Polar: A Framework for Proof Refactoring

We present a prototype refactoring framework based on graph rewriting and bidirectional transformations that is designed to be generic, extensible, and declarative. Our approach uses a language-independent graph meta-model to represent proof developments in a generic way. We use graph rewriting to enrich the meta-model with dependency information and to perform refactorings, which are written as declarative rewrite rules. Our framework, called Polar, is implemented in the GrGen rewriting engine.

[1]  Robin Milner,et al.  A Metalanguage for interactive proof in LCF , 1978, POPL.

[2]  Joe D. Warren,et al.  The program dependence graph and its use in optimization , 1987, TOPL.

[3]  Markus Wenzel,et al.  Isar - A Generic Interpretative Approach to Readable Formal Proof Documents , 1999, TPHOLs.

[4]  Michael Norrish,et al.  seL4: formal verification of an OS kernel , 2009, SOSP '09.

[5]  Oege de Moor,et al.  JunGL: a scripting language for refactoring , 2006, ICSE.

[6]  Dominik Dietrich,et al.  Assertion level proof planning with compiled strategies , 2011 .

[7]  Gudmund Grov,et al.  Towards Formal Proof Script Refactoring , 2011, Calculemus/MKM.

[8]  Timothy Bourke,et al.  Challenges and Experiences in Managing Large-Scale Proofs , 2012, AISC/MKM/Calculemus.

[9]  Martin Hofmann,et al.  Edit lenses , 2012, POPL '12.

[10]  Paris Avgeriou,et al.  A practice-driven systematic review of dependency analysis solutions , 2011, Empirical Software Engineering.

[11]  Enrico Tassi,et al.  A Modular Formalisation of Finite Group Theory , 2007, TPHOLs.

[12]  Husheng Liao,et al.  A Comparative Study of View Update Problem , 2010, 2010 International Conference on Data Storage and Data Engineering.

[13]  Dieter Hutter,et al.  SmartTies - Management of Safety-Critical Developments , 2012, ISoLA.

[14]  William F. Opdyke,et al.  Refactoring object-oriented frameworks , 1992 .

[15]  Jeremy Avigad,et al.  A Machine-Checked Proof of the Odd Order Theorem , 2013, ITP.

[16]  Hartmut Ehrig,et al.  Attributed graph transformation with node type inheritance , 2007, Theor. Comput. Sci..

[17]  Perdita Stevens,et al.  A Landscape of Bidirectional Model Transformations , 2007, GTTSE.

[18]  Daniel Grund,et al.  GrGen: A Fast SPO-Based Graph Rewriting Tool , 2006, ICGT.

[19]  Nicolas Spyratos,et al.  Update semantics of relational views , 1981, TODS.

[20]  Georges Gonthier,et al.  The Four Colour Theorem: Engineering of a Formal Proof , 2008, ASCM.

[21]  Tom Mens,et al.  Formalizing refactorings with graph transformations , 2005, J. Softw. Maintenance Res. Pract..

[22]  Thomas C. Hales,et al.  Introduction to the Flyspeck Project , 2005, Mathematics, Algorithms, Proofs.

[23]  Michael Aschbacher,et al.  Highly complex proofs and implications of such proofs , 2005, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.