Order-Sorted Inductive Types

Information and Computation

Volumn 149, Issue 1, 1999, Pages 42-76

  Barthe, Gilles ^a  

^a UNIVERSITY OF MINHO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347029507     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1006/inco.1998.2751     Document Type: Article

References (32)

1. Abadi, M., and Cardelli, L. (1996), "A Theory of Objects," Springer-Verlag, Berlin/New York.
2. Aspinall, D., and Compagnoni, A. (1996), Subtyping dependent types, in "Proceedings, LICS'96," pp. 86-97, IEEE Computer Society Press, Los Alamitos, CA.
3. Aczel, P. (1977), An introduction to inductive definitions, in "Handbook of Mathematical Logic" (J. Bacwise, Ed.), Vol. 90, Studies in Logic and the Foundations of Mathematics, pp. 739-782, North-Holland, Amsterdam.
4. Barendregt, H. (1992), Lambda calculi with types, in "Handbook of Logic in Computer Science" (S. Abramsky, D. Gabay, and T. Maibaum, Eds.), Vol. 2, pp. 117-309, Oxford Science Publications, London.
5. Bastiansen, T. J. (1995), "Parametric Subtypes in ABEL," Technical Report 207, Department of Informatics, University of Oslo.
6. Betarte, G. (1998), "Dependent Record Types and Algebraic Structures in Type Theory," Ph.D. thesis, Department of Computer Science, Chalmers Tekniska Högskola.
7. ≤, manuscript, D.E.C..
8. Compagnoni, A. (1995), "Higher-Order Subtyping with Intersection Types," Ph.D. thesis, Department of Computer Science, University of Nijmegen.
9. Coquand, T. (1992), Pattern matching in type theory, in "Informal Proceedings of Logical Frameworks'92" (B. Nordström, Ed.), pp. 66-79.
10. Cornes, C. (1997), "Conception d'un langage de haut niveau de représentation de preuves: Récurrence par filtrage de motifs; Unification en présence de types inductifs primitifs; Synthèse de lemmes d'inversion," Ph.D. thesis, Université de Paris 7.
11. Dahl, O.-J., Owe, O., and Bastiansen, T. J. (1998), Subtyping and constructive specification, Nordic J. Computing 5(1).
12. Dybjer, P. (1994), Inductive families, Formal Aspects Comput. 6, 440-465.
13. Elbers, H. (1998), "Connecting Formal and Informal Mathematics," Ph.D. thesis, Technische Universiteit, Eindhoven.
14. Freeman, T., and Pfenning, F. (Refinement types for ML), in "Proceedings, PLDI'91," pp. 268-277, Assoc. Comput. Mach., New York.
15. Goguen, J., and Diaconescu, R. (1994), An Oxford survey of order sorted algebra, Math. Struct. Comput. Sci. 4, 363-392.
16. Goguen, J., and Meseguer, J. (1985), Completeness of many-sorted equational logic, Houston J. Math. 11(3), 307-334.
17. Goguen, J., and Meseguer, J. (1992), Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations, Theoretic. Comput. Sci. 105(2), 216-273.
18. Hallgren, T. (1993), "Subtypes in Polymorphic Functional Languages," Licenciate thesis, Department of Computer Science, Chalmers Tekniska Högskola.
19. Hofmann, M., and Pierce, B. (1995), A unifying type-theoretic framework for objects, J. Funct. Programming 5(4), 593-635.
20. Kahn, G. (1987), Natural semantics, in "Proceedings, Symposium on Theoretical Aspects of Computer Science," pp. 22-39, Lecture Notes in Computer Science, Vol. 247, Springer-Verlag, Berlin/New York.
21. Kristroffersen, B., and Dahl, O.-J. (1998), On introducing higher order functions in ABEL, Nordic J. Comput. 5(1).
22. Klop, J. W., van Oostrom, V., and van Raamsdonk, F. (1993), Combinatory reduction systems: Introduction and survey, Theoret. Comput. Sci. 121(1-2), 279-308.
23. Luo, Z. (Coercive subtyping), J. Logic Comput., to appear.
24. Meseguer, J., and Goguen, J. (1985), Initiality, induction and computability, in "Algebraic Methods in Semantics" (M. Nivat and J. Reynolds, Eds.), pp. 459-541, Cambridge Univ. Press, Cambridge, UK.
25. Nordström, B., Petersson, K., and Smith, J. (1990), "Programming in Martin-Löf's Type Theory. An Introduction," International Series of Monographs on Computer Science, Vol. 7, Oxford Univ. Press, London.
26. Owe, O., and Dahl, O.-J. (1991), Generator induction in order-sorted algebras, Formal Aspects Comput. 3(1), 2-20.
27. Pfenning, F. (1993), Refinement types for logical frameworks, in "Informal Proceedings of TYPES'93" (H. Geuvers, Ed.), pp. 285-299.
28. Paulin-Mohring, C. (1993), Inductive definitions in the system Coq. Rules and properties, in "Proceedings, TLCA'93" (M. Bezem and J. F. Groote, Eds.), Lectures Notes in Computer Science, pp. 328-345, Vol. 664, Springer-Verlag, Berlin/New York.
29. Pollack, R. (1994), "The Theory of LEGO: A Proof Checker for the Extended Calculus of Constructions," Ph.D. thesis, University of Edinburgh.
30. Pierce, B., and Steffen, M. (1997), Higher-order subtyping, Theoret. Comput. Sci. 176(1-2), 253-282.
31. Pierce, B., and Turner, D. (1994), Simple type-theoretic foundations for object-oriented programming, J. Funct. Programming 4(2), 207-247.
32. Steffen, M. (1997), "Polarized Higher-Order Subtyping," Ph.D. thesis, Department of Computer Science, University of Erlangen.