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
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
YALE: yet another lambda evaluator based on interaction nets
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Explicit substitution on the edge of strong normalization
Theoretical Computer Science
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Closed reduction: explicit substitutions without $\alpha$-conversion
Mathematical Structures in Computer Science
The Implementation of Functional Programming Languages (Prentice-Hall International Series in Computer Science)
Encoding Distributed Process Calculi into LMNtal
Electronic Notes in Theoretical Computer Science (ENTCS)
LMNtal: a language model with links and membranes
WMC'04 Proceedings of the 5th international conference on Membrane Computing
Call-by-name and call-by-value as token-passing interaction nets
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
ICTAC '09 Proceedings of the 6th International Colloquium on Theoretical Aspects of Computing
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Fine-grained reformulation of the lambda calculus is expected to solve several difficulties with the notion of substitutions--definition, implementation and cost properties. However, previous attempts including those using explicit substitutions and those using Interaction Nets were not ideally simple when it came to the encoding of the pure (as opposed to weak) lambda calculus. This paper presents a novel, fine-grained, and highly asynchronous encoding of the pure lambda calculus using LMNtal, a hierarchical graph rewriting language, and discusses its properties. The major strength of the encoding is that it is significantly simpler than previous encodings, making it promising as an alternative formulation, rather than just the encoding, of the pure lambda calculus. The membrane construct of LMNtal plays an essential role in encoding colored tokens and operations on them. The encoding has been tested using the publicly available LMNtal implementation.