Cited By
View all- Rahli VBickford MAvigad JChlipala A(2016)A nominal exploration of intuitionismProceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs10.1145/2854065.2854077(130-141)Online publication date: 18-Jan-2016
A Note on Forcing and Type Theory
Pages 43 - 52
Abstract
The goal of this note is to show the uniform continuity of definable functional in intuitionistic type theory as an application of forcing with dependent type theory.
References
[1]
S. Allen. A Non-Type-Theoretic Definition of Martin-Löf's Types. Proceedings of the Second IEE Symposium LICS 1987, 215-224.
[2]
H. Barendregt. The impact of the lambda calculus. Bulletin of Symbolic Logic, Volume 3, 1997, 181-215.
[3]
M.J. Beeson. Foundations of Constructive Mathematics. Springer-Verlag, 1985.
[4]
E.W. Beth. The foundations of mathematics. North-Holland, Amsterdam, 1965.
[5]
L.E.J. Brouwer. Über Definitionsbereiche von Funktionen. Mathematische Annalen, 97:60-75. English translation in van Heijenoort, (1967, 446-463).
[6]
P. Cohen. The discovery of forcing. Rocky Mountain J. Math. 32 (2002), 1071-110.
[7]
K. Gödel. On a hitherto unexploited extension of the finitary standpoint. in Collected Works, Vol. II. Publications 1938-1974, Oxford University Press, 1990.
[8]
D. Hilbert. Über das Unendliche. Mathematische Annalen, 95:161-190. Lecture given in Münster, 4 june 1925. English translation in van Heijenoort, (1967, 367-392).
[9]
J.L. Krivine. Structures de réalisabilité, RAM et ultrafiltre sur N. To appear, 2010.
[10]
P. Martin-Löf. On the strength of intuitionistic reasoning. Unpublished report, talk at the Bucharest conference, 1971.
[11]
P. Martin-Löf. An intuitionistic theory of types in Twenty-Five Years of Type Theory, G. Sambin and J. Smith Eds., Oxford University Press, 1998 (reprinted version of an unpublished report from 1972).
[12]
R. Platek. Generalized Recursion Theory, Stanford and Me. In: Odifreddi, P. (ed.) Kreiseliana, About and Around Georg Kreisel (1996).
[13]
W.W. Tait. Intensional interpretations of functional of finite types I. Journal of Symbolic Logic 32 (1967), 198-212.
[14]
J. van Heijenoort (ed.) From Frege to Hilbert: A Source Book in Mathematical Logic, 1897-1941. Harvard University Press, 1967.
Index Terms
- A Note on Forcing and Type Theory
Recommendations
Type-preserving CPS translation of Σ and Π types is not not possible
Dependently typed languages such as Coq are used to specify and prove functional correctness of source programs, but what we ultimately need are guarantees about correctness of compiled code. By preserving dependent types through each compiler pass, we ...
Partial Gradual Dependent Type Theory
SPLASH 2023: Companion Proceedings of the 2023 ACM SIGPLAN International Conference on Systems, Programming, Languages, and Applications: Software for HumanityGradual typing supports imprecise types in the type system, allowing incremental migration from untyped code to typed in the same language. Through the gradual typing approach, our ongoing work proposes a new theory based on the Martin-Löf type theory ...
Canonicity for 2-dimensional type theory
POPL '12: Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languagesHigher-dimensional dependent type theory enriches conventional one-dimensional dependent type theory with additional structure expressing equivalence of elements of a type. This structure may be employed in a variety of ways to capture rather coarse ...
Comments
Information & Contributors
Information
Published In
Publisher
IOS Press
Netherlands
Publication History
Published: 01 January 2010
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 01 Nov 2024
Other Metrics
Citations
Cited By
View all- Rahli VBickford MAvigad JChlipala A(2016)A nominal exploration of intuitionismProceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs10.1145/2854065.2854077(130-141)Online publication date: 18-Jan-2016
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in