Many models of the untyped -calculus are so-called webbed models. This means that the domain over which the -calculus is interpreted is a substructure of the algebraic lattice
for some set . The set is called the web of the model.
The terminology appears to be due to [Berline 2000].
The construction of many webbed models is fairly elementary. Thus, they are often used in the semantics of various applied calculi.
Webbed models include:
Berline, Chantal. ‘From Computation to Foundations via Functions and Application: The λ-Calculus and Its Webbed Models’. Theoretical Computer Science 249, no. 1 (2000): 81–161. https://doi.org/10.1016/S0304-3975(00)00057-8.
@article{berline_2000,
title = {From computation to foundations via functions and application: The λ-calculus and its webbed models},
volume = {249},
doi = {10.1016/S0304-3975(00)00057-8},
pages = {81--161},
number = {1},
journaltitle = {Theoretical Computer Science},
author = {Berline, Chantal},
date = {2000},
}
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