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Abstract: Induction-recursion is a schema which formalizes the principles for introducing new sets in Martin-Lof's type theory. It states that we may inductively define a set while simultaneously defining a function from this set into an arbitrary type by structural recursion. This extends the notion of an inductively defined set substantially and allows us to introduce universes and higher order universes (but not a Mahlo universe). In this article we give a finite axiomatization of inductive-recursive... (Update)
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BibTeX entry: (Update)
P. Dybjer and A. Setzer. A finite axiomatization of inductive-recursive definitions. Draft paper, April 1998. http://citeseer.ist.psu.edu/dybjer98finite.html More
@inproceedings{ dybjer99finite,
author = "Peter Dybjer and Anton Setzer",
title = "A Finite Axiomatization of Inductive-Recursive Definitions",
booktitle = "Typed Lambda Calculus and Applications",
pages = "129-146",
year = "1999",
url = "citeseer.ist.psu.edu/dybjer98finite.html" }
Citations (may not include all citations):236 Intuitionistic Type Theory (context) - Martin-Lof - 1984
73 Inductively defined types (context) - Coquand, Paulin - 1990
62 Programming in Martin-Lof 's Type Theory: an Introduction (context) - Nordstrom, Petersson et al. - 1990
49 Inductive definitions in the system Coq - rules and properti.. - Paulin-Mohring - 1993
41 Inductive sets and families in Martin-Lof's type theory and .. - Dybjer - 1991
39 A Non-Type-Theoretic Semantics for Type-Theoretic Language (context) - Allen - 1987
35 Formal Aspects of Computing (context) - Dybjer - 1994
25 A general formulation of simultaneous inductive-recursive de.. - Dybjer
21 Hauptsatz for the intuitionistic theory of iterated inductiv.. (context) - Martin-Lof - 1971
17 Proof theoretical strength of Martin-Lof Type Theory with W-.. (context) - Setzer - 1993
17 Proof theoretical strength of Martin-Lof Type Theory with Wt.. (context) - Setzer - 1993
12 Predicative type universes and primitive recursion (context) - Mendler - 1991
11 Set Theory - an Introduction to Large Cardinals (context) - Drake - 1974
10 Inaccessibility in constructive set theory and type theory - Rathjen, Griffor et al. - 1998
10 Extending Martin-Lof Type Theory by one Mahlo-universe - Setzer
8 the syntax of Martin-Lof's type theories (context) - Troelstra - 1987
8 Inductive Definitions and Universes in Martin-Lof 's Type Th.. (context) - Palmgren, Point - 1991
8 Pointfree Approach to Constructive Analysis in Type Theory - Cederquist - 1997
7 Well-ordering proofs for Martin-Lof type theory - Setzer - 1998
5 On relating type theories and set theories - Aczel
4 A model for a type theory with Mahlo universe - Setzer - 1996
4 The strength of some Martin-Lof type theories (context) - Griffor, Rathjen - 1994
3 An upper bound for the proof theoretical strength of Martin-.. - Setzer - 1996
1 editors: Twenty-Five Years of Constructive Type Theory (context) - Palmgren, in et al.
The graph only includes citing articles where the year of publication is known.
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