### Combining Symbolic Constraint Solvers on Algebraic Domains

Hélène Kirchner, Christophe Ringeissen
1994 Journal of symbolic computation
In the context of constraint logic programming and theorem proving, the development of constraint solvers on algebraic domains and their combination is of prime interest. As an example, a constraint solver in nite algebras is presented for a constraint language including for instance equations, disequations and inequations. By extending techniques used for the combination of uni cation in disjoint equational theories, we show how to combine constraint solvers on di erent algebraic domains that
more » ... ay share some constant symbols. We illustrate this technique by combining the constraint solver in nite algebras with other uni cation algorithms, and with another constraint solver on a di erent nite algebra. Definition 2.1. Let = (S; F; P) be a rst-order signature, a constraint language CL A ; X] is given by: A set of constraints C ; X] de ned as the smallest set such that { T; F 2 C ; X], { p ? (t 1 ; : : :; t m ) 2 C ; X] if p 2 P and t 1 ; : : :; t m 2 T (S; F; X), { c^c 0 2 C ; X] if c; c 0 2 C ; X]. { (9x : c) 2 C ; X] if c 2 C ; X]. The set V(c) of free variables of the constraint c is de ned as follows: { V(T) = V(F) = ;, { V(p ? (t 1 ; : : :; t m )) An interpretation A, which is a -structure, and a solution mapping that associates to each constraint the set of assignments Sol A (c) de ned as follows: