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Conor McBride. “Everybody’s Got To Be Somewhere”. In Proceedings MSFP 2018, EPTCS 275, 2018, pp. 53-69.
Girard's linear logic can be used to model programming languages in which each bound variable name has exactly one "occurrence"—i.e., no variable can have implicit "fan-out"; multiple uses require explicit duplication. Among other nice properties, "linear" languages need no garbage collector, yet have no dangling reference problems. We show a natural equivalence between a "linear" programming language and a stack machine in which the top items can undergo arbitrary permutations. Such permutation stack machines can be considered combinator abstractions of Moore's Forth programming language.
@article{McBride_2018,
title={Everybody’s Got To Be Somewhere},
volume={275},
ISSN={2075-2180},
url={http://dx.doi.org/10.4204/EPTCS.275.6},
DOI={10.4204/eptcs.275.6},
journal={Electronic Proceedings in Theoretical Computer Science},
publisher={Open Publishing Association},
author={McBride, Conor},
year={2018},
month=jul, pages={53–69} }