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Abstract: We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F : C D : G and transformations Id C ) GF and Id D ) FG, and (2) their exponentials ! are related by distributive laws % : ! : ! M G ) G ! N commuting to the promotion rule. The key ingredient of the proof is a notion of back-and-forth translation between the hierarchies of types induced by M... (Update)
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BibTeX entry: (Update)
P-A. Mellies. Comparing hierarchies of types in models of linear logic. Prepublication de l'equipe PPS (December 2002, number 14). Information and Computation, Volume 189, Issue 2, Pages 202-234, March 2004. http://citeseer.ist.psu.edu/mellies03comparing.html More
@misc{ mellies02comparing,
author = "P. Mellies",
title = "Comparing hierarchies of types in models of linear logic",
text = "P-A. Mellies. Comparing hierarchies of types in models of linear logic.
Prepublication de l'equipe PPS (December 2002, number 14). Information and
Computation, Volume 189, Issue 2, Pages 202-234, March 2004.",
year = "2002",
url = "citeseer.ist.psu.edu/mellies03comparing.html" }
Citations (may not include all citations):562 Categories for the Working Mathematician (context) - Lane - 1971
242 Linear logic (context) - Girard - 1987
175 Games and full completeness for multiplicative linear logic - Abramsky, Jagadeesan - 1994
68 On full abstraction for PCF (context) - Hyland, Ong - 2000
66 What is a categorical model of intuitionistic linear logic - Bierman - 1995
61 Sequential algorithms on concrete data structures (context) - Berry, Curien - 1982
58 Fully abstract game semantics for general reference (context) - Abramsky, Honda et al. - 1998
50 Domains and Lambda-Calculi (context) - Amadio, Curien - 1998
31 Concurrent games and full completeness - Abramsky, Melli - 1999
30 Hypercoherences: a strongly stable model of linear logic - Ehrhard - 1993
24 Fully Abstract Semantics for Observably Sequential Languages (context) - Cartwright, Curien et al. - 1994
22 Game Semantics - Abramsky, McCusker - 1999
21 games and linear logic (context) - Lamarche - 1992
19 Sequentiality and strong stability (context) - Bucciarelli, Ehrhard - 1991
16 The sequentially realizable functionals (context) - Longley - 2002
14 Game Semantics (context) - Hyland - 1997
11 Games and Full Abstraction for Nondeterministic Languages (context) - Harmer - 2000
11 the symmetry of sequentiality (context) - Curien - 1993
10 cat egories et machines (context) - Lafont - 1988
10 Remarques sur la theorie des jeux a deux personnes (context) - Joyal - 1977
8 Available as ECS-LFCS (context) - Longley, Language et al. - 1995
7 Abstract Games for Linear Logic (context) - Hyland, Schalk - 1999
6 A relative definability result for strongly stable functions.. (context) - Ehrhard - 1997
4 Anatomy of an extensional collapse - Barreiro, Ehrhard - 1998
3 The separated extensional Chu category - Barr - 1998
3 algebras and cohomology (context) - Beck - 1967
2 Hypercoh erences et Jeux (context) - Boudes - 2002
2 Parallel and serial hypercoherences - Ehrhard - 2000
1 Categorical models of linear logic revisited (context) - es
1 Bi-models: relational versus domain-theoretic approaches (context) - Bucciarelli - 1997
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Semantic Types: A Fresh Look at the Ideal Model for Types - Vouillon, Mellies, Diderot (2004) (Correct)
Double Categories: a modular model of multiplicative linear logic - Mellies (Correct)
Asynchronous Games 2 - The true concurrency of innocence - Mellies (2004) (Correct)
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