From Reversible Programs to Univalent Universes and Back
arXiv:1708.02710 · doi:10.1016/j.entcs.2018.03.013
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.