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Conjecture Synthesis for Inductive Theories

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.

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Correspondence to Moa Johansson.

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Johansson, M., Dixon, L. & Bundy, A. Conjecture Synthesis for Inductive Theories. J Autom Reasoning 47, 251–289 (2011). https://doi.org/10.1007/s10817-010-9193-y

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Keywords

  • Theory formation
  • Induction
  • Synthesis
  • Theorem proving
  • Lemma discovery