Abstract
Quotients, subtypes, and other forms of type abstraction are ubiquitous in formal reasoning with higher-order logic. Typically, users want to build a library of operations and theorems about an abstract type, but they want to write definitions and proofs in terms of a more concrete representation type, or “raw” type. Earlier work on the Isabelle Quotient package has yielded great progress in automation, but it still has many technical limitations.
We present an improved, modular design centered around two new packages: the Transfer package for proving theorems, and the Lifting package for defining constants. Our new design is simpler, applicable in more situations, and has more user-friendly automation.
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References
Coen, C.S.: A Semi-reflexive Tactic for (Sub-)Equational Reasoning. In: Filliâtre, J.-C., Paulin-Mohring, C., Werner, B. (eds.) TYPES 2004. LNCS, vol. 3839, pp. 98–114. Springer, Heidelberg (2006)
Haftmann, F., Krauss, A., Kunčar, O., Nipkow, T.: Data Refinement in Isabelle/HOL. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 100–115. Springer, Heidelberg (2013)
Harrison, J.: Theorem Proving with the Real Numbers. Springer (1998)
Homeier, P.V.: A Design Structure for Higher Order Quotients. In: Hurd, J., Melham, T. (eds.) TPHOLs 2005. LNCS, vol. 3603, pp. 130–146. Springer, Heidelberg (2005)
Kaliszyk, C., Urban, C.: Quotients revisited for Isabelle/HOL. In: Proc. of the 26th ACM Symposium on Applied Computing (SAC 2011), pp. 1639–1644. ACM (2011)
Krauss, A.: Simplifying Automated Data Refinement via Quotients. Tech. rep., TU München (2011), http://www21.in.tum.de/~krauss/papers/refinement.pdf
Lammich, P.: Automatic data refinement. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 84–99. Springer, Heidelberg (2013)
Magaud, N.: Changing data representation within the Coq system. In: Basin, D., Wolff, B. (eds.) TPHOLs 2003. LNCS, vol. 2758, pp. 87–102. Springer, Heidelberg (2003)
Mitchell, J.C.: Representation Independence and Data Abstraction. In: POPL, pp. 263–276. ACM Press (January 1986)
Paulson, L.C.: Defining functions on equivalence classes. ACM Trans. Comput. Logic 7(4), 658–675 (2006)
Reynolds, J.C.: Types, Abstraction and Parametric Polymorphism. In: IFIP Congress, pp. 513–523 (1983)
Slotosch, O.: Higher Order Quotients and their Implementation in Isabelle HOL. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 291–306. Springer, Heidelberg (1997)
Sozeau, M.: A New Look at Generalized Rewriting in Type Theory. In: 1st Coq Workshop Proceedings (2009)
Wadler, P.: Theorems for free! In: Functional Programming Languages and Computer Architecture, pp. 347–359. ACM Press (1989)
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Huffman, B., Kunčar, O. (2013). Lifting and Transfer: A Modular Design for Quotients in Isabelle/HOL. In: Gonthier, G., Norrish, M. (eds) Certified Programs and Proofs. CPP 2013. Lecture Notes in Computer Science, vol 8307. Springer, Cham. https://doi.org/10.1007/978-3-319-03545-1_9
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DOI: https://doi.org/10.1007/978-3-319-03545-1_9
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