Journal of Automated Reasoning

, Volume 47, Issue 3, pp 251–289

Conjecture Synthesis for Inductive Theories


DOI: 10.1007/s10817-010-9193-y

Cite this article as:
Johansson, M., Dixon, L. & Bundy, A. J Autom Reasoning (2011) 47: 251. doi:10.1007/s10817-010-9193-y


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 

Copyright information

© 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