  We develop a denotational semantics for general reference types in an
impredicative version of guarded homotopy type theory, an adaptation of
synthetic guarded domain theory to Voevodsky's univalent foundations. We
observe for the first time the profound impact of univalence on the
denotational semantics of mutable state. Univalence automatically ensures that
all computations are invariant under symmetries of the heap -- a bountiful
source of program equivalences. In particular, even the most simplistic
univalent model enjoys many new equations that do not hold when the same
constructions are carried out in the universes of traditional set-level
(extensional) type theory.
