A Proof of Strong Normalization for the Theory of Constructions Using a Kripke-Like Interpretation

We give a proof that all terms that type-check in the theory of contructions are strongly normalizing (under ß-reduction). The main novelty of this proof is that it uses a "Kripke-like" interpretation of the types and kinds, and that it does not use infinite contexts. We explore some consequences of strong normalization, consistency and decidability of typechecking. We also show that our proof yields another proof of strong normalization for LF (under ß-reduction), using the reducibility method.