Conditional rewrite rules: Confluence and termination
Journal of Computer and System Sciences
Common LISP: the language
Computing in Horn clause theories
Computing in Horn clause theories
A computational logic handbook
A computational logic handbook
Confluence of conditional rewrite systems
1st international workshop on Conditional Term Rewriting Systems
Positive/negative conditional rewriting
1st international workshop on Conditional Term Rewriting Systems
ML for the working programmer
Semantics of order-sorted specifications
Theoretical Computer Science
Handbook of logic in computer science (vol. 1): background: mathematical structures
Handbook of logic in computer science (vol. 1): background: mathematical structures
A constructor-based approach to positive/negative-conditional equational specifications
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Handbook of logic in artificial intelligence and logic programming
Handbook of logic in artificial intelligence and logic programming
Handbook of logic in artificial intelligence and logic programming (vol. 1)
Handbook of logic in artificial intelligence and logic programming (vol. 1)
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
A framework for operational equational specifications with pre-defined structures
Journal of Symbolic Computation
Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
Logicality of conditional rewrite systems
Theoretical Computer Science - Trees in algebra and programming
Swinging types = functions + relations + transition systems
Theoretical Computer Science
Formal Techniques in Artificial Intelligence: A SourceBook
Formal Techniques in Artificial Intelligence: A SourceBook
Handbook of Theoretical Computer Science
Handbook of Theoretical Computer Science
Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
Programming of Future Generation Computers II: Proceedings of the 2nd Franco-Japanese Symposium
Programming of Future Generation Computers II: Proceedings of the 2nd Franco-Japanese Symposium
On Conditional Rewrite Systems with Extra Variables and Deterministic Logic Programs
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
Weak Orthogonality Implies Confluence: The Higher Order Case
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Function Definition in Higher-Order Logic
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Completion-Time Optimization of Rewrite-Time Goal Solving
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
Level-Confluence of Conditional Rewrite Systems with Extra Variables in Right-Hand Sides
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Higher Order Conditional Rewriting and Narrowing
CCL '94 Proceedings of the First International Conference on Constraints in Computational Logics
Confluence without Termination via Parallel Critical Pairs
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
Canonical Conditional Rewrite Systems
Proceedings of the 9th International Conference on Automated Deduction
On Notions of Inductive Validity for First-Oder Equational Clauses
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Semantics for Positive/Negative Conditional Rewrite Systems
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
A New Parallel Closed Condition for Church-Rossser of Left-Linear Term Rewriting Systems
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Handbook of automated reasoning
Handbook of automated reasoning
Mechanizing Mathematical Reasoning: Essays in Honor of Jörg H. Siekmann on the Occasion of His 60th Birthday (Lecture Notes in Computer Science / Lecture Notes in Artificial Intelligence)
An Even Closer Integration of Linear Arithmetic into Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
lim+, δ+, and Non-Permutability of β-Steps
Journal of Symbolic Computation
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Recursion can be conveniently modeled with left-linear positive/negative-conditional term rewriting systems, provided that non-termination, non-trivial critical overlaps, non-right-stability, non-normality, and extra variables are admitted. For such systems we present novel sufficient criteria for shallow confluence and arrive at the first decidable confluence criterion admitting non-trivial critical overlaps. To this end, we restrict the introduction of extra variables of right-hand sides to binding equations and require the critical pairs to have somehow complementary literals in their conditions. Shallow confluence implies [level] confluence, has applications in functional logic programming, and guarantees the object-level consistency of the underlying data types in the inductive theorem prover QuodLibet.