Artificial Intelligence
A many-sorted calculus based on resolution and paramodulation
A many-sorted calculus based on resolution and paramodulation
Automatic proofs by induction in theories without constructors
Information and Computation
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The Use of Planning Critics in Mechanizing Inductive Proofs
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Deduction in the Verification Support Environment (VSE)
FME '96 Proceedings of the Third International Symposium of Formal Methods Europe on Industrial Benefit and Advances in Formal Methods
Using Rippling for Equational Reasoning
KI '96 Proceedings of the 20th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
How to Prove Algebraic Inductive Hypotheses Without Induction
Proceedings of the 5th Conference on Automated Deduction
The Karlsruhe Induction Theorem Proving System
Proceedings of the 8th International Conference on Automated Deduction
The Use of Explicit Plans to Guide Inductive Proofs
Proceedings of the 9th International Conference on Automated Deduction
Proceedings of the 10th International Conference on Automated Deduction
Extensions to the Rippling-Out Tactic for Guiding Inductive Proofs
Proceedings of the 10th International Conference on Automated Deduction
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Synthesis of Induction Orderings for Existence Proofs
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Equations and rewrite rules: a survey
Equations and rewrite rules: a survey
Annals of Mathematics and Artificial Intelligence
Managing Structural Information by Higher-Order Colored Unification
Journal of Automated Reasoning
VSE: Controlling the Complexity in Formal Software Developments
FM-Trends 98 Proceedings of the International Workshop on Current Trends in Applied Formal Method: Applied Formal Methods
System Description: inka 5.0 - A Logic Voyager
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Strategic Issues, Problems and Challenges in Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
A survey of automated deduction
Artificial intelligence today
Reasoning, Action and Interaction in AI Theories and Systems
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In this article we present an approach to prove the equality between terms in a goal-directed way developed in the field of inductive theorem proving. The two terms to be equated are syntactically split into expressions that are common to both and those that occur only in one term. According to the computed differences we apply appropriate equations to the terms in order to reduce the differences in a goal-directed way. Although this approach was developed for purposes of inductive theorem proving – we use this technique to manipulate the conclusion of an induction step to enable the use of the hypothesis – it is also a powerful method for the control of equational reasoning in general.