A model of guarded recursion via generalised equilogical spaces

Abstract

We present a new model, called GuardedEqu, of guarded dependent type theory using generalised equilogical spaces. GuardedEqu models guarded recursive types, which can be used to program with coinductive types and we prove that GuardedEqu ensures that all definable functions on coinductive types, e.g., streams, are continuous with respect to the natural topology. We present a direct, elementary, construction of the new model, which, importantly, is coherent (split) by construction.