In February 1987, at the occasion of a research visit to ICOT, Prof. Bruno Buchberger proposed using advanced methods in computer algebra (the Gröbner bases method, quantifier elimination, etc.) for dealing with nonlinear constraints in logic programming. The use of algebraic methods in non-linear constraint logic programming has meanwhile been pursued by various groups in the world. At RISC-Linz, the emphasis was on non-linear and quantifier constraint solving including the development of distributed and parallel algorithms with a new degree of efficiency in particular in practical examples.
At the same time, at the SCORE group of Professor Ida at Tsukuba University, the research line of functional logic programming was developed in detail, in particular with respect to powerful narrowing techniques. Recently they have developed a new deterministic lazy conditional narrowing strategy and implemented it in the computer algebra system Mathematica.
Based on our combined experience, we pursue in the frame of this project the integration of constraint solving packages developed at RISC-Linz into the lazy narrowing system developed at SCORE such that the functional logic language serves as a ``coordination language'' distributing sets of constraints to a network of constraint solving engine. For this purpose, the functional logic language and its Mathematica implementation are extended by the mechanism to specify non-linear constraints over the real numbers and to formulate OR parallelism among different clauses of a predicate such that parts of the solution space can be investigated independently and simultaneously of each other.