Normalisation of the Theory T of Cartesian Closed Categories and Conservativity of Extensions T [ x ] of T - Preller, Anne; Duroux, P. (RAIRO. Informatique théorique et applications, 1999)
Using an inductive definition of normal terms of the theory of Cartesian Closed Categories with a given graph of distinguished morphisms, we give a reduction free proof of the decidability of this theory. This inductive definition enables us to show via functional completeness that extensions of such a theory by new constants (“indeterminates”) are conservative.