Infinite objects in type theory
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NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
AMAST '97 Proceedings of the 6th International Conference on Algebraic Methodology and Software Technology
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TYPES '94 Selected papers from the International Workshop on Types for Proofs and Programs
General Recursion on Second Order Term Algebras
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Abstract Syntax and Variable Binding
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Confluence of the coinductive λ-calculus
Theoretical Computer Science
Substitution in non-wellfounded syntax with variable binding
Theoretical Computer Science - Selected papers of CMCS'03
Continuous Functions on Final Coalgebras
Electronic Notes in Theoretical Computer Science (ENTCS)
A finite semantics of simply-typed lambda terms for infinite runs of automata
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
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This work aims at explaining the syntactical properties of continuous normalization, as introduced in proof theory by Mints, and further studied by Ruckert, Buchholz and Schwichtenberg.In an extension of the untyped coinductive 驴-calculus by void constructors (so-called repetition rules), a primitive recursive normalization function is defined. Compared with other formulations of continuous normalization, this definition is much simpler and therefore suitable for analysis in a coalgebraic setting. It is shown to be continuous w.r.t. the natural topology on non-wellfounded terms with the identity as modulus of continuity. The number of repetition rules is locally related to the number of 脽-reductions necessary to reach the normal form (as represented by the B枚hm tree) and the number of applications appearing in this normal form.