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Are subsets necessary in Martin-Lof type theory?
Simon Thompson
In J. P. Myers Jr. and M. J. O'Donnell, editors, Constructivity in Computer Science, volume 613 of Lecture Notes in Computer Science, pages 46-57. Springer-Verlag, January 1992.Abstract
After introducing Martin-Lof's type theory, the paper introduces the rules proposed by various authors for adding subset types to the system, and the justification given for their addition.
These justifications are examined, and it is argued that by a combination of lazy evaluation and transformation using the Axiom of Choice that subsets need not be added to the system to make it usable.
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Bibtex Record
@conference{202,
author = {Simon Thompson},
title = {Are subsets necessary in {M}artin-{L}of type theory?},
month = {January},
year = {1992},
pages = {46-57},
keywords = {constructivity Martin-Lof computational irrelevance subsets},
note = {},
doi = {},
url = {http://www.cs.kent.ac.uk/pubs/1992/202},
ISBN = {3-540-55631-1},
booktitle = {Constructivity in Computer Science},
editor = {J. P. Myers Jr. and M. J. O'Donnell},
publisher = {Springer-Verlag},
refereed = {yes},
series = {Lecture Notes in Computer Science},
volume = {613},
}