Normalisation of the Theory T of Cartesian Closed Categories and Conservativity of Extensions T [ x ] of T

• Published in: RAIRO. Informatique théorique et applications Vol. 33; no. 3; pp. 227 - 257
• Main Authors: Preller, Anne, Duroux, P.
• Format: Journal Article
• Language: English
• Published: Paris EDP Sciences 01.05.1999
• Subjects: Algebra; Category theory, homological algebra; Computer Science; Exact sciences and technology; General logic; Logic and foundations; Logic in Computer Science; Mathematical logic, foundations, set theory; Mathematics; Proof theory and constructive mathematics; Sciences and techniques of general use; Slide rule; Chemical reduction; Rewrite system; Evaluation; Decidability; Completeness; Category theory; Normal form; Automatic proving; Church Roser system; Evaluation rule; Complexity; cc:18D15; cc:03F05; cc:03B25

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 suc...