Algebraic approaches to program semantics
Algebraic approaches to program semantics
New foundations for the geometry of interaction
Information and Computation
Proof-nets and the Hilbert space
Proceedings of the workshop on Advances in linear logic
Geometry of interaction III: accommodating the additives
Proceedings of the workshop on Advances in linear logic
Network Algebra
Recursion from Cyclic Sharing: Traced Monoidal Categories and Models of Cyclic Lambda Calculi
TLCA '97 Proceedings of the Third 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
Glueing and orthogonality for models of linear logic
Theoretical Computer Science - Category theory and computer science
A categorical framework for finite state machines
Mathematical Structures in Computer Science
Geometry of Interaction and linear combinatory algebras
Mathematical Structures in Computer Science
Unique decomposition categories, Geometry of Interaction and combinatory logic
Mathematical Structures in Computer Science
A relational model of non-deterministic dataflow
Mathematical Structures in Computer Science
Partially additive categories and fully complete models of linear logic
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Electronic Notes in Theoretical Computer Science (ENTCS)
Towards a typed geometry of interaction
Mathematical Structures in Computer Science
Towards a typed geometry of interaction
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
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We analyze the categorical foundations of Girard's Geometry of Interaction Program for Linear Logic. The motivation for the work comes from the importance of viewing GoI as a new kind of semantics and thus trying to relate it to extant semantics. In an earlier paper we showed that a special case of Abramsky's GoI situations-ones based on Unique Decomposition Categories (UDC's)-exactly captures Girard's functional analytic models in his first GoI paper, including Girard's original Execution formula in Hilbert spaces, his notions of orthogonality, types, datum, algorithm, etc. Here we associate to a UDC-based GoI Situation a denotational model (a *- autonomous category (without units) with additional exponential structure). We then relate this model to some of the standard GoI models via a fully-faithful embedding into a double-gluing category, thus connecting up GoI with earlier Full Completeness Theorems.