Two Guarded Recursive Powerdomains for Applicative Simulation

Clocked Cubical Type Theory is a new type theory combining the power of guarded recursion with univalence and higher inductive types (HITs). This can be used as metalanguage for synthetic domain in which one solve recursive equations, also negative variable occurrences, use these to construct models reasoning about programming languages. Combining this HITs allows constructors familiar from set-theory based approaches semantics, such quotients finite powersets models. In paper we show how reason combination non-determinism theory. Unlike traditional takes an ordering programs primitive, notion computation step primitive form modal operator. We extra intensional information define two (finite) powerdomain constructions differing way interacts steps. As example application prove applicative similarity congruence cases may- must-convergence untyped lambda calculus non-determinism. Such results are usually proved using operational Howe's method. Here adaptation denotational method developed by Pitts context