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.