Substitution up to isomorphism

P.-L. Curien

Diagrammes (1990)

  • Volume: 23, page 43-66
  • ISSN: 0224-3911

How to cite


Curien, P.-L.. "Substitution up to isomorphism." Diagrammes 23 (1990): 43-66. <>.

author = {Curien, P.-L.},
journal = {Diagrammes},
keywords = {categorical semantics of dependent types; coherence problems; modelling of substitution in types by pullbacks; interpretation of dependent types in a locally Cartesian closed category},
language = {eng},
pages = {43-66},
publisher = {Université Paris 7, Unité d'enseignement et de recherche de mathématiques},
title = {Substitution up to isomorphism},
url = {},
volume = {23},
year = {1990},

AU - Curien, P.-L.
TI - Substitution up to isomorphism
JO - Diagrammes
PY - 1990
PB - Université Paris 7, Unité d'enseignement et de recherche de mathématiques
VL - 23
SP - 43
EP - 66
LA - eng
KW - categorical semantics of dependent types; coherence problems; modelling of substitution in types by pullbacks; interpretation of dependent types in a locally Cartesian closed category
UR -
ER -


  1. [ACCL] M. Abadi, L. Cardelli, P.-L. Curien, J.-J. Lévy, Explicit Substitutions, in Proc. ACM Principles of Programming Languages, San Francisco ( 1990). MR1140338
  2. [Brui] N. De Bruijn, Lambda-calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, Indag Math. 34 ( 1972). Zbl0253.68007
  3. [Cart] J. Cartmell, Generalized Algebraic Theories and Contextual Categories, Thesis, Oxford ( 1978). 
  4. [Coq] T. Coquand, Metamathematical Investigations of a Calculus of Constructions, Technical Report, Cambridge University ( 1987). 
  5. [CoqEhr] T. Coquand, T. Ehrhard, An Equational Presentation of Higher-Order Logic, Proc. 2nd Conf. on Category Theory and Computer Science, Lecture Notes in Comput. Sci. 283 ( 1987). Zbl0643.03050MR925223
  6. [CouCurMau] G. Cousineau, P.-L. Curien, M. Mauny, The Categorical Abstract Machine, Science of Computer Programming 8, pp. 173-202 ( 1987). Zbl0634.68078MR896255
  7. [CuGhe] P.-L. Curien, G. Ghelli, Coherence of Subsumption, accepted at CAAP 90, Copenhaguen. Zbl0759.03009
  8. [Cur1] P.-L. Curien, Categorical Combinators, Sequential Algorithms and Functional Programming, Pitman ( 1986). Zbl0643.68004MR840874
  9. [Cur2] P.-L. Curien, α-conversion, Conditions on Variables and Categorical Logic, Studia Logica, to appear. Zbl0701.03036MR1059246
  10. [Ehr] T. Ehrhard, A Categorical Semantics of Constructions, LICS 88, Edinburgh ( 1988). 
  11. [Guit] R. Guitart, Relations et Carrés Exacts, Annales Sci. Math, du Québec, Vol. IV , No2, pp. 103-125 ( 1980). Zbl0495.18008MR599050
  12. [HarLa] T. Hardin, A. Laville, Proof of Termination of the Rewriting System Subst on CCL, Theoret. Comput. Sci. 46, pp. 305-312 ( 1986). Zbl0618.68031MR869211
  13. [HueOp] G. Huet, D. Oppen, Equations and Rewrite Rules: a Survey, in FormalLanguages, Perspectives and Open Problems, R. Book ed., Academie Press ( 1980). 
  14. [HyPit] M. Hyland, A. Pitts, The Theory of Constructions: Categorical Semantics and Topos-theoretic Models, Proc. Conf. on Categories in Computer Science and Logic, to appear as Contemporary Mathematics volume, Boulder ( 1987). Zbl0721.03048MR925222
  15. [Jac] B. Jacobs, Some Notes on Fibred Categories and the Semantics of Dependent Types, Technical Report 22/89, Universita di Pisa, ( 1989). 
  16. [Laf] Y. Lafont, Personal communication. 
  17. [Lam] F. Lamarche, A Simple Model of the Theory of Constructions, in J. Gray and A. Scedrov (eds), Categories in Computer Science and Logic, Contemporary Mathematics 92, 1989. Zbl0683.18006MR1003200
  18. [Law] W. Lawvere, Adjointness in Foundations, Dialectica 23(3/4) ( 1969). Zbl0341.18002
  19. [MacLaPar] S. Mac Lane, R. Paré, Coherence for Bicategories and Indexed Categories, Journal of Pure and Applied Logic 37, 59-80 ( 1985). Zbl0567.18003MR794793
  20. [Mar] P. Martin-Löf, Intuitionistic Type Theory, Bibliopolis ( 1984). Zbl0571.03030MR769301
  21. [MeyRein] A. Meyer, M. Reinhold, Type' is not a Type, Proc. LICS 86. 
  22. [Ob] A. Obtulowicz, Categorical and Algebraic Aspects of Martin-Löf Type Theory, Studia Logica, to appear. Zbl0714.03050MR1059245
  23. [Pow] A. Power, A 2-categorical Pasting Theorem, Journal of Algebra, to appear. Zbl0698.18005
  24. [Rod]E.G. Rodeja F., editor of various technical reports of theDepartamento of Algebra y Fundamentos del Universidad de Santiago de Compostela, starting withTeoria de Triples by J.R. Caruncho Castro . 
  25. [Se] R. Seely, Locally cartesian closed categories and type theory, Math. Proc. Camb. Phil. Soc. 95 ( 1984). Zbl0539.03048MR727078
  26. [Stre] T. Streicher, Correctness and Completeness of a Semantics of the Calculus of Constructions with Respect to Interpretation in Doctrines of Constructions, Thesis, Universität Passau ( 1988). Zbl0684.03025
  27. [Tay] P. Taylor, Recursive Domains, Indexed Category Theory and Polymorphism, PhD Thesis, University of Cambridge ( 1986). 

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