## Journal of Symbolic Logic

### Strong normalization proof with CPS-translation for second order classical natural deduction

#### Abstract

This paper points out an error of Parigot’s proof of strong normalization of second order classical natural deduction by the CPS-translation, discusses erasing-continuation of the CPS-translation, and corrects that proof by using the notion of augmentations.

#### Article information

Source
J. Symbolic Logic, Volume 68, Issue 3 (2003), 851- 859.

Dates
First available in Project Euclid: 17 July 2003

https://projecteuclid.org/euclid.jsl/1058448444

Digital Object Identifier
doi:10.2178/jsl/1058448444

Mathematical Reviews number (MathSciNet)
MR2000483

Zentralblatt MATH identifier
1058.03060

#### Citation

Nakazawa, Koji; Tatsuta, Makoto. Strong normalization proof with CPS-translation for second order classical natural deduction. J. Symbolic Logic 68 (2003), no. 3, 851-- 859. doi:10.2178/jsl/1058448444. https://projecteuclid.org/euclid.jsl/1058448444

#### References

• P. de Groote A CPS-translation for the $\lambda\mu$-calculus, Lecture Notes in Computer Science, vol. 787, Springer-Verlag,1994.
• K. Fujita Domain-free $\lambda\mu$-calculus, Theoretical Informatics and Applications, vol. 34 (2000), pp. 433--466.
• J.-Y. Girard, P. Taylor, and Y. Lafont Proofs and types, Cambridge University Press,1989.
• K. Nakazawa Confluency and strong normalizability of call-by-value $\lambda\mu$-calculus, Theoretical Computer Science, vol. 290 (2003), no. 1, pp. 429--463.
• M. Parigot $\lambda\mu$-calculus: an algorithmic interpretation of natural deduction, Proceedings of the international conference on logic programming and automated reasoning, Lecture Notes in Computer Science, vol. 624, Springer-Verlag,1992, pp. 190--201.
• G. D. Plotkin Call-by-name, call-by-value and the $\lambda$-calculus, Theoretical Computer Science, vol. 1 (1975), pp. 125--159.