Three years of experience with Sledgehammer, a Practical Link Between Automatic and Interactive Theorem Provers

Sledgehammer is a highly successful subsystem of Isabelle/HOL that calls automatic theorem provers to assist with interactive proof construction. It requires no user configuration: it can be invoked with a single mouse gesture at any point in a proof. It automatically finds relevant lemmas from all those currently available. An unusual aspect of its architecture is its use of unsound translations, coupled with its delivery of results as Isabelle/HOL proof scripts: its output cannot be trusted, but it does not need to be trusted. Sledgehammer works well with Isar structured proofs and allows beginners to prove challenging theorems.

[1]  Nachum Dershowitz,et al.  In handbook of automated reasoning , 2001 .

[2]  Tobias Nipkow,et al.  Sledgehammer: Judgement Day , 2010, IJCAR.

[3]  David A. McAllester Ontic: A Knowledge Representation System for Mathematics , 1989, CADE.

[4]  Stephan Schulz,et al.  System Description: E 0.81 , 2004, IJCAR.

[5]  Lawrence C. Paulson,et al.  Translating Higher-Order Clauses to First-Order Clauses , 2007, Journal of Automated Reasoning.

[6]  Makarius Wenzel Isabelle/Isar — a Generic Framework for Human-Readable Proof Documents , 2007 .

[7]  Lawrence C. Paulson,et al.  Lightweight relevance filtering for machine-generated resolution problems , 2009, J. Appl. Log..

[8]  Lawrence C. Paulson,et al.  Source-Level Proof Reconstruction for Interactive Theorem Proving , 2007, TPHOLs.

[9]  Gertrud Bauer,et al.  Calculational Reasoning Revisited (An Isabelle/Isar Experience) , 2001, TPHOLs.

[10]  Christoph Weidenbach,et al.  Computing Small Clause Normal Forms , 2001, Handbook of Automated Reasoning.

[11]  Larry Wos,et al.  What Is Automated Reasoning? , 1987, J. Autom. Reason..

[12]  Lawrence Charles Paulson,et al.  Isabelle/HOL: A Proof Assistant for Higher-Order Logic , 2002 .

[13]  Peter B. Andrews An introduction to mathematical logic and type theory - to truth through proof , 1986, Computer science and applied mathematics.

[14]  Chad E. Brown,et al.  Analytic Tableaux for Higher-Order Logic with Choice , 2010, Journal of Automated Reasoning.

[15]  Journal of automated reasoning , 1986 .

[16]  Roman. Matuszewski,et al.  From insight to proof : Festschrift in honour of Andrzej Trybulec , 2007 .

[17]  Hans de Nivelle,et al.  Automated Proof Construction in Type Theory Using Resolution , 2000, Journal of Automated Reasoning.

[18]  Lawrence C. Paulson Three Years of Experience with Sledgehammer, a Practical Link between Automatic and Interactive Theorem Provers , 2012 .

[19]  J. Hurd First-Order Proof Tactics in Higher-Order Logic Theorem Provers In Proc , 2003 .

[20]  Lawrence C. Paulson,et al.  The foundation of a generic theorem prover , 1989, Journal of Automated Reasoning.

[21]  Bernhard Beckert,et al.  Integrating Automated and Interactive Theorem Proving , 1998 .

[22]  Christoph Weidenbach,et al.  Combining Superposition, Sorts and Splitting , 2001, Handbook of Automated Reasoning.

[23]  Lawrence C. Paulson,et al.  Set theory for verification: I. From foundations to functions , 1993, Journal of Automated Reasoning.

[24]  Lawrence C. Paulson,et al.  Automation for interactive proof: First prototype , 2006, Inf. Comput..

[25]  Andrei Voronkov,et al.  Vampire 1.1 (System Description) , 2001, IJCAR.

[26]  Lawrence C. Paulson,et al.  Set theory for verification. II: Induction and recursion , 1995, Journal of Automated Reasoning.

[27]  Josef Urban,et al.  MaLARea: a Metasystem for Automated Reasoning in Large Theories , 2007, ESARLT.

[28]  Tjark Weber,et al.  Bounded Model Generation for Isabelle/HOL , 2005, D/PDPAR@IJCAR.

[29]  Andrei Voronkov,et al.  System Description: Vampire 1.0 , 2000, ARW.

[30]  Tobias Nipkow,et al.  A Tutorial Introduction to Structured Isar Proofs , 2008 .

[31]  Jörg H. Siekmann,et al.  Proof Development with Ωmega: The Irrationality of \(\sqrt 2\) , 2003 .

[32]  Richard J. Boulton,et al.  Theorem Proving in Higher Order Logics , 2003, Lecture Notes in Computer Science.

[33]  Geoff Sutcliffe System Description: SystemOn TPTP , 2000, CADE.

[34]  Markus Wenzel,et al.  Type Classes and Overloading in Higher-Order Logic , 1997, TPHOLs.

[35]  Andreas Meier System Description: TRAMP: Transformation of Machine-Found Proofs into ND-Proofs at the Assertion Level , 2000, CADE.

[36]  Alonzo Church,et al.  A formulation of the simple theory of types , 1940, Journal of Symbolic Logic.

[37]  Volker Sorge,et al.  -Ants { An open approach at combining Interactive and Automated Theorem Proving , 2002 .

[38]  Andrei Voronkov,et al.  Limited resource strategy in resolution theorem proving , 2003, J. Symb. Comput..

[39]  Lawrence C. Paulson,et al.  Tool support for logics of programs , 1997 .

[40]  Chad E. Brown,et al.  Analytic Tableaux for Higher-Order Logic with Choice , 2010, IJCAR.

[41]  Joe Hurd Integrating Gandalf and HOL , 1999, TPHOLs.

[42]  M. Gordon,et al.  Introduction to HOL: a theorem proving environment for higher order logic , 1993 .