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Extending Hindley-Milner Type Inference with Coercive Structural Subtyping

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Programming Languages and Systems (APLAS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7078))

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Abstract

We investigate how to add coercive structural subtyping to a type system for simply-typed lambda calculus with Hindley-Milner polymorphism. Coercions allow to convert between different types, and their automatic insertion can greatly increase readability of terms. We present a type inference algorithm that, given a term without type information, computes a type assignment and determines at which positions in the term coercions have to be inserted to make it type-correct according to the standard Hindley-Milner system (without any subtypes). The algorithm is sound and, if the subtype relation on base types is a disjoint union of lattices, also complete. The algorithm has been implemented in the proof assistant Isabelle.

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References

  1. Benke, M.: Complexity of type reconstruction in programming languages with subtyping. Ph.D. thesis, Warsaw University (1997)

    Google Scholar 

  2. Bourdoncle, F., Merz, S.: On the integration of functional programming, class-based object-oriented programming, and multi-methods. Research Report 26, Centre de Mathématiques Appliquées, Ecole des Mines de Paris (March 1996)

    Google Scholar 

  3. Coq development team: The Coq proof assistant reference manual. INRIA (2010), http://coq.inria.fr version 8.3

  4. Frey, A.: Satisfying subtype inequalities in polynomial space. Theor. Comput. Sci. 277(1-2), 105–117 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fuh, Y.C., Mishra, P.: Type inference with subtypes. In: Ganzinger, H. (ed.) ESOP 1988. LNCS, vol. 300, pp. 94–114. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  6. Luo, Z.: Coercions in a polymorphic type system. Mathematical Structures in Computer Science 18(4), 729–751 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Milner, R.: A theory of type polymorphism in programming. J. Comput. Syst. Sci. 17(3), 348–375 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mitchell, J.C.: Coercion and type inference. In: POPL, pp. 175–185 (1984)

    Google Scholar 

  9. Mitchell, J.C.: Type inference with simple subtypes. J. Funct. Program. 1(3), 245–285 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Nipkow, T.: Order-sorted polymorphism in Isabelle. In: Huet, G., Plotkin, G. (eds.) Logical Environments, pp. 164–188. CUP (1993)

    Google Scholar 

  11. Nordlander, J.: Polymorphic subtyping in O’Haskell. Sci. Comput. Program. 43(2-3), 93–127 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pierce, B.C.: Types and Programming Languages. MIT Press, Cambridge (2002)

    MATH  Google Scholar 

  13. Pottier, F.: Simplifying subtyping constraints: a theory. Information & Computation 170(2), 153–183 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pratt, V.R., Tiuryn, J.: Satisfiability of inequalities in a poset. Fundam. Inform. 28(1-2), 165–182 (1996)

    MathSciNet  MATH  Google Scholar 

  15. Saïbi, A.: Typing algorithm in type theory with inheritance. In: POPL, pp. 292–301 (1997)

    Google Scholar 

  16. Shields, M., Peyton Jones, S.: Object-oriented style overloading for Haskell. In: First Workshop on Multi-language Inferastructure and Interoperability (BABEL 2001), Firenze, Italy (September 2001)

    Google Scholar 

  17. Simonet, V.: Type Inference with Structural Subtyping: A Faithful Formalization of an Efficient Constraint Solver. In: Ohori, A. (ed.) APLAS 2003. LNCS, vol. 2895, pp. 283–302. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  18. Tiuryn, J.: Subtype inequalities. In: LICS, pp. 308–315 (1992)

    Google Scholar 

  19. Traytel, D., Berghofer, S., Nipkow, T.: Extending Hindley-Milner type inference with coercive subtyping (long version) (2011), www.in.tum.de/~nipkow/pubs/coercions.pdf

  20. Wand, M., O’Keefe, P.: On the complexity of type inference with coercion. In: FPCA 1989: Functional Programming Languages and Computer Architecture, pp. 293–298. ACM, New York (1989)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Dmitriy Traytel, Stefan Berghofer & Tobias Nipkow

Authors
  1. Dmitriy Traytel
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  2. Stefan Berghofer
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  3. Tobias Nipkow
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Parks Road, OX1 3QD, Oxford, UK

    Hongseok Yang

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Traytel, D., Berghofer, S., Nipkow, T. (2011). Extending Hindley-Milner Type Inference with Coercive Structural Subtyping. In: Yang, H. (eds) Programming Languages and Systems. APLAS 2011. Lecture Notes in Computer Science, vol 7078. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25318-8_10

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  • DOI: https://doi.org/10.1007/978-3-642-25318-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25317-1

  • Online ISBN: 978-3-642-25318-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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