Proofs and types
Theoretical Computer Science - Special issue: algebraic development techniques
Theoretical Computer Science - Special issue on theories of types and proofs
Inductive definition in type theory
Inductive definition in type theory
A categorical programming language
A categorical programming language
A predicative analysis of structural recursion
Journal of Functional Programming
Journal of Functional Programming
Least and Greatest Fixpoints in Game Semantics
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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We present a new strong normalisation proof for a λ-calculus with interleaving strictly positive inductive types λµ which avoids the use of impredicative reasoning, i.e., the theorem of Knaster-Tarski. Instead it only uses predicative, i.e., strictly positive inductive definitions on the metalevel. To achieve this we show that every strictly positive operator on types gives rise to an operator on saturated sets which is not only monotone but also (deterministically) set based - a concept introduced by Peter Aczel in the context of intuitionistic set theory. We also extend this to coinductive types using greatest fixpoints of strictly monotone operators on the metalevel.