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Initial Experiments on Deriving a Complete HOL Simplification Set

10 pagesPublished: May 27, 2013

Abstract

Rewriting is a common functionality in proof assistants, that allows to simplify theorems and goals. The set of equations to use in a rewrite step has to be manually specified, and therefore often includes rules which may lead to non-termination. Even in the case of termination another desirable property of a simplification set would be confluence. A well-known technique from rewriting to transform a terminating system into a terminating and confluent one is completion. But the sets of equations we find in the context of proof assistants are typically huge and most state-of-the-art completion tools only work on relatively small problems. In this paper we describe our initial experiments with the aim to close the gap and use rewriting to compute a complete first-order simplification set for a HOL-based proof assistant fully automatically.

Keyphrases: completion, higher-order logic, HOL Light, proof assistants, rewriting, simple type theory

In: Jasmin Christian Blanchette and Josef Urban (editors). PxTP 2013. Third International Workshop on Proof Exchange for Theorem Proving, vol 14, pages 77--86

Links:
BibTeX entry
@inproceedings{PxTP2013:Initial_Experiments_on_Deriving,
  author    = {Cezary Kaliszyk and Thomas Sternagel},
  title     = {Initial Experiments on Deriving a Complete HOL Simplification Set},
  booktitle = {PxTP 2013. Third International Workshop on Proof Exchange for Theorem Proving},
  editor    = {Jasmin Christian Blanchette and Josef Urban},
  series    = {EPiC Series in Computing},
  volume    = {14},
  pages     = {77--86},
  year      = {2013},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/h6b},
  doi       = {10.29007/95qb}}
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