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From Reversible Programs to Univalent Universes and Back (1708.02710v1)
Published 9 Aug 2017 in cs.PL and cs.LO
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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