In this paper we describe collaborative constraint functional logic programming and the system called Open CFLP that supports this programming paradigm. The system solves equations by collaboration of various equational constraint solvers. The solvers include higher-order lazy narrowing calculi that serve as the interpreter of higher-order functional logic programming, and specialized solvers for solving equations over specific domains, such as a polynomial solver and a differential equation solver. The constraint solvers are distributed in an open environment such as the Internet. They act as providers of constraint solving services. The collaboration between solvers is programmed in a coordination language embedded in a host language. In Open CFLP the user can solve equations in a higher-order functional logic programming style and yet exploit solving resources in the Internet without giving low-level programs of distributions of resources or specifying details of solvers deployed in the Internet.

We present outside-in conditional narrowing for orthogonal conditional term rewriting systems, and show the completeness of leftmost-outside-in conditional narrowing with respect to normalizable solutions. We consider orthogonal conditional term rewriting systems whose conditions consist of strict equality only. Completeness results are obtained for systems both with and without extra variables. The result bears practical significance since orthogonal conditional term rewriting systems can be viewed as a computation model for functional-logic programming languages and leftmost-outside-in conditional narrowing is the computing mechanism for the model.

In a recent paper, Yang proposes an integer labeling algorithm for determining whether an arbitrary simplex P in Rn contains an integer point or not. The problem under consideration is a very difficult one in the sense that it is NP-complete. The algorithm is based on a specific integer labeling rule and a specific triangulation of Rn. In this paper we discuss a practical implementation of the algorithm and present a computer program (ILIN) for solving integer programming using integer labeling algorithm. We also report on the solution of a number of tested examples with up to 500 integer variables. Numerical results indicate that the algorithm is computationally simple, flexible, efficient and stable.

The classical algebraic modelling approach for integer programming (IP) is not suitable for some real world IP problems, since the algebraic formulations allow only for the description of mathematical relations, not logical relations. In this paper, we present a language + for IP, in which we write logical specification of an IP problem. + is a language based on the predicate logic, but is extended with meta predicates such as at_least(m,S), where m is a non-negative integer, meaning that at least m predicates in the set S of formulas hold. The meta predicates facilitate reasoning about a model of an IP problem rigorously and logically. + is executable in the sense that formulas in + are mechanically translated into a set of mathematical formulas, called IP formulas, which most of existing IP solvers accept. We give a systematic method for translating formulas in + to IP formulas. The translation is rigorously defined, verified and implemented in Mathematica 3.0. Our work follows the approach of McKinnon and Williams, and elaborated the language in that (1) it is rigorously defined, (2) transformation to IP formulas is more optimised and verified, and (3) the transformation is completely given in Mathematica 3.0 and is integrated into IP solving environment as a tool for IP.