Journal of Automated Reasoning

, Volume 47, Issue 3, pp 251–289 | Cite as

Conjecture Synthesis for Inductive Theories

  • Moa JohanssonEmail author
  • Lucas Dixon
  • Alan Bundy


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.


Theory formation Induction Synthesis Theorem proving Lemma discovery 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità degli Studi di VeronaVeronaItaly
  2. 2.School of InformaticsUniversity of EdinburghEdinburghUK

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