A formulae-as-type notion of control
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Call-by-need and continuation-passing style
Lisp and Symbolic Computation
Reasoning about programs in continuation-passing style
Lisp and Symbolic Computation - Special issue on continuations—part I
A semantics of evidence for classical arithmetic
Journal of Symbolic Logic
ACM Transactions on Programming Languages and Systems (TOPLAS)
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Free Deduction: An Analysis of "Computations" in Classical Logic
Proceedings of the First Russian Conference on Logic Programming
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Dependent choice, 'quote' and the clock
Theoretical Computer Science
A confluent λ-calculus with a catch/throw mechanism
Journal of Functional Programming
The call-by-need lambda calculus
Journal of Functional Programming
The call-by-need lambda calculus
Journal of Functional Programming
A Computational Interpretation of Open Induction
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Algorithmic equality in Heyting arithmetic modulo
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
Computational interpretations of analysis via products of selection functions
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
An Intuitionistic Logic that Proves Markov's Principle
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Classical call-by-need and duality
TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
On the degeneracy of Σ-types in presence of computational classical logic
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Classical call-by-need sequent calculi: the unity of semantic artifacts
FLOPS'12 Proceedings of the 11th international conference on Functional and Logic Programming
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Martin-Löf's type theory has strong existential elimination (dependent sum type) that allows to prove the full axiom of choice. However the theory is intuitionistic. We give a condition on strong existential elimination that makes it computationally compatible with classical logic. With this restriction, we lose the full axiom of choice but, thanks to a lazily-evaluated coinductive representation of quantification, we are still able to constructively prove the axiom of countable choice, the axiom of dependent choice, and a form of bar induction in ways that make each of them computationally compatible with classical logic.