Normalization and the Yoneda embedding

Mathematical Structures in Computer Science

Volumn 8, Issue 2, 1998, Pages 153-192

  Čubrić, Djordje ^a   Dybjer, Peter ^b   Scott, Philip ^c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^c UNIVERSITY OF OTTAWA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000453245     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129597002508     Document Type: Article

References (37)

1. Aczel, P. (1993) Galois: a theory development project. In: A report on work in progress for the Turin meeting on the Representation of Logical Frameworks.
2. Altenkirch, T., Hofmann, M. and Streicher, T. (1995) Categorical reconstruction of a reduction-free normalisation proof. Proc. CTCS '95. Springer-Verlag Lecture Notes in Computer Science 953 182–199.
3. Barendregt, H. P. (1984) The Lambda Calculus, Studies in Logic 103, North-Holland.
4. Barendregt, H.P. (1992) Lambda Calculus with Types. In: Abramsky, S., Gabbay, D. and Maibaum, T. (eds.) Handbook of Logic in Computer Science, Vol. 2, Oxford University Press.
5. Beeson, M. (1985) Foundations of Constructive Mathematics, Springer-Verlag.
6. Berger, U. and Schwichtenberg, H. (1991) An inverse to the evaluation functional for typed λ-calculus. Proc. of the 6th Annual IEEE Symposium of Logic in Computer Science 203–211.
7. Beylin, I. and Dybjer, P. (1996) Extracting a proof of coherence for monoidal categories from a proof of normalization for monoids. In: Berardi, S. and Coppo, M. (eds.) Types for Proofs and Programs (= TYPES '95). Springer-Verlag Lecture Notes in Computer Science 1158 47–61
8. Breazu-Tannen, V. (1988) Combining algebra and higher-order types. Proc. Logic in Computer Science (LICS) 82–90.
9. Coquand, C. (1993) From Semantics to Rules: a Machine Assisted Analysis. In: Gurevich, Y. and Meinke, K. (eds.) Proceedings of CSL '93, Egon Borger. Springer-Verlag Lecture Notes in Computer Science 832.
10. Coquand, T. and Dybjer, P. (1997) Intuitionistic Model Constructions and Normalization Proofs. Mathematical Structures in Computer Science 7 75-94.
11. Crole, R. (1993) Categories for Types, Cambridge Mathematical Textbooks.
12. Čubrić D. (to appear) Embedding of a free cartesian closed category into the category of Sets. To appear in J. Pure and Applied algebra.
13. Di Cosmo, R. (1995) Isomorphism of Types: from 2-calculus to information retrieval and language design, Birkhauser.
14. Duval, D. and Reynaud, J.-C. (1994) Sketches and computation I: basic definitions and static evaluation. Mathematical Structures in Computer Science 4 185–238.
15. Friedman, H. (1975) Equality between functionals. Logic Colloquium '73. Springer-Verlag Lecture Notes in Mathematics 453 22–37.
16. Girard, J. Y. (1987) Proof Theory and Logical Complexity, vol. 1, Bibliopolis.
17. Girard, J.Y., Lafont, Y. and Taylor, P. (1989) Proofs and Types, Cambridge Tracts in Theoretical Computer Science 7, Cambridge University Press.
18. Gordon, R., Power, A. and Street, R. (1996) Coherence for tricategories, Memoirs of the American Mathematical Society.
19. Harnik, V. and Makkai, M. (1992) Lambek's categorical proof theory and Lauchli's abstract realizability. J. Symbolic Logic 57 200–230.
20. Huet, G. (1976) Resolution d'equations dans les langages d’ordre 1,2, …, co, These d'Etat, U. Paris 7.
21. Huet, G. and Saibi, A. (1995) Constructive Category Theory. Proceedings of the Joint CLICS-TYPES Workshop on Categories and Type Theory (Goteborg), January 1995.
22. Joyal, A. and Street, R. (1993) Braided tensor categories. Advances in Mathematics 102 (1) 20–79.
23. Jouannaud, J.-P. and Okada, M. (1991) A Computation Model for Executable Higher-Order Algebraic Specification Languages. LICS 6 (sixth Annual IEEE Symp. on Logic in Computer Science) 350–361.
24. Kelly, G. M. (1982) Basic Concepts of Enriched Category Theory, London Math. Soc. Lecture Notes 64, Cambridge University Press.
25. Lack, S. G. (1995) The algebra of distributive and extensive categories, Ph.D. thesis, University of Cambridge.
26. Lafont, Y. (1988) Logiques, categories et machines, These de doctorat, Universite Paris 7.
27. Lambek, J. (1968) Deductive Systems and Categories I. J. Math. Systems Theory 2 278–318.
28. Lambek, J. and Scott, P. J. (1986) Introduction to Higher Order Categorical Logic, Cambridge Studies in Advanced Mathematics 7, Cambridge University Press.
29. Mac Lane, S. (1971) Categories for the Working Mathematician, Graduate Texts in Mathematics 5, Springer-Verlag.
30. Martin-Lof, P. (1975a) An Intuitionistic Theory of Types: Predicative Part. In: Rose, H.E. and Shepherdson, J. C. (eds.) Logic Colloquium 73, North-Holland 73–118.
31. Martin-Lof, P. (1975b) About Models for Intuitionistic Type Theories and The Notion of Def-initional Equality. In: Kanger, S. (ed.) Proceedings of the 3rd Scandinavian Logic Symposium, North-Holland 81–109.
32. Mitchell, J. C. (1990) Type Systems for Programming Languages. In: Van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, Vol. B, (Formal Models and Semantics), North-Holland 365–458.
33. Mitchell, J. C. and Scott, P.J. (1989) Typed Lambda Models and Cartesian Closed Categories. In: Gray, J. and Scedrov, A. (eds.) Contemp. Math.: Categories in Computer Science and Logic 92 301–316.
34. Pitts, A. (1997) Categorical Logic. In: Abramsky, S., Gabbay, D.M. and Maibaum, T. S.E. (eds.) Handbook of Logic in Computer Science, Vol. 6, Oxford University Press (to appear).
35. Power, J. (1989) A general coherence result. J. Pure and Applied Algebra 57 165–173.
36. Statman, R. (1985) Logical Relations and the Typed Lambda Calculus. Inf. and Control 65 85–97.
37. Troelstra, A. S. (1973) Metamathematical investigations of intuitionistic arithmetic and analysis. Springer-Verlag Lecture Notes in Mathematics 344.