A General Formulation of Simultaneous Inductive-Recursive Definitions in Type Theory

A General Formulation of Simultaneous Inductive-Recursive Definitions in Type Theory (1998)

Cached

Download Links

[www.cs.chalmers.se]

Other Repositories/Bibliography

DBLP

by Peter Dybjer

Venue:	Journal of Symbolic Logic
Citations:	56 - 9 self

Versions

Version History

Metadata Version 3

User correction supplied by SystemCorrections

Datum	Value	Source
TITLE	A General Formulation of Simultaneous Inductive-Recursive Definitions in Type Theory	user correction - Legacy Corrections
AUTHOR NAME	Peter Dybjer	SVM HeaderParse 0.1
AUTHOR AFFIL	Department of Computing Science; Chalmers University of Technology	SVM HeaderParse 0.2
AUTHOR ADDR	S-412 96 Goteborg, Sweden	SVM HeaderParse 0.1
ABSTRACT	The first example of a simultaneous inductive-recursive definition in intuitionistic type theory is Martin-Löf's universe à la Tarski. A set U0 of codes for small sets is generated inductively at the same time as a function T0 , which maps a code to the corresponding small set, is defined by recursion on the way the elements of U0 are generated. In this paper we argue that there is an underlying general notion of simultaneous inductiverecursive definition which is implicit in Martin-Löf's intuitionistic type theory. We extend previously given schematic formulations of inductive definitions in type theory to encompass a general notion of simultaneous induction-recursion. This enables us to give a unified treatment of several interesting constructions including various universe constructions by Palmgren, Griffor, Rathjen, and Setzer and a constructive version of Aczel's Frege structures. Consistency of a restricted version of the extension is shown by constructing a realisability model ...	user correction - Legacy Corrections
YEAR	1998	user correction - Legacy Corrections
VENUE	Journal of Symbolic Logic	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	2000	INFERENCE
VOLUME	65	INFERENCE
CITATIONS	45 found	ParsCit 1.0