A rationale for conditional equational programming
Theoretical Computer Science - Special issue on the international conference on fifth generation computer systems. Tokyo, 1988
Handbook of theoretical computer science (vol. B)
Confluence of the lambda calculus with left-linear algebraic rewriting
Information Processing Letters
Adding algebraic rewriting to the untyped lambda calculus
Information and Computation
Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Completeness of combinations of conditional constructor systems
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Polymorphic rewriting conserves algebraic confluence
Information and Computation
ALP Proceedings of the fourth international conference on Algebraic and logic programming
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Weak Orthogonality Implies Confluence: The Higher Order Case
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Lambda-Calculi with Conditional Rules
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Higher Order Conditional Rewriting and Narrowing
CCL '94 Proceedings of the First International Conference on Constraints in Computational Logics
Journal of Automated Reasoning
Modularity of strong normalization in the algebraic-λ-cube
Journal of Functional Programming
Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
Advanced Topics in Term Rewriting
Advanced Topics in Term Rewriting
On the confluence of lambda-calculus with conditional rewriting
Theoretical Computer Science
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
| Hi-index | 0.00 |
The confluence of untyped λ-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of λ-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Müller and Dougherty for unconditional rewriting. Two cases are considered, whether beta-reduction is allowed or not in the evaluation of conditions. Moreover, Dougherty's result is improved from the assumption of strongly normalizing β-reduction to weakly normalizing β-reduction. We also provide examples showing that outside these conditions, modularity of confluence is difficult to achieve. Second, we go beyond the algebraic framework and get new confluence results using a restricted notion of orthogonality that takes advantage of the conditional part of rewrite rules.