Infinite Objects in Type Theory

Infinite Objects in Type Theory (0)

by Thierry Coquand

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Datum	Value	Source
TITLE	Infinite Objects in Type Theory	user correction - Legacy Corrections
AUTHOR NAME	Thierry Coquand	SVM HeaderParse 0.1
AUTHOR AFFIL	Programming Methodology Group. Department of Computer Sciences. Chalmers; University of Technology and University of Goteborg	SVM HeaderParse 0.2
AUTHOR ADDR	S-412 96 Goteborg, Sweden	SVM HeaderParse 0.1
ABSTRACT	. We show that infinite objects can be constructively understood without the consideration of partial elements, or greatest fixedpoints, through the explicit consideration of proof objects. We present then a proof system based on these explanations. According to this analysis, the proof expressions should have the same structure as the program expressions of a pure functional lazy language: variable, constructor, application, abstraction, case expressions, and local let expressions. 1 Introduction The usual explanation of infinite objects relies on the use of greatest fixed-points of monotone operators, whose existence is justified by the impredicative proof of Tarski's fixed point theorem. The proof theory of such infinite objects, based on the so called co-induction principle, originally due to David Park [21] and explained with this name for instance in the paper [18], reflects this explanation. Constructively, to rely on such impredicative methods is somewhat unsatisfactory (see fo...	user correction - Legacy Corrections
YEAR	0	user correction - Legacy Corrections
CITATIONS	26 found	ParsCit 1.0