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Hypercoherences: a strongly stable model of linear logic

Thomas Ehrhard
1993 Mathematical Structures in Computer Science  
We present a model of classical linear logic based on the notion of strong stability that was introduced in BE], a work about sequentiality written jointly with Antonio Bucciarelli.  ...  model of linear logic discovered by Girard (see G2] ).  ...  A model of classical linear logic The goal of this section is to interpret in the category HCohL the connectives of classical linear logic.  ... 
doi:10.1017/s0960129500000281 fatcat:kg5344kpgvdwhdjvzesdngzx64

Non-Uniform Hypercoherences

Pierre Boudes
2003 Electronical Notes in Theoretical Computer Science  
In [BE01] , Bucciarelli and Ehrhard propose a general tool for building a wide class of models of linear logic where a formula is interpreted as a set (the web) together with a kind of phase valued "coherence  ...  We provide a new non-uniform semantics of linear logic where this property of determinism is preserved.  ...  Moreover, the introduction of these objects simplified the presentation of the strongly stable semantics and provided a strongly stable interpretation of (second order) Linear Logic.  ... 
doi:10.1016/s1571-0661(04)80559-0 fatcat:mgpmw4xnhrdxrmocgamchqsre4

Parallel and serial hypercoherences

Thomas Ehrhard
2000 Theoretical Computer Science  
Studying the connection between strongly stable functions and sequential algorithms, two dual classes of hypercoherences naturally arise: the parallel and serial hypercoherences.  ...  Intuitively, it makes explicit the computational time of a hypercoherence.  ...  Acknowledgements I would like to thank Laurent Regnier, with whom I had many exciting discussion on these topics, as well as the referees and the editor of this paper, who made many valuable and constructive  ... 
doi:10.1016/s0304-3975(00)00173-0 fatcat:q7b2qg4ibbh4xjubsjexmxb7ne

Generalizing Coherence Spaces and Hypercoherences

François Lamarche
1995 Electronical Notes in Theoretical Computer Science  
g we de ne a category of \sets with values in Q and Q-respecting relations" which g i v es us a model of full classical linear logic, thus generalizing both the category of coherence spaces 9] and that  ...  of hypercoherences 7].  ...  f1g -SCoh is equivalent t o the category of hypercoherences and strongly stable linear maps.  ... 
doi:10.1016/s1571-0661(04)00021-0 fatcat:vtiw7ethwjex3kv6nyrw2wgrhq

Softness of hypercoherences and MALL full completeness

Richard Blute, Masahiro Hamano, Philip Scott
2005 Annals of Pure and Applied Logic  
We prove a full completeness theorem for multiplicative-additive linear logic (i.e. MALL) using a double gluing construction applied to Ehrhard's * -autonomous category of hypercoherences.  ...  However it is impossible to extend Tan's full completeness theorem for Coh to Multiplicative Additive Linear Logic (MALL) because Coh, although it has (co)products, admits a variant of Berry's Gustave  ...  The second author's research was supported by a Grant-in-Aid for Young Scientists of the Ministry of Education, Science and Culture of Japan.  ... 
doi:10.1016/j.apal.2004.05.002 fatcat:tssndg4n7revjbim2d5xohd5ju

Sequential algorithms and strongly stable functions

Paul-André Melliès
2005 Theoretical Computer Science  
. • The strongly stable model is linearized by Ehrhard as a hypercoherence space model of linear logic. The model refines Girard coherence space model, just like strong stability refines stability.  ...  Ehrhard shows in [Ehrhard 1993] that the hypercoherence space model linearizes the strongly stable model of PCF.  ...  This clarifies the sequential nature of hypercoherence spaces, and the reasons why the sequential algorithm hierarchy collapses extensionally to Bucciarelli-Ehrhard strongly stable hierarchy.  ... 
doi:10.1016/j.tcs.2005.05.015 fatcat:ydwhkkizqvez5cvgvyhotw3fju

Page 1754 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
Xiang Li (PRC-GUIZ; Guiyang) 95c:68142 68Q55 03B70 03F50 03G30 Ehrhard, Thomas (F-PARIS7-BP; Paris) Hypercoherences: a strongly stable model of linear logic. (English summary) Math.  ...  Linearising the notion of morphism gives another category, HCohL, which provides an elegant, new model of full classical linear logic.  ... 

Non uniform (hyper/multi)coherence spaces [article]

Pierre Boudes
2006 arXiv   pre-print
In (hyper)coherence semantics, the argument of a (strongly) stable functional is always a (strongly) stable function.  ...  Intuitively, vertices represent results of computations and the edge relation witnesses the ability of being assembled into a same piece of data or a same (strongly) stable function, at arrow types.  ...  Moreover, the introduction of these objects simplified the presentation of the strongly stable semantics and provided a strongly stable interpretation of (second order) linear logic.  ... 
arXiv:cs/0609021v1 fatcat:7cc3vsxcknfi3phpilhubraspi

Around finite second-order coherence spaces [article]

Lê Thành Dũng Nguyên
2019 arXiv   pre-print
We exhibit such a finite semantics for a polymorphic purely linear language: more precisely, we show that in Girard's semantics of second-order linear logic using coherence spaces and normal functors,  ...  We also establish analogous results for a second-order extension of Ehrhard's hypercoherences; while finiteness holds for the same reason as in coherence spaces, effectivity presents additional difficulties  ...  deg(F ) is the supremum of a finite subset of N and is therefore finite.  ... 
arXiv:1902.00196v3 fatcat:vyvzyqyuhvc7heye3pjewgbide

Non-uniform (hyper/multi)coherence spaces

PIERRE BOUDES
2010 Mathematical Structures in Computer Science  
The cardinality ♯[a i | i ∈ I] of a multiset [a i | i ∈ I] is the cardinality ♯I of the set I. The disjoint sum operation on sets is defined by setting A + B = {1} × A ∪ {0} × B.  ...  function which is named after a private joke about the huge number of french scientists whose first name is Gérard, among which Berry.  ...  Moreover, the introduction of these objects simplified the presentation of the strongly stable semantics and provided a strongly stable interpretation of (second order) linear logic.  ... 
doi:10.1017/s0960129510000320 fatcat:blkahzeezrcediy5kbwchvlegu

A Relative PCF-Definability Result for Strongly Stable Functions and some Corollaries

Thomas Ehrhard
1999 Information and Computation  
Applying a logical relation technique, we derive from this result that the strongly stable model of PCF is the extensional collapse of its sequential algorithms model. ]  ...  We prove that, in the hierarchy of simple types based on the type of natural numbers, any finite strongly stable function is equal to the application of the semantics of a PCF-definable functional to some  ...  We denote by HC the category of hypercoherences and strongly stable functions. Let X and Y be hypercoherences.  ... 
doi:10.1006/inco.1998.2781 fatcat:kt4kaeujf5hyvddwx5tkzgbuo4

A Characterization of Hypercoherent Semantic Correctness in Multiplicative Additive Linear Logic [chapter]

Paolo Tranquilli
Lecture Notes in Computer Science  
We give a graph theoretical criterion on multiplicative additive linear logic (MALL) cut-free proof structures that exactly characterizes those whose interpretation is a hyperclique in Ehrhard's hypercoherent  ...  of coherent spaces for proof nets of the multiplicative fragment of linear logic.  ...  The Gustave function G is however rejected by Bucciarelli and Ehrhard's strongly stable model [3] , and starting from it Ehrhard developed in [5] a new model of LL extending the coherent one: the hypercoherent  ... 
doi:10.1007/978-3-540-87531-4_19 fatcat:5pqmquz3snasdoxjespjh66hey

Comparing hierarchies of types in models of linear logic

Paul-André Melliès
2004 Information and Computation  
of linear logic may be interpreted in two different ways, inducing either a "qualitative" or a "quantitative" model of proofs: • The qualitative exponential !  ...  set over the category COH, which "linearizes" Berry's stable model of PCF, in the sense that the co-kleisli category associated to !  ...  Models of linear logic over a class of constants A model M of intuitionistic linear logic over a class K of constants, is a model of intuitionistic linear logic equipped, for every constant type Ä ∈ K,  ... 
doi:10.1016/j.ic.2003.10.003 fatcat:vnaybrq3gfft3k7h4rd2ldimpm

Bistructures, Bidomains and Linear Logic

Gordon Plotkin, Glynn Winskel
1994 BRICS Report Series  
Bistructures form a categorical model of Girard's classical linear logic in which the involution of linear logic is modelled, roughly speaking, by a reversal of the roles of input and output.  ...  The comonad of the model has associated co-Kleisli category which is equivalent to a cartesian-closed full subcategory of Berry's bidomains.  ...  , a model of classical linear logic.  ... 
doi:10.7146/brics.v1i9.21661 fatcat:hv6scw7ohzbyhctkm7wxqmygaq

Bistructures, bidomains and linear logic [chapter]

Gordon Plotkin, Glynn Winskel
1994 Lecture Notes in Computer Science  
Bistructures form a categorical model of Girard's classical linear logic in which the involution of linear logic is modelled, roughly speaking, by a reversal of the roles of input and output.  ...  Bistructures are a generalisation of event structures which allow a representation of spaces of functions at higher types in an orderextensional setting.  ...  , a model of classical linear logic.  ... 
doi:10.1007/3-540-58201-0_81 fatcat:3cdbeajorvfgpgg3pkvnlywtyq
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