Isacosy: Synthesis of Inductive Theorems

Abstract

We have implemented a program for inductive theory formation, called IsaCoSy, which synthesises conjectures about recursively defined datatypes and functions. Only irreducible terms are generated, which keeps the search space tractably small. The synthesised terms are filtered through counter-example checking and then passed on to the automatic inductive prover IsaPlanner. Experiments have given promising results, with high recall of 83% for natural numbers and 100% for lists when compared to libraries for the Isabelle theorem prover. However, precision is somewhat lower, 38-63%.