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PER models of subtyping, recursive types and higher-order polymorphism

Authors:

Kim Bruce,

John C. MitchellAuthors Info & Claims

POPL '92: Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Pages 316 - 327

https://doi.org/10.1145/143165.143230

Published: 01 February 1992 Publication History

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References

[1]

R.M. Amadio. Recursion over realizability structures. Information and Computation, 91(1):55-86, 1991.

Digital Library

Google Scholar

[2]

S. Abramsky, J. Mitchell, A. Scedrov, and P. Wadler. Relators. Manuscript, 1991.

Google Scholar

[3]

M Abadi and G.D. Plotkin. A PER model of polymorphism and recursive types. In Proc. IEEE Syrup. on Logic in Computer Science, pages 355-365, 1990.

Crossref

Google Scholar

[4]

H.P. Barendregt. The Lambda Calculus: Its Syntax and Semantics. North- Holland, Amsterdam, 1984. Second edition.

Google Scholar

[5]

K. Bruce and G. Longo. A modest model of records, inheritance and bounded quantification. Information and Computation, 87(1/2):196-240, 1990.

Digital Library

Google Scholar

[6]

K.B. Bruce, A. 1%. Meyer, and J. C. Mitchell. The semantics of second-order lambda calculus. Information and Computation, 85(1):76-134, 1990. Reprinted in Logical Foundations of Functional Programming, ed. G. Huet, Addison-Wesley (1990) 213-273.

Digital Library

Google Scholar

[7]

V. Breazu-Tannen, T. Coquand, C.A. Gunter, and A. Scedrov. Computing with coercions, in Proc. A CM Conference on Lisp and Functional Programming, pages 44-61, 1990.

Digital Library

Google Scholar

[8]

V. Breazu-Tannen, T. Coquand, C.A. Gunter, and A. Scedrov. Inheritance as explicit coercion, information and Computation, 93(1):t72-221, 1991.

Digital Library

Google Scholar

[9]

L. Ca.rdelli. A semantics of multiple inheritance. Information and Computation, 76:t38-164, 1988. Special issue devoted to Syrup. on Semantics of Data Types, Sophia-Antipolis (France), 1984.

Digital Library

Google Scholar

[10]

F. Cardone. Relational semantics for recursive types and bounded quantification. In ICALP, pages 164-178, Berlin, 1989. Springer LNCS 372.

Digital Library

Google Scholar

[11]

L. Cardelli. Examples of type recursion. Personal communication, 1991.

Google Scholar

[12]

P. Canning, W. Cook, W. Hill, J. Mitchell, and W. Olthoff. F-bounded quantification for object-oriented programming. In Functional Prog. and Computer Architecture, pages 273-280, 1989.

Digital Library

Google Scholar

[13]

P. Canning, W. Cook, and W. Hill. Examples of type recursion. Personal communication, 1991.

Google Scholar

[14]

W. Cook, W. Hill, and P. Canning. Inheritance is not subtyping, in Proc. 17th A CM Syrup. on Principles of Programming Languages, pages 125-135, January 1990.

Digital Library

Google Scholar

[15]

L. Cardelli and G. Longo. A semantic basis for Quest. Technical Report 55, DEC Systems Research Center, 1990. To appear in J. Functional Programming.

Digital Library

Google Scholar

[16]

L. Cardelli and J.C. Mitchell. Operations on records. Math. Structures in Computer Science, 1(1):3-48, 1991. Summary in Math. Foundations of Prog. Lang. Semantics, Springer LNCS 442, 1990, pp 22-52.

Digital Library

Google Scholar

[17]

W.R. Cook. A proposal for making Eiffel type-safe. In European Conf. on Objec#Oriented Programming, pages 57- 72, 1989.

Digital Library

Google Scholar

[18]

M. Coppo. A completeness theorem for recursively-defined types. In Proc. ICALP, pages 120-130, Berlin, 1985. Springer LNCS 194.

Digital Library

Google Scholar

[19]

L. Cardelli and P. Wegner. On understanding types, data abstraction, and polymorphism. Computing Surveys, 17(4):471-522, 19S5.

Digital Library

Google Scholar

[20]

P. Freyd, G. Rosolini, P. Mulry, and D.S. Scott. Extens ional P EP~'s. in Proc. IEEE Symp. on Logic in Computer Science, pages 346-354. IEEE, 1990.

Google Scholar

[21]

J.-Y. Girard. Interpretation fonctionelle et elimination des coupures de l'arithmetique d'ordre superieur. These D'Etat, Universite Paris VII, 1972.

Google Scholar

[22]

C.A. Gunter and D.S. Scott. Semantic domains. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Volume B, pages 633-674. North- Holland, Amsterdam, 1990.

Digital Library

Google Scholar

[23]

F. Henglein. Polymorphic Type Inference and Semi-Unification. PhD thesis, Rutgets University, April 1989. also NYU Technical Report 443, May 1989.

Digital Library

Google Scholar

[24]

A. Kfoury, J. Tiuryn, and P. Urzyczyn. Computational consequences and partial solutions of a generalized unification problem. In Proc. IEEE Symp. on Logic in Computer Science, June 1989.

Digital Library

Google Scholar

[25]

J. Lambek and P.J. Scott. Introduction to Higher-Order Categorical Logic. Cambridge University Press, Cambridge, U.K, 1986.

Digital Library

Google Scholar

[26]

J.C. Mitchell. A type-inference approach to reduction properties and semantics of polymorphic expressions. In A CM Conference on LISP and Functional Programming, pages 308-319, August 198(;. Revised version in Logical Foundations of Functional Programming, ed. G. Huet, Addison-Wesley (1990) 195-212.

Digital Library

Google Scholar

[27]

J.C. Mitchell. Toward a typed foundation for method specialization and inheritance. In Proc. 17th A CM Syrup. on Principles of Programming Languages, pages t09-124, January 1990.

Digital Library

Google Scholar

[28]

J.C. Mitchell. Type systems for programming languages. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Volume B, pages 365-458. North-Holland, Amsterdam, 1990.

Digital Library

Google Scholar

[29]

A. Mycroft. Polymorphic type schemes and recursive definitions. In Proc. 6th Int. Conf. on Programming, LNCS 167, 1984.

Digital Library

Google Scholar

[30]

M. Smyth and G.D. Plotkin. The category-theoretic solution of recursive domain equations. SIAM J. Computing, 11:761-783, 1982.

Digital Library

Google Scholar

[31]

A.S. Troelstra. Maihema~icat I~vee~igation of Intuitionistic Arithmetic and Analysis. Springer LNM 344, Berlin, 1973.

Google Scholar

Cited By

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Compagnoni APierce B(2018)Higher-order intersection types and multiple inheritanceMathematical Structures in Computer Science10.1017/S09601295000700436:5(469-501)Online publication date: 19-Apr-2018
https://doi.org/10.1017/S0960129500070043
Abel ACoquand TPagano M(2011)A Modular Type-checking algorithm for Type Theory with Singleton Types and Proof IrrelevanceLogical Methods in Computer Science10.2168/LMCS-7(2:4)20117:2Online publication date: 7-May-2011
https://doi.org/10.2168/LMCS-7(2:4)2011
Hofmann MPierce B(2008)A unifying type-theoretic framework for objectsJournal of Functional Programming10.1017/S09567968000014905:04(593-635)Online publication date: 7-Nov-2008
https://doi.org/10.1017/S0956796800001490
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PER models of subtyping, recursive types and higher-order polymorphism

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Published In

POPL '92: Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

February 1992

376 pages

ISBN:0897914538

DOI:10.1145/143165

Chairman:
Ravi Sethi
AT&T Bell Labs., Murray Hill, NJ

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 February 1992

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POPL92

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POPL92: 19th ACM Symposium on Principles of Programming Languages

January 19 - 22, 1992

New Mexico, Albuquerque, USA

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POPL '92 Paper Acceptance Rate 30 of 204 submissions, 15%;

Overall Acceptance Rate 824 of 4,130 submissions, 20%

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The 52nd Annual ACM SIGPLAN Symposium on Principles of Programming Languages

January 19 - 25, 2025

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Cited By

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Compagnoni APierce B(2018)Higher-order intersection types and multiple inheritanceMathematical Structures in Computer Science10.1017/S09601295000700436:5(469-501)Online publication date: 19-Apr-2018
https://doi.org/10.1017/S0960129500070043
Abel ACoquand TPagano M(2011)A Modular Type-checking algorithm for Type Theory with Singleton Types and Proof IrrelevanceLogical Methods in Computer Science10.2168/LMCS-7(2:4)20117:2Online publication date: 7-May-2011
https://doi.org/10.2168/LMCS-7(2:4)2011
Hofmann MPierce B(2008)A unifying type-theoretic framework for objectsJournal of Functional Programming10.1017/S09567968000014905:04(593-635)Online publication date: 7-Nov-2008
https://doi.org/10.1017/S0956796800001490
Pierce BTurner D(2008)Simple type-theoretic foundations for object-oriented programmingJournal of Functional Programming10.1017/S09567968000010404:02(207-247)Online publication date: 7-Nov-2008
https://doi.org/10.1017/S0956796800001040
van Bakel Sde’Liguoro U(2008)Logical Equivalence for Subtyping Object and Recursive TypesTheory of Computing Systems10.1007/s00224-007-9079-542:3(306-348)Online publication date: 5-Feb-2008
https://dl.acm.org/doi/10.1007/s00224-007-9079-5
Mellies PVouillon J(2005)Recursive Polymorphic Types and Parametricity in an Operational FrameworkProceedings of the 20th Annual IEEE Symposium on Logic in Computer Science10.1109/LICS.2005.42(82-91)Online publication date: 26-Jun-2005
https://dl.acm.org/doi/10.1109/LICS.2005.42
Slotosch O(2005)Higher order quotients and their implementation in Isabelle HOLTheorem Proving in Higher Order Logics10.1007/BFb0028401(291-306)Online publication date: 17-Jun-2005
https://doi.org/10.1007/BFb0028401
Compagnoni A(2005)Decidability of higher-order subtyping with intersection typesComputer Science Logic10.1007/BFb0022246(46-60)Online publication date: 15-Jun-2005
https://doi.org/10.1007/BFb0022246
Poll E(2005)System F with width-subtyping and record updatingTheoretical Aspects of Computer Software10.1007/BFb0014562(439-457)Online publication date: 9-Jun-2005
https://doi.org/10.1007/BFb0014562
Tiuryn J(2005)A sequent calculus for subtyping polymorphic typesMathematical Foundations of Computer Science 199610.1007/3-540-61550-4_144(135-155)Online publication date: 2-Jun-2005
https://doi.org/10.1007/3-540-61550-4_144
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