Theoretical Computer Science
The geometry of optimal lambda reduction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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
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
Paracategories I: internal paracategories and saturated partial algebras
Theoretical 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
Towards a quantum programming language
Mathematical Structures in Computer Science
On the Geometry of Interaction for Classical Logic
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
A categorical model for the geometry of interaction
Theoretical Computer Science - Automata, languages and programming: Logic and semantics (ICALP-B 2004)
Elementary Complexity and Geometry of Interaction
Fundamenta Informaticae - Typed Lambda Calculi and Applications (TLCA'99)
Stratified Bounded Affine Logic for Logarithmic Space
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
On traced monoidal closed categories
Mathematical Structures in Computer Science
From Geometry of Interaction to Denotational Semantics
Electronic Notes in Theoretical Computer Science (ENTCS)
A token machine for full geometry of interaction
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Towards a typed geometry of interaction
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
A Representation Theorem for Unique Decomposition Categories
Electronic Notes in Theoretical Computer Science (ENTCS)
Hi-index | 0.00 |
Girard's Geometry of Interaction (GoI) develops a mathematical framework for modelling the dynamics of cut elimination. We introduce a typed version of GoI, called Multiobject GoI for both multiplicative linear logic (MLL) and multiplicative exponential linear logic (MELL) with units. We present a categorical setting that includes our previous (untyped) GoI models, as well as more general models based on monoidal *-categories. Our development of multiobject GoI depends on a new theory of partial traces and trace classes, which we believe is of independent interest, as well as an abstract notion of orthogonality (which is related to work of Hyland and Schalk). We develop Girard's original theory of types, data and algorithms in our setting, and show his execution formula to be an invariant of cut elimination (under some restrictions). We prove soundness theorems for the MGoI interpretation (for Multiplicative and Multiplicative Exponential Linear Logic) in partially traced *-categories with an orthogonality. Finally, we briefly discuss the relationship between our GoI interpretation and other categorical interpretations of GoI.