Some logical and syntactical observations concerning the first-order dependent type system λP

Mathematical Structures in Computer Science

Volumn 9, Issue 4, 1999, Pages 335-359

  Uvers, Herman Ge ^a   Barendsen, Erik ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11444254339     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0960129599002856     Document Type: Article

References (24)

1. Avron, A., Honsell, F. and Mason, I. (1987) Using typed lambda calculus to implement formal systems on a machine. Report 31–37, LFCS Edinburgh, UK.
2. Barendregt, H. P. (1992) Typed lambda calculi. In: Abramsky et al. (eds.) Handbook of Logic in Computer Science, Oxford University Press.
3. Barendsen, E. and Geuvers, H. (1989) λP is conservative over first-order predicate logic. Manuscript, Faculty of Mathematics and Computer Science, University of Nijmegen, Netherlands.
4. Berardi, S. (1990) Type dependence and constructive mathematics, Ph. D. thesis, Universita di Torino, Italy.
5. Bezem, M. and Springintveld, J. (1996) A simple proof of the undecidability of inhabitation in λP. Journal of Functional Programming 6 (5) 757–761.
6. de Bruijn, N. G. (1980) A survey of the project Automath, In: Seldin, J. P. and Hindley, J. R. (eds.) To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, New York 580–606.
7. Coquand, Th. (1991) An algorithm for testing conversion in type theory. In: Huet, G. and Plotkin, G. (eds.) Logical Frameworks, Cambridge University Press.
8. Coquand, Th. and Huet, G. (1988) The calculus of constructions. Information and Computation 76 95–120.
9. Coquand, Th. and Huet, G. (1985) Constructions: a higher order proof system for mechanizing mathematics. Proceedings of EUROCAL ’85, Linz. Springer-Verlag Lecture Notes in Computer Science 203.
10. van Daalen, D. (1973) A description of AUTOMATH and some aspects of its language theory. In: Braffort, P. (ed.) Proceedings of the symposium on APL, Paris.
11. Dowek, G. (1993) The undecidability of typability in the λPπ-calculus. In: Bezem, M. and Groote, J. F. (eds.) Typed Lambda calculi and applications. Springer-Verlag Lecture Notes in Computer Science 664 139–145.
12. Geuvers, J. H. and Nederhof, M.J. (1991) A modular proof of strong normalisation for the calculus of constructions. Journal of Functional Programming 1 (2) 155–189.
13. Geuvers, J.H. (1992) The Church—Rosser property for βμ-reduction in typed lambda calculi. In: Proceedings of the seventh annual symposium on Logic in Computer Science, Santa Cruz, Cal., IEEE 453–460.
14. Geuvers, J. H. (1993) Logics and Type systems, Ph. D. Thesis, University of Nijmegen, Netherlands.
15. Geuvers, J. H. (1995) A short and flexible proof of Strong Normalization for the Calculus of Constructions. In: Dybjer, P., Nordstrom, B. and Smith, J. (eds.) Types for Proofs and Programs, Int. Workshop, Bastad, Sweden. Springer-Verlag Lecture Notes in Computer Science 996 14–38.
16. Harper, R., Honsell, F. and Plotkin, G. (1987) A framework for defining logics. Proceedings Second Symposium on Logic in Computer Science, (Ithaca, N.Y.), IEEE, Washington DC 194–204.
17. Harper, R., Honsell, F. and Plotkin, G. (1993) A framework for defining logics. Journal of the ACM 143–184.
18. Hindley, J. R. and Seldin, J. P. (1986) Introduction to Combinators and λ-Calculus, London Math. Soc. Student Texts 1, Cambridge University Press.
19. Howard, W. A. (1980) The formulas-as-types notion of construction. In: Seldin, J. P. and Hindley, J. R. (eds.) To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, New York 479–490.
20. Martin-Lof, P. (1975) An intuitionistic theory of types: predicative part. In: Rose, H. E. et al. (eds.) Logic Colloquium 1973, North-Holland 73–118.
21. Mohring, Ch. (1986) Algorithm development in the Calculus of Constructions. In: Proceedings First Symposium on Logic in Computer Science, (Cambridge, Mass.), IEEE, Washington DC 84–91.
22. Nederpelt, R. P. Geuvers, J. H. and de Vrijer, R. C. (eds.) (1994) Selected Papers on Automath. Studies in Logic and the Foundations of Mathematics 133, North-Holland, Amsterdam, 1024.
23. Salvesen, A. (1989) The Church-Rosser Theorem for LF with n reduction. Notes of a talk presented at the BRA-Logical Frameworks meeting, Antibes 1990.
24. Swaen, M. (1989) Weak and strong sum-elimination in intuitionistic type theory, Ph. D. thesis, Faculty of Mathematics and Computer Science, University of Amsterdam, Netherlands, September 1989.