Abstract data types and the development of data structures
Communications of the ACM
Abstract data types and software validation
Communications of the ACM
A simplifier based on efficient decision algorithms
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A methodology for verifying programs
Proceedings of the international conference on Reliable software
Verifying programs by algebraic and logical reduction
Proceedings of the international conference on Reliable software
Proving termination and multiset orderings
Proving termination and multiset orderings
The specification and application to programming of abstract data types.
The specification and application to programming of abstract data types.
Automated theorem proving: mapping logic into AI
ISMIS '86 Proceedings of the ACM SIGART international symposium on Methodologies for intelligent systems
A knowledge-based system for computer algebra
ACM SIGSAM Bulletin
History and basic features of the critical-pair/completion procedure
Journal of Symbolic Computation
Critical pair criteria for completion
Journal of Symbolic Computation
Only prime superpositions need be considered in the Knuth-Bendix completion procedure
Journal of Symbolic Computation
Inductive methods for reasoning about abstract data types
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Stepwise refinement process with modularity
ICSE '89 Proceedings of the 11th international conference on Software engineering
A strong restriction of the inductive completion procedure
Journal of Symbolic Computation
Journal of Symbolic Computation
Automating inductionless induction using test sets
Journal of Symbolic Computation
Deductive and inductive synthesis of equational programs
Journal of Symbolic Computation - Special issue on automatic programming
Equational inference, canonical proofs, and proof orderings
Journal of the ACM (JACM)
Abstract Implementations and Their Correctness Proofs
Journal of the ACM (JACM)
A general framework to build contextual cover set
Journal of Symbolic Computation - Calculemus-99: integrating computation and deduction
Computer experiments with the REVE term rewriting system generator
POPL '83 Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Coloring Terms to Control Equational Reasoning
Journal of Automated Reasoning
Modular Verification of Data Abstractions with Shared Realizations
IEEE Transactions on Software Engineering
Heuristics for completion in automatic proofs by structural induction
Nordic Journal of Computing
Test Sets for the Universal and Existential Closure of Regular Tree Languages
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Reasoning Inductively about Z Specifications via Unification
ZB '00 Proceedings of the First International Conference of B and Z Users on Formal Specification and Development in Z and B
A constructive alternative to axiomatic data type definitions
LFP '80 Proceedings of the 1980 ACM conference on LISP and functional programming
Computer algebra handbook
Rapid prototyping: in the OBJ executable specification language
Proceedings of the workshop on Rapid prototyping
ACM SIGSOFT Software Engineering Notes
Sound generalizations in mathematical induction
Theoretical Computer Science
Automatic case analysis in proof by induction
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Annals of Mathematics and Artificial Intelligence
Strategic Issues, Problems and Challenges in Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
Inductive synthesis of equational programs
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Mechanizing inductive reasoning
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Inductive decidability using implicit induction
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Dealing with non-orientable equations in rewriting induction
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Coverset induction with partiality and subsorts: a powerlist case study
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Order-Sorted equality enrichments modulo axioms
WRLA'12 Proceedings of the 9th international conference on Rewriting Logic and Its Applications
Regular Tree Languages And Rewrite Systems
Fundamenta Informaticae
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The equational axioms of an algebraic specification of a data type (such as finite sequences) often can be formed into a convergent set of rewrite rules; i.e. such that all sequences of rewrites are finite and uniquely terminating. If one adds a rewrite rule corresponding to a data type property whose proof requires induction (such as associativity of sequence concatenation), convergence may be destroyed, but often can be restored by using the Knuth-Bendix algorithm to generate additional rules. A convergent set of rules thus obtained can be used as a decision procedure for the equational theory for the axioms plus the property added. This fact, combined with a "full specification" property of axiomatizations, leads to a new method of proof of inductive properties--not requiring the explicit invocation of an inductive rule of inference.