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Modular proof of strong normalization for the calculus of constructions

Abstract We present a modular proof of strong normalization for the Calculus of Constructions of Coquand and Huet (1985, 1988). This result was first proved by Coquand (1986), but our proof is more perspicious. The method consists of a little juggling with some systems in the cube of Barendregt (1989), which provides a fine structure of the calculus of constructions. It is proved that the strong normalization of the calculus of constructions is equivalent with the strong normalization of Fω. In order to give the proof, we first establish some properties of various type systems. Therefore, we present a general framework of typed lambda calculi, including many well-known ones.