Abstract
Herbrand constraint solving or unification has long been understood as an efficient mechanism for type checking and inference for programs using Hindley/Milner types. If we step back from the particular solving mechanisms used for Hindley/Milner types, and understand type operations in terms of constraints we not only give a basis for handling Hindley/Milner extensions, but also gain insight into type reasoning even on pure Hindley/Milner types, particularly for type errors. In this paper we consider typing problems as constraint problems and show which constraint algorithms are required to support various typing questions. We use a light weight constraint reasoning formalism, Constraint Handling Rules, to generate suitable algorithms for many popular extensions to Hindley/Milner types. The algorithms we discuss are all implemented as part of the freely available Chameleon system.
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References
Abdennadher, S.: Operational semantics and confluence of constraint propagation rules. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 252–266. Springer, Heidelberg (1997)
Beaven, M., Stansifer, R.: Explaining type errors in polymorphic languages. ACM Letters on Programming Languages 2, 17–30 (1993)
Cheney, J., Hinze, R.: First-class phantom types. Technical Report CUCIS TR2003-1901, Cornell University (2003)
Chitil, O.: Compositional explanation of types and algorithmic debugging of type errors. In: Proc. of ICFP 2001, pp. 193–204. ACM Press, New York (2001)
Demoen, B., de la Banda, M.G., Stuckey, P.J.: Type constraint solving for parametric and ad-hoc polymorphism. In: Proc. of the 22nd Australian Computer Science Conference, pp. 217–228. Springer, Heidelberg (1999)
Duck, G.J., Peyton-Jones, S., Stuckey, P.J., Sulzmann, M.: Sound and decidable type inference for functional dependencies. In: Schmidt, D. (ed.) ESOP 2004. LNCS, vol. 2986, pp. 49–63. Springer, Heidelberg (2004)
Duggan, D., Bent, F.: Explaining type inference. Science of Computer Programming 27(1), 37–83 (1996)
Frühwirth, T.: Constraint handling rules. In: Podelski, A. (ed.) Constraint Programming: Basics and Trends. LNCS, vol. 910. Springer, Heidelberg (1995)
de la Banda, M.G., Stuckey, P.J., Wazny, J.: Finding all minimal unsatisfiable constraints. In: Proc. of PPDP 2003, pp. 32–43. ACM Press, New York (2003)
Haack, C., Wells, J.B.: Type error slicing in implicitly typed higher-order languages. In: Degano, P. (ed.) ESOP 2003. LNCS, vol. 2618, pp. 284–301. Springer, Heidelberg (2003)
Haskell 98 language report, http://research.microsoft.com/Users/simonpj/haskell98-revised/haskell98-report-html/
Heeren, B., Hage, J.: Parametric type inferencing for Helium. Technical Report UU-CS-2002-035, Utrecht University (2002)
Heeren, B., Hage, J.: Type class directives. In: Hermenegildo, M.V., Cabeza, D. (eds.) PADL 2004. LNCS, vol. 3350, pp. 253–267. Springer, Heidelberg (2005)
Heeren, B., Hage, J., Swierstra, D.: Generalizing Hindley-Milner type inference algorithms. Technical Report UU-CS-2002-031, Utrecht University (2002)
Helium home page, http://www.cs.uu.nl/~afie/helium/
Hugs home page, http://www.haskell.org/hugs/
Jones, M.P.: Type classes with functional dependencies. In: Smolka, G. (ed.) ESOP 2000. LNCS, vol. 1782, pp. 230–244. Springer, Heidelberg (2000)
Lee, O., Yi, K.: A generalized let-polymorphic type inference algorithm. Technical Memorandum ROPAS-2000-5, National Creative Research Center, Korea Advanced Institute of Science and Technology (March 2000)
Maher, M.J.: Herbrand constraint abduction. In: 20th IEEE Symposium on Logic in Computer Science (LICS 2005), pp. 397–406. IEEE Computer Society Press, Los Alamitos (2005)
Marriott, K., Stuckey, P.J.: Programming with Constraints: an Introduction. MIT Press, Cambridge (1998)
McAdam, B.J.: Generalising techniques for type debugging. Trends in Functional Programming, 49–57 (March 2000)
Milner, R.: A theory of type polymorphism in programming. Journal of Computer and System Sciences 17, 348–375 (1978)
nhc98 home page, haskell.org/nhc98/
Nilsson, H.: Dynamic optimization for functional reactive programming using generalized algebraic data types. In: Proc. of ICFP 2005, pp. 54–65. ACM Press, New York (2005)
Pottier, F., Gauthier, N.: Polymorphic typed defunctionalization. In: Proc. of POPL 2004, pp. 89–98. ACM Press, New York (2004)
Sheard, T., Pasalic, E.: Meta-programming with built-in type equality. In: Fourth International Workshop on Logical Frameworks and Meta-Languages (2004)
Shoenfield, J.R.: Mathematical Logic. Addison-Wesley, Reading (1967)
Stuckey, P.J., Sulzmann, M.: A theory of overloading. ACM Transactions on Programming Languages and Systems 27(6), 1216–1269 (2005)
Stuckey, P.J., Sulzmann, M., Wazny, J.: The Chameleon type debugger (tool demonstration). In: Ronsse, M. (ed.) Proceedings of the Fifth International Workshop on Automated Debugging, pp. 247–260 (2003), http://arxiv.org/html/cs.SE/0309027
Stuckey, P.J., Sulzmann, M., Wazny, J.: Interactive type debugging in Haskell. In: Juring, J. (ed.) Proceedings of the ACM SIGPLAN 2003 Haskell Workshop, pp. 72–83. ACM Press, New York (2003)
Stuckey, P.J., Sulzmann, M., Wazny, J.: Improving type error diagnosis. In: Proceedings of the ACM SIGPLAN 2004 Haskell Workshop, pp. 80–91. ACM Press, New York (2004)
Sulzmann, M., Wazny, J.: Chameleon, http://www.comp.nus.edu.sg/~sulzmann/chameleon
Sulzmann, M., Wazny, J., Stuckey, P.J.: A framework for extended algebraic data types. In: Hagiya, M., Wadler, P. (eds.) FLOPS 2006. LNCS, vol. 3945, pp. 47–64. Springer, Heidelberg (2006)
Wadler, P., Blott, S.: How to make ad-hoc polymorphism less ad-hoc. In: Proc. of POPL 1989, pp. 60–76. ACM Press, New York (1989)
Wazny, J.: Type inference and type error diagnosis for Hindley/Milner with extensions. PhD thesis, University of Melbourne (2006), http://www.comp.nus.edu.sg/~sulzmann/chameleon/thesis.ps.gz
Xi, H., Chen, C., Chen, G.: Guarded recursive datatype constructors. In: Proc. of POPL 2003, pp. 224–235. ACM Press, New York (2003)
Yang, J., Wells, J., Trinder, P., Michaelson, G.: Improved type error reporting. In: Proceedings of 12th International Workshop on Implementation of Functional Languages, pp. 71–86 (2000)
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Stuckey, P.J., Sulzmann, M., Wazny, J. (2006). Type Processing by Constraint Reasoning. In: Kobayashi, N. (eds) Programming Languages and Systems. APLAS 2006. Lecture Notes in Computer Science, vol 4279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11924661_1
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DOI: https://doi.org/10.1007/11924661_1
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