Conditional Lemma Discovery and Recursion Induction in Hipster

Hipster is a theory exploration tool for the proof assistant Isabelle/HOL. It automatically discovers lemmas about given recursive functions and datatypes and proves them by induction. Previously, only equational properties could be discovered. Conditional lemmas, for example required when reasoning about sorting, has been beyond the scope of theory exploration. In this paper we describe an extension to Hipster to also support discovery and proof of conditional lemmas. We also present a new automated tactic, which uses recursion induction. Recursion induction follows the recursive structure of a function definition through its termina- tion order, as opposed to structural induction, which follows that of the datatype. We find that the addition of recursion induction increases the number of proofs completed automatically, both for conditional and equational statements.

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Conditional Lemma Discovery and Recursion Induction in Hipster.

Hipster is a theory exploration tool for the proof assistant Isabelle/HOL. It automatically discovers lemmas about given recursive functions and datatypes and proves them by induction. Previously, only equational properties could be discovered. Conditional lemmas, for example required when reasoning about sorting, has been beyond the scope of theory exploration. In this paper we describe an extension to Hipster to also support discovery and proof of conditional lemmas.We also present a new automated tactic, which uses recursion induction. Recursion induction follows the recursive structure of a function definition through its termina- tion order, as opposed to structural induction, which follows that of the datatype. We find that the addition of recursion induction increases the number of proofs completed automatically, both for conditional and equational statements