Introduction to combinators and &lgr;-calculus
Introduction to combinators and &lgr;-calculus
A proof theory for general unification
A proof theory for general unification
Unification under a mixed prefix
Journal of Symbolic Computation
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
Coloring Terms to Control Equational Reasoning
Journal of Automated Reasoning
LACL '96 Selected papers from the First International Conference on Logical Aspects of Computational Linguistics
Polymorphic Rewriting Conserves Algebraic Strong Normalization and Confluence
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Higher-Order Annotated Terms for Proof Search
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Using Rippling for Equational Reasoning
KI '96 Proceedings of the 20th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
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
The Use of Proof Plans to Sum Series
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Decidable Higher-Order Unification Problems
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Higher-Order Coloured Unification and natural language semantics
ACL '96 Proceedings of the 34th annual meeting on Association for Computational Linguistics
Computing parallelism in discourse
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
Annals of Mathematics and Artificial Intelligence
System Description: inka 5.0 - A Logic Voyager
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Handbook of automated reasoning
Strategic Issues, Problems and Challenges in Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
The Use of Embeddings to Provide a Clean Separation of Term and Annotation for Higher Order Rippling
Journal of Automated Reasoning
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Coloring terms (rippling) is a technique developed for inductive theorem proving that uses syntactic differences of terms to guide the proof search. Annotations (colors) to symbol occurrences in terms are used to maintain this information. This technique has several advantages; for example, it is highly goal oriented and involves little search. In this paper we give a general formalization of coloring terms in a higher-order setting. We introduce a simply typed λ calculus with color annotations and present appropriate algorithms for the general, pre-, and pattern unification problems. Our work is a formal basis to the implementation of rippling in a higher-order setting, which is required, for example, in the case of middle-out reasoning. Another application is in the construction of natural the language semantics, where the color annotations rule out linguistically invalid readings that are possible using standard higher-order unification.