Artificial Intelligence
Automatic proofs by induction in theories without constructors
Information and Computation
A strong restriction of the inductive completion procedure
Journal of Symbolic Computation
Automating inductionless induction using test sets
Journal of Symbolic Computation
Automated theorem proving by test set induction
Journal of Symbolic Computation
Term rewriting and all that
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
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
Extending Decision Procedures with Induction Schemes
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Decidable Classes of Inductive Theorems
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Software verification with BLAST
SPIN'03 Proceedings of the 10th international conference on Model checking software
Superposition for fixed domains
ACM Transactions on Computational Logic (TOCL)
Deciding the inductive validity of ∀∃* queries
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
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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Decision procedures are widely used in automated reasoning tools in order to reason about data structures. In applications, many conjectures fall outside the theory handled by a decision procedure. Often, reasoning about user-defined functions on those data structures is needed. For this, inductive reasoning has to be employed. In this work, classes of function definitions and conjectures are identified for which inductive validity can be automatically decided using implicit induction methods and decision procedures for an underlying theory. The class of equational conjectures considered in this paper significantly extends the results of Kapur & Subramaniam (CADE, 2000) [15], which were obtained using explicit induction schemes. Firstly, nonlinear conjectures can be decided automatically. Secondly, function definitions can use other defined functions in their definitions, thus allowing mutually recursive functions and decidable conjectures about them. Thirdly, conjectures can have general terms from the decidable theory on inductive positions. These contributions are crucial for successfully integrating inductive reasoning into decision procedures, thus enabling their use in push-button mode in applications including verification and program analysis.