From Reversible Programs to Univalent Universes and Back
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Abstract
We establish a close connection between a reversible programming language based on type isomorphisms and a formally presented univalent universe. The correspondence relates combinators witnessing type isomorphisms in the programming language to paths in the univalent universe; and combinator optimizations in the programming language to 2-paths in the univalent universe. The result suggests a simple computational interpretation of paths and of univalence in terms of familiar programming constructs whenever the universe in question is computable.
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Carette, Jacques, et al. "From Reversible Programs to Univalent Universes and Back." Electronic Notes in Theoretical Computer Science, vol. 336, pp. 43610, 2018-4-16, https://doi.org/10.1016/j.entcs.2018.03.013.
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Electronic Notes in Theoretical Computer Science