SEPIA: Search for Proofs Using Inferred Automata

This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using state-based models inferred from tactic sequences. These can then be traversed automatically to identify proofs. The SEPIA system is described and its performance evaluated on three Coq datasets. Our results show that SEPIA provides a useful complement to existing automated tactics in Coq.

[1]  Yves Bertot,et al.  Interactive Theorem Proving and Program Development: Coq'Art The Calculus of Inductive Constructions , 2010 .

[2]  Hazel Duncan,et al.  The use of data-mining for the automatic formation of tactics , 2004 .

[3]  Neil Walkinshaw,et al.  STAMINA: a competition to encourage the development and assessment of software model inference techniques , 2012, Empirical Software Engineering.

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

[5]  Barak A. Pearlmutter,et al.  Results of the Abbadingo One DFA Learning Competition and a New Evidence-Driven State Merging Algorithm , 1998, ICGI.

[6]  Freek Wiedijk,et al.  Formal proof -- getting started , 2008 .

[7]  Gudmund Grov,et al.  Machine Learning in Proof General: Interfacing Interfaces , 2012, UITP.

[8]  Hugo Herbelin,et al.  The Coq proof assistant : reference manual, version 6.1 , 1997 .

[9]  Jesse Alama,et al.  Automated and Human Proofs in General Mathematics: An Initial Comparison , 2012, LPAR.

[10]  Gudmund Grov.  A statistical relational learning challenge – extracting proof strategies from exemplar proofs , 2012 .

[11]  Rajeev Raman,et al.  Mining State-Based Models from Proof Corpora , 2014, CICM.

[12]  Ron Kohavi,et al.  A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection , 1995, IJCAI.

[13]  Christoph Benzmüller,et al.  Automatic Learning of Proof Methods in Proof Planning , 2003, Log. J. IGPL.

[14]  John Derrick,et al.  Inferring extended finite state machine models from software executions , 2013, 2013 20th Working Conference on Reverse Engineering (WCRE).