Games and full completeness for multiplicative linear logic
Journal of Symbolic Logic
A semantics of evidence for classical arithmetic
Journal of Symbolic Logic
Hereditarily Sequential Functionals
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
TACS '94 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Semantics of Interaction (Abstract)
CAAP '96 Proceedings of the 21st International Colloquium on Trees in Algebra and Programming
Full abstraction, totality and PCF
Mathematical Structures in Computer Science
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In existing game models, total functionals have no simple characterization neither in term of game strategies, nor in term of the total set-theoretical functionals they define. We show that the situation changes if we extend the usual notion of game by allowing infinite plays. Total functionals are, now, exactly those having a tree-strategy in which all branches end in a last move, winning for the strategy. Total functionals now define (via an extensional collapse) all set-theoretical functionals. Our model is concrete: we used infinite computations only to have a nice characterization of totality. A computation may be infinite only when the input is a discontinous functional; in practice, never.