Theoretical Computer Science
On the Church-Rosser property for the direct sum of term rewriting systems
Journal of the ACM (JACM)
Conditional rewrite rules: Confluence and termination
Journal of Computer and System Sciences
Computable values can be classical
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Notes on the elimination of conditions
1st international workshop on Conditional Term Rewriting Systems
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Extending the lambda calculus with surjective pairing is conservative
Proceedings of the Fourth Annual Symposium on Logic in computer science
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
Polymorphic rewriting conserves algebraic confluence
Information and Computation
Parallel reductions in &lgr;-calculus
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
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
On the Representation of Data in Lambda-Calculus
CSL '89 Proceedings of the 3rd Workshop on Computer Science Logic
Confluence of the Disjoint Union of Conditional Term Rewriting Systems
Proceedings of the 2nd International CTRS Workshop on Conditional and Typed Rewriting Systems
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
On the confluence of λ-calculus with conditional rewriting
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Expression reduction systems and extensions: an overview
Processes, Terms and Cycles
| Hi-index | 5.23 |
The confluence of untyped @l-calculus with unconditional rewriting is now well un- derstood. In this paper, we investigate the confluence of @l-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Muller and Dougherty for unconditional rewriting. Two cases are considered, whether @b-reduction is allowed or not in the evaluation of conditions. Moreover, Dougherty's result is improved from the assumption of strongly normalizing @b-reduction to weakly normalizing @b-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.