&bgr;-reductions and &bgr;-developments of &lgr;-terms with the least number of steps
COLOG-88 Proceedings of the international conference on Computer logic
An algorithm for optimal lambda calculus reduction
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Handbook of logic in computer science (vol. 2)
Paths, computations and labels in the &lgr;-calculus
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
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
Perpetuality and uniform normalization in orthogonal rewrite systems
Information and Computation
The Geometry of Orthogonal Reduction Spaces
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Confluence and Superdevelopments
RTA '93 Proceedings of the 5th 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
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
The conflict-free reduction geometry
Theoretical Computer Science
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We investigate the degree of parallelism (or modularity) in the hyperbalanced 驴-calculus, 驴H, a subcalculus of 驴-calculus containing all simply typable terms (up to a restricted 驴-expansion). In technical terms, we study the family relation on redexes in 驴H, and the contribution relation on redex-families, and show that the latter is a forest (as a partial order). This means that hyperbalanced 驴-terms allow for maximal possible parallelism in computation. To prove our results, we use and further refine, for the case of hyperbalanced terms, some well known results concerning paths, which allow for static analysis of many fundamental properties of 脽-reduction.