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Abstract: . We prove strong normalization of fi-reduction+j-expansion for the Calculus of Constructions, thus providing the first strong normalization result for fi-reduction+j-expansion in calculi of dependent types and answering in the affirmative a conjecture by Di Cosmo and Ghani. In addition, we prove strong normalization of fi-reduction+j-expansion+algebraic reduction for the Algebraic Calculus of Constructions, which extends the Calculus of Constructions with first-order term-rewriting systems.... (Update)
Context of citations to this paper: More
...fij for the Calculus of Constructions, and conjectures that his results can be generalized to Pure Type Systems. In a companion paper [4], we prove strong normalization of fij for the Calculus of Constructions, thereby answering in the positive another conjecture by Di...
.... same solution for the Calculus of Constructions, although the combination of j expansion with dependent types is somewhat intricate [6, 16]. Addressing these issues should bring us closer to our overall objective, namely to integrate constructor subtyping as a primitive in...
Cited by: More
Syntactic Analysis of eta-Expansions - In Pure Type (Correct)
Constructor subtyping in the Calculus of Inductive.. - Barthe, van Raamsdonk (2000) (Correct)
Existence and Uniqueness of Normal Forms in Pure Type Systems.. - Barthe (1998) (Correct)
Active bibliography (related documents): More All
0.8: A Notion of Classical Pure Type System - Barthe, Hatcliff, Sørensen (1997) (Correct)
0.6: An Induction Principle for Pure Type Systems - Barthe, Hatcliff, Sørensen (1998) (Correct)
0.5: On the Subject Reduction Property for Algebraic Type Systems - Barthe, Melliès (1997) (Correct)
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0.7: Type-checking Injective Pure Type Systems - Barthe (1993) (Correct)
0.6: Weak Normalization Implies Strong Normalization in.. - Barthe, Hatcliff.. (1997) (Correct)
0.3: On Zucker's isomorphism for LJ and its extension to Pure Type.. - Joachimski (2003) (Correct)
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2: A modular proof of strong normalisation for the calculus of constructions (context) - Geuvers, Nederhof - 1991
2: Eta-expansion in dependent type theory --- the Calculus of Constructions - Ghani - 1997
2: The Coq Proof Assistant User's Guide (context) - Barras - 1998
BibTeX entry: (Update)
G. Barthe. Expanding the cube. In W. Thomas, editor, Proceedings of FOSSACS'99, volume 1xxx of Lecture Notes in Computer Science. Springer-Verlag, 1999. To appear. http://citeseer.ist.psu.edu/barthe99expanding.html More
@inproceedings{ barthe99expanding,
author = "Gilles Barthe",
title = "Expanding the Cube",
booktitle = "Foundations of Software Science and Computation Structure",
pages = "90-103",
year = "1999",
url = "citeseer.ist.psu.edu/barthe99expanding.html" }
Citations (may not include all citations):474 Term-rewriting systems - Klop - 1992
382 Lambda calculi with types - Barendregt - 1992
116 Ideas and results of proof theory (context) - Prawitz - 1970
89 Termination of term rewriting: Interpretation and type elimi.. - Zantema - 1994
68 Logics and type systems - Geuvers - 1993
30 Mathematical Structures in Computer Science (context) - Di Cosmo, Kesner et al. - 1994
28 Eta-expansions in dependent type theory---the calculus of co.. - Ghani - 1997
23 Introduction to Generalised Type Systems (context) - Barendregt - 1991
22 The language theory of Automath (context) - van Daalen - 1980
19 Modularity of termination and confluence in combinations of .. (context) - Barbanera, Fern'andez - 1993
15 the Church-Rosser property for expressive type systems and i.. (context) - Geuvers, Werner - 1994
14 Strong normalisation in a typed lambda calculus with lambda .. (context) - Nederpelt - 1973
13 A short and flexible proof of strong normalisation for the C.. (context) - Geuvers - 1995
13 Strong normalization in type systems: a model theoretic appr.. (context) - Terlouw - 1995
11 Modularity of strong normalisation and confluence in the alg.. (context) - Barbanera, Fern'andez et al. - 1997
9 the existence of long fij-normal forms in the cube (context) - Dowek, Huet et al. - 1993
8 Laboratory for the Foundations of Computer Science (context) - Altenkirch, inductive et al. - 1994
8 The Church-Rosser property for fij-reduction (context) - Salvesen - 1991
6 A brief history of rewriting with extensionality - Di Cosmo - 1996
5 Existence and uniqueness of normal forms in pure type system.. - Barthe - 1998
5 The relevance of proof-irrelevance (context) - Barthe - 1998
5 A generic proof of strong normalisation for pure type system.. (context) - Mellies, Werner - 1998
4 Pure Type Systems and calculi with permutative conversions (context) - Joachimski, Godel's - 1997
4 Termination of algebraic type systems: the syntactic approac.. - Barthe, van Raamsdonk - 1997
3 Strong normalisation for terms of the theory of construction.. (context) - Pottinger - 1987
1 On modular properties of higher order extensional lambda cal.. - Di Cosmo, Ghani - 1997
1 expansions with fi-reductions in the second-order polymorphi.. (context) - Xi - 1997
Documents on the same site (http://www.di.uminho.pt/~gilles/publis.html): More
On the Subject Reduction Property for Algebraic Type Systems - Barthe, Melliès (1997) (Correct)
A Simple Abstract Semantics for Equational Theories - Barthe (1995) (Correct)
Order-Sorted Inductive Types - Barthe (1999) (Correct)
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