Computational semantics of term rewriting systems
Algebraic methods in semantics
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
Optimal derivations in weak lambda-calculi and in orthogonal term rewriting systems
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Handbook of logic in computer science (vol. 2)
Event structures and orthogonal term graph rewriting
Term graph rewriting
Handbook of logic in computer science (vol. 4)
Parallel beta reduction is not elementary recursive
POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The optimal implementation of functional programming languages
The optimal implementation of functional programming languages
Minimal and Optimal Computations of Recursive Programs
Journal of the ACM (JACM)
Communication and Concurrency
Relating Conflict-Free Stable Transition and Event Models (Extended Abstract)
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Relating Two Categorial Models of Term Rewriting
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
On Relating Rewriting Systems and Graph Grammars to Event Structures
Proceedings of the International Workshop on Graph Transformations in Computer Science
Discrete Normalization and Standardization in Deterministic Residual Structures
ALP '96 Proceedings of the 5th International Conference on Algebraic and Logic Programming
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
A Factorisation Theorem in Rewriting Theory
CTCS '97 Proceedings of the 7th International Conference on Category Theory and Computer Science
Relative Normalization in Orthogonal Expression Reduction Systems
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
The conflict-free reduction geometry
Theoretical Computer Science
Residuals in higher-order rewriting
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Stable computational semantics of conflict-free rewrite systems (partial orders with duplication)
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Expression reduction systems and extensions: an overview
Processes, Terms and Cycles
Proof pearl: abella formalization of λ-calculus cube property
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
Hi-index | 5.23 |
We describe an event-style (or poset) semantics for conflict-free rewrite systems, including term and graph rewriting (possibly with bound variables), the λ-calculus, and other stable transition systems with a residual relation. Our interpretation is based on considering redex-families as events. It treats permutation-equivalent reductions as representing the same concurrent computation. Due to erasure of redexes, event structures are inadequate for such an interpretation. We therefore extend the prime event structure model in two different but equivalent ways: by axiomatizing permutation-equivalence on finite configurations, and by axiomatizing the erasure of events, for the conflict-free case, and show that these extended models are equivalent to stable transition models with axiomatized residual and family relations. We then construct finitary prime algebraic domains from the set of configurations in these extended models by defining orderings relative to stable sets of 'results'. All useful sets of results for which the normalization (by neededness) theorem can be proved are stable.