Handbook of theoretical computer science (vol. B)
Automated theorem proving by test set induction
Journal of Symbolic Computation
Constructors can be partial, too
Automated reasoning and its applications
Specification and proof in membership equational logic
Theoretical Computer Science - Trees in algebra and programming
A general framework to build contextual cover set
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Automata-driven automated induction
Information and Computation
Implementing Contextual Rewriting
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Ground reducibility is EXPTIME-complete
Information and Computation
Tree automata with memory, visibility and structural constraints
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Constructors, sufficient completeness, and deadlock freedom of rewrite theories
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
WFLP'11 Proceedings of the 20th international conference on Functional and constraint logic programming
Rewriting induction + linear arithmetic = decision procedure
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values), and may express syntactic equality, disequality, ordering and also membership in a fixed tree language. Constrained equational axioms between constructor terms are supported and can be used in order to specify complex data structures like sets, sorted lists, trees, powerlists...Our procedure is based on tree grammars with constraints, a formalism which can describe exactly the initial model of the given specification (when it is sufficiently complete and terminating). They are used in the inductive proofs first as an induction scheme for the generation of subgoals at induction steps, second for checking validity and redundancy criteria by reduction to an emptiness problem, and third for defining and solving membership constraints.We show that the procedure is sound and refutationally complete. It generalizes former test set induction techniques and yields natural proofs for several non-trivial examples presented in the paper, these examples are difficult (if not impossible) to specify and carry on automatically with other induction procedures.