Merging Inductive Relations

Inductive relations offer a powerful and expressive way of writing program specifications while facilitating compositional reasoning. Their widespread use by proof assistant users has made them particularly attractive target for engineering tools such as QuickChick, property-based testing tool Coq which can automatically derive generators values satisfying an inductive relation. However, are generally efficient, there is infrequent yet seemingly inevitable situation where their performance greatly degrades: when multiple constrain the same piece data. In this paper, we introduce algorithm merging two inductively defined properties that share index. The finds shared structure between relations, creates single merged relation provably equivalent to conjunction two. We demonstrate, through series case studies, improve automatic generation orders magnitude, well simplify mechanized proofs getting rid need nested induction tedious low-level book-keeping.