A strong restriction of the inductive completion procedure
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
Proofs and types
CADE-10 Proceedings of the tenth international conference on Automated deduction
Term rewriting and all that
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Induction = I-axiomatization + first-order consistency
Information and Computation - Special issue on RTA-98
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
SPIKE, an Automatic Theorem Prover
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Canonical Forms and Unification
Proceedings of the 5th Conference on Automated Deduction
How to Prove Algebraic Inductive Hypotheses Without Induction
Proceedings of the 5th Conference on Automated Deduction
Automated Verification by Induction with Associative-Commutative Operators
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
Journal of Automated Reasoning
HOL-λσ: an intentional first-order expression of higher-order logic
Mathematical Structures in Computer Science
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Complete Sequent Calculi for Induction and Infinite Descent
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Strong normalisation for a gentzen-like cut-elimination procedure
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
A finite first-order theory of classes
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Dealing with non-orientable equations in rewriting induction
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
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
Rewriting induction + linear arithmetic = decision procedure
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
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We present an original narrowing-based proof search method for inductive theorems in equational rewrite theories given by a rewrite system $\mathcal{R}$ and a set E of equalities. It has the specificity to be grounded on deduction modulo and to rely on narrowing to provide both induction variables and instantiation schemas. Whenever the equational rewrite system $(\mathcal{R},E)$ has good properties of termination, sufficient completeness, and when E is constructor and variable preserving, narrowing at defined-innermost positions leads to consider only unifiers which are constructor substitutions. This is especially interesting for associative and associative-commutative theories for which the general proof search system is refined. The method is shown to be sound and refutationally correct and complete. A major feature of our approach is to provide a constructive proof in deduction modulo for each successful instance of the proof search procedure.