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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| Published in | RAIRO. Informatique théorique et applications Vol. 33; no. 3; pp. 227 - 257 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Paris
EDP Sciences
01.05.1999
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| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Duroux, P. Preller, Anne |
| Author_xml | – sequence: 1 givenname: Anne surname: Preller fullname: Preller, Anne – sequence: 2 givenname: P. surname: Duroux fullname: Duroux, P. |
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| Cites_doi | 10.1007/3-540-60164-3_27 10.1016/0890-5401(87)90018-6 10.1007/978-1-4612-2572-0_6 10.1109/LICS.1991.151645 |
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| Copyright | 1999 INIST-CNRS Distributed under a Creative Commons Attribution 4.0 International License |
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| Keywords | 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 |
| Language | English |
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| SubjectTerms | 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 |
| Title | Normalisation of the Theory T of Cartesian Closed Categories and Conservativity of Extensions T [ x ] of T |
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