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Automatic proofs by induction in theories without constructors
Information and Computation
Tools for proving inductive equalities, relative completeness, and &ohgr;-completeness
Information and Computation
Handbook of theoretical computer science (vol. B)
Testing for the ground (co-)reducibility property in term-rewriting systems
CAAP '90 Selected papers of the conference on Fifteenth colloquium on trees in algebra and programming
Using induction and rewriting to verify and complete parameterized specifications
Theoretical Computer Science
ALP Proceedings of the fourth international conference on Algebraic and logic programming
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System Presentation -- CARIBOO: An induction based proof tool for termination with strategies
Proceedings of the 4th ACM SIGPLAN international conference on Principles and practice of declarative programming
Context-sensitive rewriting strategies
Information and Computation
Theoretical Computer Science - Rewriting logic and its applications
Maude: specification and programming in rewriting logic
Theoretical Computer Science - Rewriting logic and its applications
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LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Termination of Rewriting With Strategy Annotations
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
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Proceedings of the 12th Colloquium on Automata, Languages and Programming
Termination of Context-Sensitive Rewriting by Rewriting
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
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EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
TEA: Automatically Proving Termination of Programs in a Non-strict Higher-Order Functional Language
SAS '97 Proceedings of the 4th International Symposium on Static Analysis
Transforming Context-Sensitive Rewrite Systems
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Stratego: A Language for Program Transformation Based on Rewriting Strategies
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
A decidability result about sufficient-completeness of axiomatically specified abstract data types
Proceedings of the 6th GI-Conference on Theoretical Computer Science
Encompassment Properties and Automata with Constraints
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
On Proving Termination by Innermost Termination
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Proving Innermost Normalisation Automatically
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
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Proceedings of the 3rd ACM SIGPLAN international conference on Principles and practice of declarative programming
Ground Reducibility is EXPTIME-complete
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Computing constructor forms with non terminating rewrite programs
Proceedings of the 8th ACM SIGPLAN international conference on Principles and practice of declarative programming
Proofs by induction in equational theories with constructors
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
Innermost termination of context-sensitive rewriting
DLT'02 Proceedings of the 6th international conference on Developments in language theory
A pattern matching compiler for multiple target languages
CC'03 Proceedings of the 12th international conference on Compiler construction
A proof of weak termination providing the right way to terminate
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Orderings for innermost termination
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
A sufficient completeness reasoning tool for partial specifications
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Automated termination analysis for Haskell: from term rewriting to programming languages
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Termination of rewriting under strategies
ACM Transactions on Computational Logic (TOCL)
Analysis of Rewrite-Based Access Control Policies
Electronic Notes in Theoretical Computer Science (ENTCS)
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We describe in this paper an inductive proof method for properties of reduction relations. The reduction trees are simulated with proof trees generated by narrowing and an abstraction mechanism. While narrowing simulates reduction, abstraction relies on the induction principle to replace subterms by variables representing specific reduced forms that trivially satisfy the property to be proved. The induction ordering is not given a priori, but defined with ordering constraints, incrementally set during the proof. Abstraction constraints are used to control the narrowing mechanism, well-known to easily diverge. The proof method is briefly illustrated on various examples of properties.