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Abstract: We present a new strong normalisation proof for a -calculus with interleaving strictly positive inductive types 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... (Update)
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BibTeX entry: (Update)
@inproceedings{ abel99predicative,
author = "Andreas Abel and Thorsten Altenkirch",
title = "A Predicative Strong Normalisation Proof for a lambda-Calculus with Interleaving Inductive Types",
booktitle = "{TYPES}",
pages = "21-40",
year = "1999",
url = "citeseer.ist.psu.edu/abel00predicative.html" }
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132 Interpr'etation fonctionelle et 'elimination des coupures da.. (context) - Girard - 1972
121 Intensional interpretations of functionals of finite type (context) - Tait - 1967
95 An Extended Calculus of Constructions - Luo - 1990
73 Inductively defined types (context) - Coquand, Mohring - 1989
50 A Categorical Programming Language (context) - Hagino - 1987
50 Polymorphism is not set-theoretic (context) - Reynolds - 1984
46 Journal of Functional Programming (context) - Jay, Belle et al. - 1998
41 Inductive sets and families in Martin-Lof's type theory and .. - Dybjer - 1991
41 Inductive and coinductive types with iteration and recursion - Geuvers - 1992
38 by Iteration And Primitive Recursion on Monotone Inductive T.. (context) - Matthes, System - 1998
35 Theoretical Computer Science (context) - Jouannaud, Okada et al. - 1997
21 Inductive Definition in Type Theory (context) - Mendler - 1988
20 Inductive Types and Strong Normalization (context) - Altenkirch - 1993
16 Monadic presentations of lambda terms using generalized indu.. - Altenkirch, Reus - 1999
11 Equational theories for inductive types - Loader - 1997
11 A predicative analysis of structural recursion - Abel, Altenkirch - 1999
10 Notes on constructive set theory - Aczel - 1997
8 A semantic analysis of structural recursion (context) - Abel - 1999
3 To appear in Theoretical Computer Science (context) - Blanqui, Jouannaud et al. - 1999
3 Logical relation and inductivecoinductive type (context) - Altenkirch, relations et al. - 1998
1 Starke Normalisierung fur die Heyting-Arithmetik mit indukti.. (context) - Benl - 1998
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