A syntactic theory of sequential control
Theoretical Computer Science
Categorical combinators, sequential algorithms, and functional programming (2nd ed.)
Categorical combinators, sequential algorithms, and functional programming (2nd ed.)
Geometry of interaction III: accommodating the additives
Proceedings of the workshop on Advances in linear logic
Reversible, irreversible and optimal &lgr;-machines
Theoretical Computer Science - Special issue on linear logic, 1
Coherence completions of categories
Theoretical Computer Science - Special issue on linear logic, 1
Bistructures, bidomains, and linear logic
Proof, language, and interaction
Information and Computation
Objects and classes in Algol-like languages
Information and Computation - FOOL V
What is a Categorical Model of Intuitionistic Linear Logic?
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Geometry of interaction 2: deadlock-free algorithms
COLOG '88 Proceedings of the International Conference on Computer Logic
Retracting Some Paths in Process Algebra
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
A Mixed Linear and Non-Linear Logic: Proofs, Terms and Models (Extended Abstract)
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
Believe it or not, AJM's games model is a model of classical linear logic
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Proof Nets for Unit-free Multiplicative-Additive Linear Logic (Extended abstract)
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Asynchronous Games 4: A Fully Complete Model of Propositional Linear Logic
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
A structural approach to reversible computation
Theoretical Computer Science
A categorical model for the geometry of interaction
Theoretical Computer Science - Automata, languages and programming: Logic and semantics (ICALP-B 2004)
Journal of Computer and System Sciences
A token machine for full geometry of interaction
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
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We introduce the Danos-Regnier category DR(M) of a linear inverse monoid M, as a categorical description of geometries of interaction (GOI) inspired from the weight algebra. The natural setting for GOI is that of a so-called weakly Cantorian linear inverse monoid, in which case DR(M) is a kind of symmetrized version of the classical Abramsky-Haghverdi-Scott construction of a weak linear category from a GOI situation. It is well-known that GOI is perfectly suited to describe the multiplicative fragment of linear logic, and indeed DR(M) will be a *-autonomous category in this case. It is also well-known that the categorical interpretation of the other linear connectives conflicts with GOI interpretations. We make this precise, and show that DR(M) has no terminal object, no Cartesian product of any two objects, and no exponential-whatever M is, unless M is trivial. However, a form of coherence completion of DR(M) a la Hu-Joyal (which for additives resembles a layered approach a la Hughes-van Glabbeek), provides a model of full classical linear logic, as soon as M is weakly Cantorian. One finally notes that Girard's notion of coherence is pervasive, and instrumental in every aspect of this work.