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Sequential algorithms and strongly stable functions
 in the Linear Summer School, Azores
, 2003
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Comparing Hierarchies of Types in Models of Linear Logic
, 2003
"... 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 distri ..."
Abstract

Cited by 6 (3 self)
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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 backandforth translation between the hierarchies of types induced by M and N. We apply this result to compare (1) the qualitative and the quantitative hierarchies induced by the coherence (or hypercoherence) space model, (2) several paradigms of games semantics: errorfree vs. erroraware, alternated vs. nonalternated, backtracking vs. repetitive, uniform vs. nonuniform.
On dialogue games and coherent strategies ˚
"... We explain how to see the set of positions of a dialogue game as a coherence space in the sense of Girard or as a bistructure in the sense of Curien, Plotkin and Winskel. The coherence structure on the set of positions results from a Kripke translation of tensorial logic into linear logic extended w ..."
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We explain how to see the set of positions of a dialogue game as a coherence space in the sense of Girard or as a bistructure in the sense of Curien, Plotkin and Winskel. The coherence structure on the set of positions results from a Kripke translation of tensorial logic into linear logic extended with a necessity modality. The translation is done in such a way that every innocent strategy defines a clique or a configuration in the resulting space of positions. This leads us to study the notion of configuration designed by Curien, Plotkin and Winskel for general bistructures in the particular case of a bistructure associated to a dialogue game. We show that every such configuration may be seen as an interactive strategy equipped with a backward as well as a forward dynamics based on the interplay between the stable order and the extensional order. In that way, the category of bistructures is shown to include a full subcategory of games and coherent strategies of an interesting nature.
Abstract
"... Comparing hierarchies of types in models of linear logic PaulAndré Melliès 1 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 IdC ..."
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Comparing hierarchies of types in models of linear logic PaulAndré Melliès 1 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 IdC ⇒ GF and IdD ⇒ F G, and
Logical Methods in Computer Science Vol. 9(4:6)2013, pp. 1–33
, 2011
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