Needed reduction and spine strategies for the lambda calculus
Information and Computation
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
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
Combinatory weak reduction in lambda calculus
Theoretical Computer Science
Lambda-dropping: transforming recursive equations into programs with block structure
Theoretical Computer Science - Partial evaluation and semantics-based program manipulation
Optimal Normalization in Orthogonal Term Rewriting Systems
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Relative Normalization in Deterministic Residual Structures
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
A unified approach to fully lazy sharing
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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In this paper we investigate laziness and optimal evaluation strategies for functional programming languages. We consider the weak lambda-calculus as a basis of functional programming languages, and we adapt to this setting the concepts of optimal reductions that were defined for the full lambda-calculus. We prove that the usual implementation of call-by-need using sharing is optimal, that is, normalizing any lambda-term with call-by-need requires exactly the same number of reduction steps as the shortest reduction sequence in the weak lambda-calculus without sharing. Furthermore, we prove that optimal reduction sequences without sharing are not computable. Hence sharing is the only computable means to reach weak optimality.