Program extraction from normalization proofs

Studia Logica

Volumn 82, Issue 1, 2006, Pages 25-49

  Berger, Ulrich ^a   Berghofer, Stefan ^b   Letouzey, Pierre ^c   Schwichtenberg, Helmut ^d  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^c UNIVERSITÉ PARIS DESCARTES   (France)

^d UNIVERSITY OF MUNICH   (Germany)

Author keywords

Normalization by evaluation; Program extraction from proofs; Realizability; Typed lambda calculus

Indexed keywords

EID: 32044435391     PISSN: 00393215     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11225-006-6604-5     Document Type: Review

References (21)

1. ALTENKIRCH, T., 'Proving strong normalization of CC by modifying realizability semantics', in H. Barendregt and T. Nipkow, (eds.), Types for Proofs and Programs. International Workshop TYPES '93. Nijmegen, The Netherlands, May 1993, volume 806 of LNCS Springer Verlag, 1994, pp. 3-18.
2. ALTENKIRCH, T., P. DYBJER, M. HOFMANN, and P. SCOTT, 'Normalization by evaluation for typed lambda calculus with coproducts', in LICS '01: Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science, IEEE Computer Society, Washington, DC, USA, 2001, p. 303.
3. ALTENKIRCH, T., M. HOFMANN, and T. STREICHER, 'Reduction-free normalisation for a polymorphic system', in 11th Annual IEEE Symposium on Logic in Computer Science, 1996, pp. 98-106.
4. BERGER, U., 'Program extraction from normalization proofs', in M. Bezem, and J.F. Groote, (eds.), Typed Lambda Calculi and Applications, volume 664 of LNCS, Springer Verlag, 1993, pp. 91-106.
5. BERGER, U., M. EBERL, and H. SCHWICHTENBERG, 'Normalization by evaluation', in B. Möller, and J.V. Tucker, (eds.), Prospects for Hardware Foundations, volume 1546 of LNCS, Springer Verlag, 1998, pp. 117-137.
6. BERGER, U., and H. SCHWICHTENBERG, 'An inverse of the evaluation functional for typed λ-calculus', in R. Vemuri, (ed.), Proceedings of the Sixth Annual IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, Los Alamitos, 1991, pp. 203-211.
7. BERGHOFER, S., Proofs, Programs and Executable Specifications in Higher Order Logic, PhD thesis, Institut für Informatik, TU München, 2003.
8. BIERNACKA, M., O. DANVY, and K. STOVRING, 'Program extraction from proofs of weak head normalization', in Preliminary proceedings of MFPS XXI, Birmingham, UK, 2005, pp. 105-123.
9. COQUAND, C., 'From semantics to rules: A machine assisted analysis', in E. Börger, Y. Gurevich, and K. Meinke, (eds.), Computer Science Logic, 7th Workshop, Swansea 1993, volume 832 of LNCS, Springer Verlag, 1994, pp. 91-105.
10. COQUAND, T., and P. DYBJER, 'Intuitionistic model constructions and normalization proofs', Mathematical Structures in Computer Science, 7:73-94, 1997.
11. de BRUIJN, N. G., 'Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem', Indagationes Math., 34:381-392, 1972.
12. KREISEL, G., 'Interpretation of analysis by means of constructive functionals of finite types', in A. Heyting, (ed.), Constructivity in Mathematics, North-Holland, Amsterdam, 1959, pp. 101-128.
13. LARSEN, K. G., and G. WINSKEL, 'Using information systems to solve recursive domain equations', Information and Computation, 91:232-258, 1991.
14. LETOUZEY, P., 'A New Extraction for Coq', in H. Geuvers and F. Wiedijk, (eds.), Types for Proofs and Programs, Second International Workshop, TYPES 2002, volume 2646 of Lecture Notes in Computer Science. Springer-Verlag, 2003.
15. Letouzey, P., Programmation fonctionnelle certifiée - L'extraction de programmes dans l'assistant Coq. PhD thesis, Univ. Paris-Sud, 2004.
16. LETOUZEY, P., and B. SPITTERS, 'Implicit and noncomputational arguments using monads', 2005. Submitted for publication, available at http://www.lri.fr/~letouzey/down.load/Letouzey_Spitters_05.pdf.
17. ω 's programs from proofs in the Calculus of Constructions', in Sixteenth Annual ACM Symposium on Principles of Programming Languages, Austin, January 1989. ACM Press.
18. PAULIN-MOHRING, C., and B. WERNER, 'Synthesis of ML programs in the system Coq', J. Symbolic Computation, 11:1-34, 1993.
19. SCHWICHTENBERG, H., Minimal logic for computable functionals, 2004.
20. The Coq Development Team, The Coq Proof Assistant Reference Manual - Version 8.0, February 2004. Available at http://coq.inria.fr/.
21. TROELSTRA, A. S., (ed.), Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, volume 344 of Lecture Notes in Mathematics. Springer Verlag, 1973.