Abstract
Several mechanisms such as Canonical Structures [14], Type Classes [13,16], or Pullbacks [10] have been recently introduced with the aim to improve the power and flexibility of the type inference algorithm for interactive theorem provers. We claim that all these mechanisms are particular instances of a simpler and more general technique, just consisting in providing suitable hints to the unification procedure underlying type inference. This allows a simple, modular and not intrusive implementation of all the above mentioned techniques, opening at the same time innovative and unexpected perspectives on its possible applications.
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References
Barthe, G., Ruys, M., Barendregt, H.: A two-level approach towards lean proof-checking. In: Berardi, S., Coppo, M. (eds.) TYPES 1995. LNCS, vol. 1158, pp. 16–35. Springer, Heidelberg (1996)
Bertot, Y., Gonthier, G., Ould Biha, S., Pasca, I.: Canonical big operators. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 86–101. Springer, Heidelberg (2008)
Boutin, S.: Using reflection to build efficient and certified decision procedures. In: Ito, T., Abadi, M. (eds.) TACS 1997. LNCS, vol. 1281, pp. 515–529. Springer, Heidelberg (1997)
Bundy, A., Basin, D., Hutter, D., Ireland, A.: Rippling: meta-level guidance for mathematical reasoning. Cambridge University Press, New York (2005)
Delahaye, D.: A Tactic Language for the System Coq. In: Parigot, M., Voronkov, A. (eds.) LPAR 2000. LNCS, vol. 1955, pp. 85–95. Springer, Heidelberg (2000)
Gonthier, G., Mahboubi, A., Rideau, L., Tassi, E., Thery, L.: A Modular Formalisation of Finite Group Theory. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 86–101. Springer, Heidelberg (2007)
Hall, C., Hammond, K., Jones, S.P., Wadler, P.: Type classes in haskell. ACM Transactions on Programming Languages and Systems 18, 241–256 (1996)
Luo, Z.: Coercive subtyping. J. Logic and Computation 9(1), 105–130 (1999)
Luo, Z.: Manifest fields and module mechanisms in intensional type theory. In: Miculan, M., Scagnetto, I., Honsell, F. (eds.) TYPES 2007. LNCS, vol. 4941. Springer, Heidelberg (2008)
Sacerdoti Coen, C., Tassi, E.: Working with mathematical structures in type theory. In: Miculan, M., Scagnetto, I., Honsell, F. (eds.) TYPES 2007. LNCS, vol. 4941, pp. 157–172. Springer, Heidelberg (2008)
Sacerdoti Coen, C., Tassi, E.: A constructive and formal proof of Lebesgue’s dominated convergence theorem in the interactive theorem prover Matita. Journal of Formalized Reasoning 1, 51–89 (2008)
Saibi, A.: Typing algorithm in type theory with inheritance. In: The 24th Annual ACM SIGPLAN - SIGACT Symposium on Principle of Programming Language (POPL) (1997)
Sozeau, M., Oury, N.: First-class type classes. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 278–293. Springer, Heidelberg (2008)
The Coq Development Team. The Coq proof assistant reference manual (2005), http://coq.inria.fr/doc/main.html
Wadler, P., Blott, S.: How to make ad-hoc polymorphism less ad hoc. In: POPL 1989: Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pp. 60–76. ACM, New York (1989)
Wenzel, M.: Type classes and overloading in higher-order logic. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 307–322. Springer, Heidelberg (1997)
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Asperti, A., Ricciotti, W., Sacerdoti Coen, C., Tassi, E. (2009). Hints in Unification. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2009. Lecture Notes in Computer Science, vol 5674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03359-9_8
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DOI: https://doi.org/10.1007/978-3-642-03359-9_8
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