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.

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%. 1

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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.