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This paper presents an approach to lemma synthesis to support advancedinductive entailment procedures based on separation logic. We first propose amechanism where lemmas are automatically proven and systematically applied. Thelemmas may include universal guard and/or unknown predicate. While the formeris critical for expressivity, the latter is essential for supportingrelationships between multiple predicates. We further introduce lemma synthesisto support (i) automated inductive reasoning together with frame inference and(ii) theorem exploration. For (i) we automatically discover and prove auxiliarylemmas during an inductive proof; and for (ii) we automatically generate auseful set of lemmas to relate user-defined or system-generated predicates. Wehave implemented our proposed approach into an existing verification system andtested its capability in inductive reasoning and theorem exploration. Theexperimental results show that the enhanced system can automatically synthesizeuseful lemmas to facilitate reasoning on a broad range of non-trivial inductiveproofs.

Enhancing Inductive Entailment Proofs in Separation Logic with Lemma Synthesis