LiFtEr: Language to Encode Induction Heuristics for Isabelle/HOL

Abstract

Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, they did not have a systematic way to encode their expertise. To address this problem, we present our domain-specific language, LiFtEr. LiFtEr allows experienced Isabelle users to encode their induction heuristics in a style independent of any problem domain. LiFtEr's interpreter mechanically checks if a given application of induction tool matches the heuristics specified by experienced users, thus systematically transferring experienced users' expertise to new Isabelle users.1 Not to be confused with interactive theorem proving, which is a synonym of proof assistant (PA). 2 Proof methods are the Isar syntactic layer of LCF-style tactics.

Deductive Synthesis of Programs with Pointers: Techniques, Challenges, Opportunities

“…At the same time we also expect the limited size of the available dataset (i.e., the benchmarks from Table 1) would hamper the application of deep learning to SuSLik. An alternative approach is to encode feature extractors [58] and apply machine learning algorithms to the result of such feature extractors. Another approach is to learn a coarse-grained model from available data and then adjust it during search, based on the feedback from incomplete derivations, as in [6,15,82].…”

Smart Induction for Isabelle/HOL (System Description)

“…Secondly, the multi-stage screening step filters out less promising combinations induction arguments. Thirdly, the scoring step evaluates each combination to a natural number using logical feature extractors implemented in LiFtEr [13] and reorder the combinations based on their scores. Lastly, the short-listing step takes the best 10 candidates and print them in the Output panel of Isabelle/jEdit.…”

“…Step 3 carefully investigates the remaining candidates using heuristics implemented in LiFtEr [13]. LiFtEr is a domain-specific language to encode induction heuristics in a style independent of problem domains.…”

“…The interpreter returns True if the combination is compatible with the heuristic and False if not. We illustrated the details of LiFtEr in our previous work [13] with many examples. In this paper, we focus on the essence of LiFtEr and show one example heuristic used in smart induct.…”

Unprovability results for clause set cycles

“…The most prominent application of automated inductive theorem proving is the formal verification of hardware and software. Another field of application of automated inductive theorem proving is the formalization of mathematical statements, where AITP systems assist humans in formalizing statements by discharging lemmas automatically, suggest inductions [Nag19], or explore the theory [JRSC14,VJ15].…”