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Hypercoherences: a strongly stable model of linear logic

1993
*
Mathematical Structures in Computer Science
*

We present

doi:10.1017/s0960129500000281
fatcat:kg5344kpgvdwhdjvzesdngzx64
*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*. ...##
###
Non-Uniform Hypercoherences

2003
*
Electronical Notes in Theoretical Computer Science
*

In [BE01] , Bucciarelli and Ehrhard propose

doi:10.1016/s1571-0661(04)80559-0
fatcat:mgpmw4xnhrdxrmocgamchqsre4
*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*. ...##
###
Parallel and serial hypercoherences

2000
*
Theoretical Computer Science
*

Studying the connection between

doi:10.1016/s0304-3975(00)00173-0
fatcat:q7b2qg4ibbh4xjubsjexmxb7ne
*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 ...##
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Generalizing Coherence Spaces and Hypercoherences

1995
*
Electronical Notes in Theoretical Computer Science
*

g we de ne

doi:10.1016/s1571-0661(04)00021-0
fatcat:vtiw7ethwjex3kv6nyrw2wgrhq
*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. ...##
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Softness of hypercoherences and MALL full completeness

2005
*
Annals of Pure and Applied Logic
*

We prove

doi:10.1016/j.apal.2004.05.002
fatcat:tssndg4n7revjbim2d5xohd5ju
*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. ...##
###
Sequential algorithms and strongly stable functions

2005
*
Theoretical Computer Science
*

. • The

doi:10.1016/j.tcs.2005.05.015
fatcat:ydwhkkizqvez5cvgvyhotw3fju
*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. ...##
###
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]

2006
*
arXiv
*
pre-print

In (hyper)coherence semantics, the argument

arXiv:cs/0609021v1
fatcat:7cc3vsxcknfi3phpilhubraspi
*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*. ...##
###
Around finite second-order coherence spaces
[article]

2019
*
arXiv
*
pre-print

We exhibit such

arXiv:1902.00196v3
fatcat:vyvzyqyuhvc7heye3pjewgbide
*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. ...##
###
Non-uniform (hyper/multi)coherence spaces

2010
*
Mathematical Structures in Computer Science
*

The cardinality ♯[

doi:10.1017/s0960129510000320
fatcat:blkahzeezrcediy5kbwchvlegu
*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*. ...##
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A Relative PCF-Definability Result for Strongly Stable Functions and some Corollaries

1999
*
Information and Computation
*

Applying

doi:10.1006/inco.1998.2781
fatcat:kt4kaeujf5hyvddwx5tkzgbuo4
*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*. ...##
###
A Characterization of Hypercoherent Semantic Correctness in Multiplicative Additive Linear Logic
[chapter]

*
Lecture Notes in Computer Science
*

We give

doi:10.1007/978-3-540-87531-4_19
fatcat:5pqmquz3snasdoxjespjh66hey
*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*...##
###
Comparing hierarchies of types in models of linear logic

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, ...

##
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Bistructures, Bidomains and Linear Logic

1994
*
BRICS Report Series
*

Bistructures form

doi:10.7146/brics.v1i9.21661
fatcat:hv6scw7ohzbyhctkm7wxqmygaq
*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*. ...##
###
Bistructures, bidomains and linear logic
[chapter]

1994
*
Lecture Notes in Computer Science
*

Bistructures form

doi:10.1007/3-540-58201-0_81
fatcat:3cdbeajorvfgpgg3pkvnlywtyq
*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*. ...
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