Proofs and types
Lambda-calculus, types and models
Lambda-calculus, types and models
Intersection and union types: syntax and semantics
Information and Computation
A Filter Model for Concurrent $\lambda$-Calculus
SIAM Journal on Computing
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Completeness of intersection and union type assignment systems for call-by-value λ-models
Theoretical Computer Science - Special issue on theories of types and proofs
Semantic types: a fresh look at the ideal model for types
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A Proof of Strong Normalisation using Domain Theory
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Strong Normalization as Safe Interaction
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
On Krivine's Realizability Interpretation of Classical Second-Order Arithmetic
Fundamenta Informaticae - Logic for Pragmatics
Union of Reducibility Candidates for Orthogonal Constructor Rewriting
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Simple saturated sets for disjunction and second-order existential quantification
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Reducibility and ⊤⊤-lifting for computation types
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
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The straightforward elimination of union types is known to break subject reduction, and for some extensions of the lambda-calculus, to break strong normalization as well. Similarly, the straightforward elimination of implicit existential types breaks subject reduction. We propose elimination rules for union types and implicit existential quantification which use a form call-by-value issued from Girard's reducibility candidates. We show that these rules remedy the above mentioned difficulties, for strong normalization and, for the existential quantification, for subject reduction as well. Moreover, for extensions of the lambda-calculus based on intuitionistic logic, we show that the obtained existential quantification is equivalent to its usual impredicative encoding w.r.t. provability in realizability models built from reducibility candidates and biorthogonals.