Combining Symbolic Constraint Solvers on Algebraic Domains

Abstract

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 may 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.

Rewriting modulo SMT and open system analysis

“…These ideas have had an important influence in several areas, such as, for example, subsequent work on superposition theorem proving with constraints, see, e.g., [31]; and in the constrained rewriting approach by H. Kirchner and C. Ringeissen to the combination of symbolic constraint solvers [38]. In a similar vein, M. Ayala-Rincón [5] investigated, in the setting of many-sorted equational logic, the expressiveness of conditional equational systems whose conditions may use built-in predicates.…”

“…One similarity between the work in [41] and our work is that, to handle input-output in an imperative language, they allow, as we do, extra variables in the righthand sides of rewrite rules. In general, while approaches such as in [5,12,[27][28][29][38][39][40] address symbolic reasoning for equational theorem proving purposes, or apply these techniques to imperative program analysis and verification, even allowing sometimes extra variables in the right-hand sides of equations, e.g., [41,63,64], theses approaches are quite different from ours because of their predominant focus on equational reasoning for proving, often inductively, universal formulas, and/or on applications to, typically sequential, programming languages.…”

Twenty years of rewriting logic

“…• Constraint solving [68,242,266,267,472]. • Higher-order logics, procedures, and provers, explicit substitution calculi, and translations between such logics [45,56,146,147,353,430,[432][433][434].…”

Coordination of heterogeneous distributed cooperative constraint solving

“…Solver collaboration is a glass-box mechanism which enables one to link black-box tools, i.e., the solvers. BALI allows one to build solver collaborations (solver cooperation [25] and solver combination [17]) by composing component solvers using collaboration primitives (implementing, e.g., sequential, concurrent, and parallel collaboration schemes) and control primitives (such as iterators, fixed-points, and conditionals).…”

“…Solver collaboration is a glass-box mechanism which enables one to link black-box tools, i.e., the solvers. BALI allows one to build solver collaborations (solver cooperation [25] and solver combination [17]) by composing component solvers using collaboration primitives (implementing, e.g., sequential, concurrent, and parallel collaboration schemes) and control primitives (such as iterators, fixed-points, and conditionals).On the other hand, the concept of coordinating a number of activities, such that they can run concurrently in a parallel and distributed fashion, has recently received wide attention [4,5] Due to lack of explicit coordination concepts and constructs, the implementation of BALI does not fully realize its formal model: the treatment of disjunctions and the search are jeopardized and this is not completely satisfactory from a constraint solving point of view. This is mainly due to two causes: (1) the dynamic aspect of the formal model of BALI, and (2) the use of heterogeneous solvers, i.e.…”