The paradox of trees in Type Theory

The paradox of trees in Type Theory (1991)

by Thierry Coquand

Venue:	BIT
Citations:	2 - 0 self

Datum	Value	Source
TITLE	The paradox of trees in type theory	INFERENCE
AUTHOR NAME	Thierry Coquand	SVM HeaderParse 0.1
AUTHOR AFFIL	INRIA, and University of Goteborg/Chalmers; Abstract.	SVM HeaderParse 0.2
ABSTRACT	We show how to represent a paradox similar to Russell's paradox in Type Theory with W-types and a type of all types, and how to use this in order to represent a fixed-point operator in such a theory. It is still open whether or not such a construction is possible without the W-type. Introduction. It is known that Martin-Lof's Type Theory with one universe is inconsistent if this universe contains a name of itself (cf. [5,6,7,8]). Though it is possible under this hypothesis to produce a paradox similar to the one of Russell if we have an extensional equality (i.e.	SVM HeaderParse 0.1
YEAR	1992	INFERENCE
VENUE	BIT	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
VOLUME	32	INFERENCE
CITATIONS	7 found	ParsCit 1.0