The paradox of trees in type theory
Programming Logic
Received:
Revised:
- 64 Downloads
- 1 Citations
Abstract
We show how to represent a paradox similar to Russell's paradox in Type Theory withW-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 such a construction is possible without theW-type.
C.R. Categories
D.2.1 D.2.4 D.3.1 F.3.1 F.3.3Preview
Unable to display preview. Download preview PDF.
References
- 1.Martin-Löf, P.,Intuitionistic Type Theory, Bibliopolis, 1984.Google Scholar
- 2.Palmgren, E.,A construction of Type: Type in Martin-Löf's partial type theory with one universe, Unpublished manuscript.Google Scholar
- 3.Palmgren, E. and Stoltenberg-Hansen, V.,Domain Interpretations of Intuitionistic Type Theory, Uppsala University. U.U.D. Report 1989: 1.Google Scholar
- 4.Aczel, P.,The type theoretic interpretation of constructive set theory, Logic Colloquium '77 (1978), 55–66, A. Macintyre et al., editors.Google Scholar
- 5.Meyer, A. and Reinhold, M. B.,“Type” is not a type, Principles of Programming language, ACM, 1986.Google Scholar
- 6.Howe, D.,The Computational Behaviour of Girard's Paradox, Symposium on Logic in Computer Science, Ithaca, New York, 1987.Google Scholar
- 7.Hayashi, S. and Nakano, H.,Communication in the TYPES electronic forum (August 7, 1987), types theory. lcs. mit. edu.Google Scholar
- 8.Girard, J. Y.,Interprétation fonctionnelle et élimination des coupures dans l'arithmétique d'ordre supérieure, Thèse d'Etat, Paris VII, 1972.Google Scholar
Copyright information
© BIT Foundations 1992