(Enter summary)
Abstract: In a previous work, we proved that an important part of the Calculus of Inductive Constructions
(CIC), the basis of the Coq proof assistant, can be seen as a Calculus of Algebraic Constructions
(CAC), an extension of the Calculus of Constructions with functions and predicates defined
by higher-order rewrite rules. In this paper, we prove that almost all CIC can be seen as a
CAC, and that it can be further extended with non-strictly positive types and inductive-recursive
types together with... (Update)
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BibTeX entry: (Update)
F. Blanqui. Inductive types in the Calculus of Algebraic Constructions. In and Applications, Lecture Notes in Computer Science 2701, 2003. http://citeseer.ist.psu.edu/article/blanqui05inductive.html More
@misc{ blanqui03inductive,
author = "F. Blanqui",
title = "Inductive types in the Calculus of Algebraic Constructions",
text = "F. Blanqui. Inductive types in the Calculus of Algebraic Constructions.
In and Applications, Lecture Notes in Computer Science 2701, 2003.",
year = "2003",
url = "citeseer.ist.psu.edu/article/blanqui05inductive.html" }
Citations (may not include all citations):
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Rewrite Systems
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Lambda Calculi with types
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Proofs and Types (context) - Girard, Lafont et al. - 1988
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Information and Computation (context) - Coquand, Huet - 1988
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Counterexamples to termination for the direct sum of term re.. (context) - Toyama - 1987
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Inductively defined types (context) - Coquand, Paulin-Mohring - 1988
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Combinatory reduction systems: introduction and survey
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An Analysis of Girard's Paradox
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by Iteration and Primitive Recursion on Monotone Inductive T.. (context) - Matthes, Extensions - 1998
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Theoretical Computer Science (context) - Jouannaud, Okada - 1997
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Executable Higher-Order Algebraic Specification Languages (context) - Jouannaud, Okada - 1991
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Modularity of strong normalization and confluence in the alg..
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A general formulation of simultaneous inductive-recursive de..
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Inductive Definition in Type Theory (context) - Mendler - 1987
18
Dependently typed functional programs and their proofs
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14
Strong Normalizability for the Combined System of the Typed .. (context) - Okada - 1989
10
Confluence for Abstract and Higher-Order Rewriting (context) - van Oostrom - 1994
10
Termination Checking with Types
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9
Parametricity and variants of Girard's J operator
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8
Polymorphic Rewriting Conserves Algebraic Strong Normalizati.. (context) - Breazu-Tannen, Gallier - 1989
7
Une Thorie des Constructions Inductives (context) - Werner - 1994
6
Type Theory and Rewriting
- Blanqui, Thorie - 2001
5
Definitions by rewriting in the Calculus of Constructions
- Blanqui - 2005
5
Definitions by rewriting in the Calculus of Constructions
- Blanqui - 2001
4
Katholiecke Universiteit Nijmegen (context) - Stefanova, Properties - 1998
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Dependently typed records in type theory (context) - Pollack - 2002
2
Personal communication (context) - Paulin-Mohring - 2001
1
Coq-Development-Team: The Coq Proof Assistant Reference Manu.. (context) - Team, Proof et al. - 2004
1
Termination of rewriting in the Calculus of Constructions (context) - aszcz - 2003
1
Confluence of the lambda calculus with left-linear algebraic.. (context) - Mller - 1992
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