Automating inductionless induction using test sets
Journal of Symbolic Computation
Using induction and rewriting to verify and complete parameterized specifications
Theoretical Computer Science
Automated theorem proving by test set induction
Journal of Symbolic Computation
A general framework to build contextual cover set
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Studies on the Ground Convergence Property of Conditional Theories
AMAST '91 Proceedings of the Second International Conference on Methodology and Software Technology: Algebraic Methodology and Software Technology
Uniform Derivation of Decision Procedures by Superposition
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
A Mechanizable Induction Principle for Equational Specifications
Proceedings of the 9th International Conference on Automated Deduction
Proceedings of the 10th International Conference on Automated Deduction
Abstract Notions and Inference Systems for Proofs by Mathematical Induction
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
On generic representation of implicit induction procedures
On generic representation of implicit induction procedures
Combining Rewriting with Noetherian Induction to Reason on Non-orientable Equalities
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
A Schemata Calculus for Propositional Logic
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Integrating implicit induction proofs into certified proof environments
IFM'10 Proceedings of the 8th international conference on Integrated formal methods
Automated certification of implicit induction proofs
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
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We present a framework and a methodology to build and analyse automatic provers using the ’Descente Infinie’ induction principle. A stronger connection between different proof techniques like those based on implicit induction and saturation is established by uniformly and explicitly representing them as applications of this principle. The framework offers a clear separation between logic and computation, by the means of i) an abstract inference system that defines the maximal sets of induction hypotheses available at every step of a proof, and ii) reasoning modules that perform the computation and allow for modular design of the concrete inference rules. The methodology is applied to define a concrete implicit induction prover and analyse an existing saturation-based inference system.