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, thus transferring experienced users' expertise to new Isabelle users.
The most well-known approach for ITP, called waterfall @cite_18 , was invented for a first-order logic, which cannot handle induction without jeopardizing the soundness by introducing axioms. Jiang al followed this approach and ran multiple waterfalls @cite_0 to automate ITP in HOL light @cite_5 . However, when deciding induction variables, they naively picked the first free variable with recursive type and left the selection of appropriate induction variables as future work.
@cite_0 @cite_5 @cite_18
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Over the past few years, machine learning has been successfully combined with automated theorem provers to prove conjectures from proof assistants. However, such approaches do not usually focus on inductive proofs. In this work, we explore a combination of machine learning, a simple Boyer-Moore model and ATPs as a means of improving the automation of inductive proofs in the proof assistant HOL Light. We evaluate the framework using a number of inductive proof corpora. In each case, our approach achieves a higher success rate than running ATPs or the Boyer-Moore tool individually. HOL Light is a new version of the HOL theorem prover. While retaining the reliability and programmability of earlier versions, it is more elegant, lightweight, powerful and automatic; it will be the basis for the Cambridge component of the HOL-2000 initiative to develop the next generation of HOL theorem provers. HOL Light is written in CAML Light, and so will run well even on small machines, e.g. PCs and Macintoshes with a few megabytes of RAM. This is in stark contrast to the resource-hungry systems which are the norm in this field, other versions of HOL included. Among the new features of this version axe a powerful simplifier, effective first order automation, simple higher-order matching and very general support for inductive and recursive definitions.