Lifting and Transfer: A Modular Design for Quotients in Isabelle/HOL
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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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- 3.Harrison, J.: Theorem Proving with the Real Numbers. Springer (1998)Google Scholar
- 5.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)Google Scholar
- 6.Krauss, A.: Simplifying Automated Data Refinement via Quotients. Tech. rep., TU München (2011), http://www21.in.tum.de/~krauss/papers/refinement.pdf
- 9.Mitchell, J.C.: Representation Independence and Data Abstraction. In: POPL, pp. 263–276. ACM Press (January 1986)Google Scholar
- 11.Reynolds, J.C.: Types, Abstraction and Parametric Polymorphism. In: IFIP Congress, pp. 513–523 (1983)Google Scholar
- 13.Sozeau, M.: A New Look at Generalized Rewriting in Type Theory. In: 1st Coq Workshop Proceedings (2009)Google Scholar
- 14.Wadler, P.: Theorems for free! In: Functional Programming Languages and Computer Architecture, pp. 347–359. ACM Press (1989)Google Scholar