Information and Computation - Semantics of Data Types
Extracting &ohgr;'s programs from proofs in the calculus of constructions
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A category-theoretic characterization of functional completeness
Theoretical Computer Science
Lambda-calculus, types and models
Lambda-calculus, types and models
A general storage theorem for integers in call-by-name &lgr;-calculus
Theoretical Computer Science
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
A Generic Normalisation Proof for Pure Type Systems
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
On Relating Type Theories and Set Theories
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
Dependent choice, 'quote' and the clock
Theoretical Computer Science
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
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We show how to extract classical programs expressed in Krivine λc-calculus from proof-terms built in a proof-irrelevant and classical version of the calculus of constructions with universes. For that, we extend Krivine's realisability model of classical second-order arithmetic to the calculus of constructions with universes using a structure of Π-set which is reminiscent of ω-sets, and show that our realisability model validates Peirce's law and proof-irrelevance. Finally, we extend the extraction scheme to a primitive data-type of natural numbers in a way which preserves the whole compatibility with the classical realisability interpretation of second-order arithmetic.