Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.

This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.

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Many automatic testing, analysis, and verification techniques for programs can be effectively reduced to a constraint-generation phase followed by a constraint-solving phase. This separation of concerns often leads to more effective and maintainable tools. The increasing efficiency of off-the-shelf constraint solvers makes this approach even more compelling. However, there are few effective and sufficiently expressive off-the-shelf solvers for string constraints generated by analysis techniques for string-manipulating programs. We designed and implemented Hampi, a solver for string constraints over fixed-size string variables. Hampi constraints express membership in regular languages and fixed-size context-free languages. Hampi constraints may contain context-free-language definitions, regular-language definitions and operations, and the membership predicate. Given a set of constraints, Hampi outputs a string that satisfies all the constraints, or reports that the constraints are unsatisfiable. Hampi is expressive and efficient, and can be successfully applied to testing and analysis of real programs. Our experiments use Hampi in: static and dynamic analyses for finding SQL injection vulnerabilities in Web applications; automated bug finding in C programs using systematic testing; and compare Hampi with another string solver. Hampi’s source code, documentation, and the experimental data are available at

... this paper, and it is the starting point for proving some novel results about the undecidability of second-order unification presented in the rest of the paper. We prove that second-order unification is undecidable in the following three cases: (1) each second-order variable occurs at most twice and there are only two second-order variables; (2) there is only one second-order variable and it is unary; (3) the following conditions (i)#(iv) hold for some fixed integer n: (i) the arguments of all second-order variables are ground terms of size <n, (ii) the arity of all second-order variables is <n, (iii) the number of occurrences of second-order variables is #5, (iv) there is either a single second-order variable or there are two second-order variables and no first-order variables.

this paper is to define a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associativity and commutativity and of the theory of a partial lexicographic path ordering. 1. Introduction

In this article we propose an extension of term rewriting techniques to automate the deduction in monotone pre-order theories. To prove an inclusion a ⊆ b from a given set I of them, we generate from I, using a completion procedure, a bi-rewrite system 〈R⊆, R⊇〉, that is, a pair of rewrite relations −−− → R ⊆ and −−− → R ⊇ , and seek a common term c such that a −−−→ R ⊆ c and b −−−→

A minimal and complete unification procedure for a theory with individual and sequence variables, free constants and free fixed and flexible arity function symbols is described and a brief overview of an extension with pattern-terms is given.

We introduce equality up-to constraints over finite trees and investigate their expressiveness. Equality up-to constraints subsume equality constraints, subtree constraints, and one-step rewriting constraints.

We propose a unified flamework in which to treat semantic underspecification and parallelism phenomena in discourse. The framework employs a constraint language that can express equality and subtree relations between finite trees. In addition, our constraint language can express the equality up-to relation over trees which captures parallelism between them. The constraints are solved by context unification. We demonstrate the use of our framework at the examples of quantifier scope, ellipsis, and their interaction. 1 I