Modeling concurrency with geometry
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A type-theoretical alternative to ISWIM, CUCH, OWHY
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Games and full completeness for multiplicative linear logic
Journal of Symbolic Logic
Linear logic: its syntax and semantics
Proceedings of the workshop on Advances in linear logic
Domains and lambda-calculi
Parallel and serial hypercoherences
Theoretical Computer Science
On full abstraction for PCF: I, II, and III
Information and Computation
Information and Computation
Hereditarily Sequential Functionals
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Games on Graphs and Sequentially Realizable Functionals
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
On the Symmetry of Sequentiality
Proceedings of the 9th International Conference on Mathematical Foundations of Programming Semantics
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
What is a Categorical Model of Intuitionistic Linear Logic?
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
A Stability Theorem in Rewriting Theory
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Concurrent Games and Full Completeness
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Comparing hierarchies of types in models of linear logic
Information and Computation
Asynchronous games 2: the true concurrency of innocence
Theoretical Computer Science - Concurrency theory (CONCUR 2004)
Thick Subtrees, Games and Experiments
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
Concrete Data Structures as Games
Electronic Notes in Theoretical Computer Science (ENTCS)
Understanding Game Semantics Through Coherence Spaces
Electronic Notes in Theoretical Computer Science (ENTCS)
Non-uniform (hyper/multi)coherence spaces
Mathematical Structures in Computer Science
Tω as a Stable Universal Domain
Electronic Notes in Theoretical Computer Science (ENTCS)
| Hi-index | 0.00 |
Intuitionistic proofs and PCF programs may be interpreted as functions between domains, or as strategies on games. The two kinds of interpretation are inherently different: static vs. dynamic, extensional vs. intentional. It is thus extremely instructive to compare and to connect them. In this article, we investigate the extensional content of the sequential algorithm hierarchy [-]SDS introduced by Berry and Curien. We equip every sequential game [T]SDS of the hierarchy with a realizability relation between plays and extensions. In this way, the sequential game [T]SDS becomes a directed acyclic graph, instead of a tree. This enables to define a hypergraph [T]HC on the extensions (or terminal leaves) of the game [T]SDS. We establish that the resulting hierarchy [-]HC coincides with the strongly stable hierarchy introduced by Bucciarelli and Ehrhard. We deduce from this a gametheoretic proof of Ehrhard's collapse theorem, which states that the strongly stable hierarchy coincides with the extensional collapse of the sequential algorithm hierarchy.