Conjecture Synthesis for Inductive Theories

  • Authors:

  • Moa Johansson;Lucas Dixon;Alan Bundy

  • Affiliations:

  • Dipartimento di Informatica, Università degli Studi di Verona, Verona, Italy 371 34;School of Informatics, University of Edinburgh, Edinburgh, UK EH8 9AB;School of Informatics, University of Edinburgh, Edinburgh, UK EH8 9AB

  • Venue:
  • Journal of Automated Reasoning
  • Year:
  • 2011

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Abstract

We have developed a program for inductive theory formation, called IsaCoSy, which synthesises conjectures `bottom-up' from the available constants and free variables. The synthesis process is made tractable by only generating irreducible terms, which are then filtered through counter-example checking and passed to the automatic inductive prover IsaPlanner. The main technical contribution is the presentation of a constraint mechanism for synthesis. As theorems are discovered, this generates additional constraints on the synthesis process. We evaluate IsaCoSy as a tool for automatically generating the background theories one would expect in a mature proof assistant, such as the Isabelle system. The results show that IsaCoSy produces most, and sometimes all, of the theorems in the Isabelle libraries. The number of additional un-interesting theorems are small enough to be easily pruned by hand.