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
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 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)
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
Electronic Notes in Theoretical Computer Science (ENTCS)
A general framework for sound and complete Floyd-Hoare logics
ACM Transactions on Computational Logic (TOCL)
Towards a typed geometry of interaction
Mathematical Structures in Computer Science
Towards a geometry of recursion
Theoretical Computer Science
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
PLPV '12 Proceedings of the sixth workshop on Programming languages meets program verification
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
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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 (MGoI) for multiplicative linear logic without units in categories which include previous (untyped) GoI models, as well as models not possible in the original untyped version. The development of MGoI depends on a new theory of partial traces and trace classes, as well as an abstract notion of orthogonality (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. We prove Soundness and Completeness Theorems for the MGoI interpretation in partially traced categories with an orthogonality.