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Abstract: The Barendregt-Geuvers-Klop conjecture states that every weakly normalizing pure type system is also strongly normalizing. We show that this is true for a uniform class of systems which includes, e.g., the left hand side of Barendregt's -cube as well as the system U . This seems to be the first result giving a positive answer to the conjecture not merely for some concrete systems for which strong normalization is known to hold, but for a uniform class of systems in which not all systems are... (Update)
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...Proposition 14. Universes are connected so we may encode universes as sorts or variables this encoding is defined in more detail in [10]. Moreover, we encode every function symbol f : oe 1 Theta : Theta : oe n as x 1 : oe 1 : xn : oe n :c . Putting...
...relation R is terminating on the set of pseudo terms of A. Using regularity, we can show using similar techniques to the one presented in [8], that termination of (L(S; fi) fi ) implies termination of (L(A; mix 0 ) fi ) It then follows by Theorem 19 that (L(A; mix 0 )...
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8: Lambda Calculi with Types - Barendregt - 1992
7: A modular proof of strong normalisation for the calculus of constructions (context) - Geuvers, Nederhof - 1991
6: The Lambda Calculus: Its Syntax and Semantics (context) - Barendregt - 1984
BibTeX entry: (Update)
G. Barthe, J. Hatcliff, and M.H. Sørensen. Weak Normalization implies Strong Normalization in Generalized Non-Dependent Pure Type Systems. Submitted for publication, March 1997. http://citeseer.ist.psu.edu/barthe97weak.html More
@article{ barthe01weak,
author = "Gilles Barthe and John Hatcliff and Morten Heine S{\o}rensen",
title = "Weak normalization implies strong normalization in a class of non-dependent pure type systems",
journal = "Theoretical Computer Science",
volume = "269",
number = "1--2",
pages = "317--361",
year = "2001",
url = "citeseer.ist.psu.edu/barthe97weak.html" }
Citations (may not include all citations):729 The Lambda Calculus: Its Syntax and Semantics (context) - Barendregt - 1984
434 A framework for defining logics - Harper, Honsell et al. - 1987
382 Lambda calculi with types - Barendregt - 1992 ACM
283 Theoretical Computer Science (context) - Plotkin, call-by-value et al. - 1975 ACM
174 Combinatory Reduction Systems (context) - Klop - 1980
68 Logics and Type Systems - Geuvers - 1993
56 Explicit polymorphism and CPS conversion - Harper, Lillibridge - 1993
45 Strong normalization for a typed lambda calculus with lambda.. (context) - Nederpelt - 1973
39 A modular proof of strong normalization for the calculus of .. (context) - Geuvers, Nederhof - 1991
35 New notions of reduction and non-semantic proofs of fi-stron.. (context) - Kfoury, Wells
29 Transactions of the American Mathematical Society (context) - Church, Rosser et al. - 1936
24 Domain-free pure type systems - Barthe, Srensen - 1997 ACM DBLP
20 translation and looping combinators in pure type systems - Coquand, Herbelin - 1994
15 CPS translations and applications: the cube and beyond - Barthe, Hatcliff et al. - 1997 DBLP
12 The conservation theorem revisited - de Groote - 1993 ACM DBLP
11 Strong normalization from weak normalization in typed -calcu.. (context) - Srensen - 1997
11 Extensions of pure type systems - Barthe - 1995 ACM DBLP
10 Form Reduction Systems and Reductions of Contracted Forms an.. (context) - Khasidashvili - 1988
10 Delayability (context) - Karr - 1985
7 the adequacy of representing higher order intuitionistic log.. (context) - Tonino, Fujita - 1992
6 Universita di Torino (context) - Berardi, Constructive et al. - 1990
3 Manuscript announced on the types mailing list (context) - Xi, strong - 1996
1 Conservativity between logics and typed lambda-calculi (context) - Geuvers - 1993
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