  We contribute the first denotational semantics of polymorphic dependent type
theory extended by an equational theory for general (higher-order) reference
types and recursive types, based on a combination of guarded recursion and
impredicative polymorphism; because our model is based on recursively defined
semantic worlds, it is compatible with polymorphism and relational reasoning
about stateful abstract datatypes. We then extend our language with modal
constructs for proof-relevant relational reasoning based on the "logical
relations as types" principle, in which equivalences between imperative
abstract datatypes can be established synthetically. What is new in relation to
prior typed denotational models of higher-order store is that our Kripke worlds
need not be syntactically definable, and are thus compatible with relational
reasoning in the heap. Our work combines recent advances in the operational
semantics of state with the purely denotational viewpoint of synthetic guarded
domain theory.
