Abstract

Hammers are tools for employing external automated theorem provers (ATPs) to improve automation in formal proof assistants. Strong automation can greatly ease the task of developing formal proofs. An essential component of any hammer is the translation of the logic of a proof assistant to the format of an ATP. Formalisms of state-of-the-art ATPs are usually first-order, so some method for eliminating lambda-abstractions is needed. We present an experimental comparison of several combinatory abstraction algorithms for HOLHammer – a hammer for HOL Light. The algorithms are compared on problems involving non-trivial lambda- abstractions selected from the HOL Light core library and a library for multivariate analysis. We succeeded in developing algorithms which outperform both lambda-lifting and the simple Schönfinkel’s algorithm used in Sledgehammer for Isabelle/HOL. This increases the ATPs’ success rate on translated problems, thus enhancing automation in proof assistants.

BibTeX

@inproceedings{LC-CPP16,
  author    = "{\L}ukasz Czajka",
  title     = "Improving Automation in Interactive Theorem Provers by Efficient Encoding
               of Lambda-Abstractions",
  booktitle = "Proceedings of the 5th {ACM} {SIGPLAN} Conference on Certified Programs
               and Proofs (CPP 2016)",
  pages     = "49--57",
  year      = 2016,
  doi       = "10.1145/2854065.2854069"
}