Proofs and types
Type fixpoints: iteration vs. recursion
Proceedings of the fourth ACM SIGPLAN international conference on Functional programming
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Monotone Fixed-Point Types and Strong Normalization
Proceedings of the 12th International Workshop on Computer Science Logic
A CPS-Translation of the Lambda-µ-Calculus
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Inductive Definition in Type Theory
Inductive Definition in Type Theory
Classical logic, continuation semantics and abstract machines
Journal of Functional Programming
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A new proof of strong normalization of Parigot's (second order) λµ-calculus is given by a reduction-preserving embedding into system (second order polymorphic λ-calculus). The main idea is to use the least stable supertype for any type. These non-strictly positive inductive types and their associated iteration principle are available in system F, and allow to give a translation vaguely related to CPS translations (corresponding to the Kolmogorov embedding of classical logic into intuitionistic logic). However, they simulate Parigot's µ-reductions whereas CPS translations hide them. As a major advantage, this embedding does not use the idea of reducing stability (¬ ¬ φ → φ) to that for atomic formulae. Therefore, it even extends to non-interleaving positive fixed-point types. As a non-trivial application, strong normalization of λµcalculus, extended by primitive recursion on monotone inductive types, is established.