An algorithm for optimal lambda calculus reduction
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The geometry of optimal lambda reduction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A natural semantics for lazy evaluation
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A call-by-need lambda calculus
POPL '95 Proceedings of the 22nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
On global dynamics of optimal graph reduction
ICFP '97 Proceedings of the second ACM SIGPLAN international conference on Functional programming
Combinatory weak reduction in lambda calculus
Theoretical Computer Science
The optimal implementation of functional programming languages
The optimal implementation of functional programming languages
Explicit Substitutions and Programming Languages
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
Closed Reductions in the lambda-Calculus
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
(Optimal) duplication is not elementary recursive
Information and Computation
A Fully Labelled Lambda Calculus: Towards Closed Reduction in the Geometry of Interaction Machine
Electronic Notes in Theoretical Computer Science (ENTCS)
Minimality in a Linear Calculus with Iteration
Electronic Notes in Theoretical Computer Science (ENTCS)
The weak lambda calculus as a reasonable machine
Theoretical Computer Science
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Despite decades of research in the λ-calculus, the syntactic properties of the weak λ-calculus did not receive great attention. However, this theory is more relevant for the implementation of programming languages than the usual theory of the strong λ-calculus. In fact, the frameworks of weak explicit substitutions, or computational monads, or λ-calculus with a let statement, or super-combinators, were developed for adhoc purposes related to programming language implementation. In this paper, we concentrate on sharing of subterms in a confluent variant of the weak λ-calculus. We introduce a labeling of this calculus that expresses a confluent theory of reductions with sharing, independent of the reduction strategy. We finally state that Wadsworth's evaluation technique with sharing of subterms corresponds to our formal setting.