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The complexity of type inference for higher-order lambda calculi

Authors:

Fritz Henglein,

Harry G. MairsonAuthors Info & Claims

POPL '91: Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Pages 119 - 130

https://doi.org/10.1145/99583.99602

Published: 03 January 1991 Publication History

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References

[1]

L. Cardelli. Typeful programming. Lecture Notes for the IFIP Advanced Seminar on Formal Methods in Programming Language Semantics, Rio de Janeiro, Brazil, 1989. See also SRC Report 45, Digital Equipment Corporation.

Google Scholar

[2]

L. Damas. Type assignment in programming languages. Ph.D. dissertation, CST- 33-85, Computer Science Department, Edinburgh University, 1985.

Google Scholar

[3]

L. Damas and R. Milner. Principal type schemes for functional programs. In 9- th ACM Symposium on Principles of Programming Languages, pp. 207-212, January 1982.

Digital Library

Google Scholar

[4]

C. Dwork, P. Kanellakis, and j. C. Mitchell. On the sequential nature of unification. Journal of Logic Programming 1:35-50, 1984.

Digital Library

Google Scholar

[5]

Edinburgh University. Postgraduate Examination Que~tion~ in Computation Theory, 1978-1988. Laboratory for Foundations of Computer Science, Report ECS- LFCS-88-64.

Google Scholar

[6]

P. Giannini and S. Ronchi Della Rocca. Characterization of typings in polymorphic type discipline. In Proceedings of the 3-rd IEEE Symposium on Logic in Computer Science, pp. 61-70, July 1988.

Google Scholar

[7]

J.-Y. Girard. Interprdtation Fonc. lionelle el Elimination des Coupures de l'Arilhmelique d'Ordre Superieur. Th~se de Doctorat d'Etat, Universit~ de Paris VII, 1972.

Google Scholar

[8]

J.-Y. Girard, Y. Lafont, and P. Taylor. Proofs and Types. Cambridge University Press, 1989.

Digital Library

Google Scholar

[9]

R. Harper, R. Milner, M. Torte. The Definition of Standard ML. MIT Press, 1990.

Digital Library

Google Scholar

[10]

J. Hartmanis and R. E. Stearns. On the computational complexity of algorithms. Transactions of the American Mathematieal Society 117, pp. 285-306.

Crossref

Google Scholar

[11]

F. Henglein. A lower bound for fult polymorphic type inference: Girard/Reynolds typability is DEXPTIME-hard. University of Utrecht, Technical Report RUU-CS-90- 14, April 1990.

Google Scholar

[12]

1%. Hindley. The principal type scheme of an object in combinatory logic. Transactions of the American Mathematical Society 146:29-60, 1969.

Google Scholar

[13]

J.E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison Wesley, 1979.

Digital Library

Google Scholar

[14]

P. Hudak and P. L. Wadler, editors. Report on the functional programming language Haskell. Yale University Technical Report YALEU/DCS/RR656, 1988.

Google Scholar

[15]

P. C. Kanellakis and }. C. Mitchell. Polymorphic unification and ML typing. Brown University Technical Report CS- 89-40, August 1989. Also in Proceedings of the 16-th ACM Symposium on the Principles of Programming Languages, pp. 105-115, January 1989.

Digital Library

Google Scholar

[16]

P.C. Kanellakis, H. G. Mairson, and J. C. Mitchell. Unification and ML type reconstruction. In Computational Logic: Essays in Honor of Alan Robinson, ed. j.-L. Lassez and G. Plotkin. MIT Press, 1990.

Google Scholar

[17]

A.j. Kfoury, J. Tiuryn, and P. Urzyczyn. ML typability is DEXPTIME-complete. Proceedings of the 15-th Colloquium on Trees in Algebra and Programming, May 1990. (See also Boston University Technical Report, October 1989).

Digital Library

Google Scholar

[18]

A.J. Kfoury and j. Tiuryn. Type reconstruction in finite rank fragments of the second-order lambda calculus. Technical Report BUCS 89-011, Boston University, October 1989. Also in Proceedings of the 5-th IEEE Symposium on Logic in Computer Science, pp. 2-11, June 1990.

Google Scholar

[19]

P. Landin. The next 700 programming languages. Communications of the ACM 9(3): 157-166.

Digital Library

Google Scholar

[20]

H.G. Mairson. Deciding ML typability is complete for deterministic exponential time. In Proceedings of the 17-th ACM Symposium on the Principles of Programming Languages, pp. 382- 401, January 1990.

Digital Library

Google Scholar

[21]

R. Milner. A theory of type polymorphism in programming. Journal of Computer and System Sciences 17, pp. 348-375, 1978.

Crossref

Google Scholar

[22]

J.C. Mitchell. Type systems for programming languages. To appear as a chapter in the Handbook of Theoretical Computer Science, van Leeuwen et al., eds. North-Holland, 1990.

Digital Library

Google Scholar

[23]

M.S. Paterson and M. N. Wegman. Linear unification. Journal of Computer and System Sciences 16, pp. 158-167, 1978.

Crossref

Google Scholar

[24]

B. Pierce, S. Dietzen, and S. Michaylov. Programming in higher-order typed lambda calculi. Technical Report CMU-CS-89- 111, Carnegie Mellon University, March 1989.

Google Scholar

[25]

F. Pfenning and P. Lee. LEAP: a language with eval and polymorphism. TAP- SOFT 1989: Proceedings of the International Joint Conference on Theory and Practice in Software Development, Barcelona, Spain. See also CMU Ergo Report 88-065.

Digital Library

Google Scholar

[26]

J.C. Reynolds. Towards a theory of type slruclure. In Proeeedhags of the Paris Colloquium on Programming, Lecture Notes in Computer Science 19, Springer Verlag, pp. 408-425, 1974.

Crossref

Google Scholar

[27]

J.A. Robinson. A machine oriented logic based on the resolution principle. Journal of the ACM 12(1):23-41, 1965.

Digital Library

Google Scholar

[28]

H. Schwictenberg. Complexity of normalization in the pure typed lambda calculus. The L. E. J. Brouwer Centenary Symposium, A. S. Troelstra and D. van Daalen (eds.), pp. 453-457. North- Holland, 1982.

Crossref

Google Scholar

[29]

D. Scott. Logic and programming languages. Communications of the ACM 20(9):634-641, 1977.

Digital Library

Google Scholar

[30]

C. Strachey. The varieties of programming language. Technical Monograph PRG- 10, Programming Research Group, Oxford University, 1973.

Google Scholar

[31]

D.A. Turner. Miranda: A non-strict functional language with polymorphic types. In IFIP International Conference on Functional Programming and Computer Architecture, Nancy, Lecture Notes in Computer Science 201, pp. 1-16, Springer-Verlag, 1985.

Crossref

Google Scholar

[32]

M. Wand. A simple algorithm and proof for type inference. Fundamenta Informaticae 10 (1987).

Google Scholar

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Sestoft PSestoft P(2017)Polymorphic TypesProgramming Language Concepts10.1007/978-3-319-60789-4_6(97-118)Online publication date: 3-Sep-2017
https://doi.org/10.1007/978-3-319-60789-4_6
Fellows MGaspers SRosamond F(2011)Multivariate Complexity TheoryComputer Science10.1007/978-1-4614-1168-0_13(269-293)Online publication date: 22-Oct-2011
https://doi.org/10.1007/978-1-4614-1168-0_13
Fellows M(2009)Parameterized ComplexityProceedings of the 12th International Symposium on Algorithms and Computation10.1007/3-540-45678-3_26(291-307)Online publication date: 24-Jun-2009
https://dl.acm.org/doi/10.1007/3-540-45678-3_26
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The complexity of type inference for higher-order lambda calculi

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POPL '91: Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

January 1991

366 pages

ISBN:0897914198

DOI:10.1145/99583

Chairman:
David Wise
Indiana Univ., Bloomington

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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Published: 03 January 1991

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POPL91: 18th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages

January 21 - 23, 1991

Florida, Orlando, USA

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POPL '91 Paper Acceptance Rate 31 of 152 submissions, 20%;

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

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Sestoft PSestoft P(2017)Polymorphic TypesProgramming Language Concepts10.1007/978-3-319-60789-4_6(97-118)Online publication date: 3-Sep-2017
https://doi.org/10.1007/978-3-319-60789-4_6
Fellows MGaspers SRosamond F(2011)Multivariate Complexity TheoryComputer Science10.1007/978-1-4614-1168-0_13(269-293)Online publication date: 22-Oct-2011
https://doi.org/10.1007/978-1-4614-1168-0_13
Fellows M(2009)Parameterized ComplexityProceedings of the 12th International Symposium on Algorithms and Computation10.1007/3-540-45678-3_26(291-307)Online publication date: 24-Jun-2009
https://dl.acm.org/doi/10.1007/3-540-45678-3_26
Van Horn DMairson H(2008)Flow Analysis, Linearity, and PTIMEProceedings of the 15th international symposium on Static Analysis10.1007/978-3-540-69166-2_17(255-269)Online publication date: 16-Jul-2008
https://dl.acm.org/doi/10.1007/978-3-540-69166-2_17
Van Horn DMairson H(2007)Relating complexity and precision in control flow analysisACM SIGPLAN Notices10.1145/1291220.129116642:9(85-96)Online publication date: 1-Oct-2007
https://dl.acm.org/doi/10.1145/1291220.1291166
Van Horn DMairson HHinze RRamsey N(2007)Relating complexity and precision in control flow analysisProceedings of the 12th ACM SIGPLAN international conference on Functional programming10.1145/1291151.1291166(85-96)Online publication date: 3-Oct-2007
https://dl.acm.org/doi/10.1145/1291151.1291166
Mairson H(2005)Outline of a proof theory of parametricityFunctional Programming Languages and Computer Architecture10.1007/3540543961_15(313-327)Online publication date: 6-Jul-2005
https://doi.org/10.1007/3540543961_15
Kanellakis PHillebrand GMairson H(2005)An analysis of the Core-ML language: Expressive power and type reconstructionAutomata, Languages and Programming10.1007/3-540-58201-0_60(83-105)Online publication date: 29-May-2005
https://doi.org/10.1007/3-540-58201-0_60
Downey RFellows MKapron BHallett MWareham H(2005)The parameterized complexity of some problems in logic and linguisticsLogical Foundations of Computer Science10.1007/3-540-58140-5_10(89-100)Online publication date: 7-Jun-2005
https://doi.org/10.1007/3-540-58140-5_10
Fellows M(2002)Parameterized ComplexityElectronic Notes in Theoretical Computer Science10.1016/S1571-0661(04)00301-961(1-19)Online publication date: Jan-2002
https://doi.org/10.1016/S1571-0661(04)00301-9
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Type checking and typability in domain-free lambda calculi

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