We present a new approach to introducing an extensional propositional equality in Intensional Type Theory. Our construction is based on the observation that there is a sound, inte...
In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general m...
Abstract. We consider an extensional version, called qmTT, of the intensional Minimal Type Theory mTT, introduced in a previous paper with G. Sambin, enriched with proof-irrelevanc...
A definitional extension LNGMIt of the Calculus of Inductive Constructions (CIC), that underlies the proof assistant Coq, is presented that allows also to program with nested dat...