On termination of the direct sum of term-rewriting systems
Information Processing Letters
Theoretical Computer Science
An algorithm for optimal lambda calculus reduction
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Recursive applicative program schemes
Handbook of theoretical computer science (vol. B)
Handbook of logic in computer science (vol. 2)
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ACM Transactions on Programming Languages and Systems (TOPLAS)
Relating conflict-free stable transition and event models via redex families
Theoretical Computer Science
Relating Conflict-Free Stable Transition and Event Models (Extended Abstract)
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
beta-reductions and beta developments of lambda terms with the least number of steps
COLOG '88 Proceedings of the International Conference on Computer Logic
The Geometry of Orthogonal Reduction Spaces
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Static Analysis of Modularity of beta-Reduction in the Hyperbalanced lambda-Calculus
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Optimal Normalization in Orthogonal Term Rewriting Systems
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Discrete Normalization and Standardization in Deterministic Residual Structures
ALP '96 Proceedings of the 5th International Conference on Algebraic and Logic Programming
Normalization of Typable Terms by Superdevelopments
Proceedings of the 12th International Workshop on Computer Science Logic
Relative Normalization in Deterministic Residual Structures
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
An introduction to event structures
Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop
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CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Relative Normalization in Orthogonal Expression Reduction Systems
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
Expression reduction systems and extensions: an overview
Processes, Terms and Cycles
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We investigate mutual dependencies of subexpressions of computable expressions in orthogonal rewrite systems, and identify conditions for their independent concurrent computation. To this end, we introduce concepts familiar from ordinary Euclidean Geometry (such as basis, projection, distance, etc.) for reduction spaces. We show how a basis at an expression can be constructed so that any reduction starting from that expression can be decomposed as the sum of its projections on the axes of the basis. To make the concepts computationally more relevant, we relativize them w.r.t. stable sets of results (such as the set of normal forms, head-normal forms, and weak-head-normal forms, in the λ-calculus), and show that an optimal concurrent computation of an expression w.r.t. S consists of optimal computations of its S-independent subexpressions. All these results are obtained in the framework of Deterministic Family Structures, which are Abstract Reduction Systems with axiomatized residual and family relations on redexes, that model all orthogonal rewrite systems.