its requirements. In a number of cases subtle security flaws have been found in protocols some time after they were published. These flaws were independent of the strengths or weakness of the cryptographic algorithms used. Examples include the N...

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 propose a direct and fully automated translation from standard security protocol descriptions to rewrite rules. This compilation defines non-ambiguous operational semantics for protocols and intruder behavior: they are rewrite systems executed by applying a variant of ac-narrowing. The rewrite rules are processed by the theorem-prover daTac. Multiple instances of a protocol can be run simultaneously as well as a model of the intruder (among several possible). The existence of flaws in the protocol is revealed by the derivation of an inconsistency. Our implementation of the compiler CASRUL, together with the prover daTac, permitted us to derive security flaws in many classical cryptographic protocols.

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...

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 ...

Higher-order constructs provide the necessary level of abstraction for concise and natural formulations in many areas of computer science. We present constructive methods for higher-order equational reasoning with applications ranging from theorem proving to novel programming concepts. A major problem of higher-order programming is the undecidability of higher-order unification. In the first part, we develop several classes with decidable second-order unification. As the main result, we show that the unification of a linear higher-order pattern s with an arbitrary second-order term that shares no variables with s is decidable and finitely solvable. This is the unification needed for second-order functional-logic programming. The second main contribution is a framework for solving higher-order equational problems by narrowing. In the first-order case, narrowing is the underlying computation rule for the integration of logic programming and functional programming. We argue that there are...

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

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.