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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 a particularly attractive target for proof engineering tools such as QuickChick, a property-based testing tool for Coq which can automatically derive generators for values satisfying an inductive relation. However, while such generators are generally efficient, there is an infrequent yet seemingly inevitable situation where their performance greatly degrades: when multiple inductive relations constrain the same piece of data. In this paper, we introduce an algorithm for merging two such inductively defined properties that share an index. The algorithm finds shared structure between the two relations, and creates a single merged relation that is provably equivalent to the conjunction of the two. We demonstrate, through a series of case studies, that the merged relations can improve the performance of automatic generation by orders of magnitude, as well as simplify mechanized proofs by getting rid of the need for nested induction and tedious low-level book-keeping.
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A Computational Understanding of Classical (Co)Recursion
Recursion and induction are mature, well-understood topics in programming. Yet their duals, co-recursion and co-induction, are still exotic and underdeveloped programming features. We aim to put them on equal footing by giving a foundation for co-recursion based on computation, analogous to the original computational foundation of recursion. At the lower level, we show how the connection between the two can be strengthened through their implementation details in an abstract machine. At the higher level, we develop a syntactic equational theory for inductive and co-inductive reasoning based on control flow. We also observe the impact of evaluation strategy: call-by-name has efficient recursion and strong co-inductive reasoning, but call-by-value has efficient co-recursion and strong inductive reasoning.
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- Award ID(s):
- 1719158
- PAR ID:
- 10173477
- Date Published:
- Journal Name:
- Symposium on Principles and Practice of Declarative Programming
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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