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

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...

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Bibliographic Details
Published inRAIRO. Informatique théorique et applications Vol. 33; no. 3; pp. 227 - 257
Main Authors Preller, Anne, Duroux, P.
Format Journal Article
LanguageEnglish
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
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Summary: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.
ISSN:0988-3754
1290-385X
DOI:10.1051/ita:1999115