Automated deduction in nonclassical logics
Automated deduction in nonclassical logics
A formulae-as-type notion of control
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Intuitionistic and classical natural deduction systems with the catch and the throw rules
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
A Curry-Howard foundation for functional computation with control
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
On Transforming Intuitionistic Matrix Proofs into Standard-Sequent Proofs
TABLEAUX '95 Proceedings of the 4th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
T-String Unification: Unifying Prefixes in Non-classical Proof Methods
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
Call-by-value is dual to call-by-name
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
A confluent λ-calculus with a catch/throw mechanism
Journal of Functional Programming
A Formulae-as-Types Interpretation of Subtractive Logic
Journal of Logic and Computation
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
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The well-known embedding of intuitionistic logic into classical modal logic means that intuitionistic logic can be viewed as a calculus of labelled deduction on multiple-conclusion sequents, where the labels are the Kripke worlds of the modal embedding. The corresponding natural deduction system constitutes a type system for programs using control operators such as letcc that capture the current program continuation, which has a modal restriction on the use of such continuations that enforces constructive validity. This allows us to develop a rich dependent type theory incorporating letcc, which is known to be otherwise highly problematic for computational interpretations of classical logic. Moreover, we give a novel constructive proof for the soundness of this labelled deduction system, whose algorithmic content is a non-deterministic translation of programs that eliminates uses of letcc and is fully compatible with dependent types and therefore with program verification. This proof has been formally verified on the propositional fragment in the Twelf meta-logical framework.