@tito @julesh @fl Tito has some very interesting work with Cécilia Pradic on the expressivity problem in extensions of simply-typed lambda calculus with a affine/linear/ordered linear implication, see the "Implicit automata in typed λ-calculi" series (https://nguyentito.eu/2023-06-oxford.pdf). One of their exciting results is that in the planar case you can recover exactly the star-free languages (https://en.wikipedia.org/wiki/Star-free_language).
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