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HOL Zero’s Solutions for Pollack-Inconsistency

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Interactive Theorem Proving (ITP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9807))

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Abstract

HOL Zero is a basic theorem prover that aims to achieve the highest levels of reliability and trustworthiness through careful design and implementation of its core components. In this paper, we concentrate on its treatment of concrete syntax, explaining how it manages to avoid problems suffered in other HOL systems related to the parsing and pretty printing of HOL types, terms and theorems, with the goal of achieving well-behaved parsing/printing and Pollack-consistency. Included are an explanation of how Hindley-Milner type inference is adapted to cater for variable-variable overloading, and how terms are minimally annotated with types for unambiguous printing.

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Notes

  1. 1.

    Although in hol90, type variable names must start with a single-quote character.

  2. 2.

    We refer here to the “vanilla” version of the HOL language, implemented by all HOL systems except Isabelle/HOL and HOL Omega.

  3. 3.

    Note that, in HOL Zero, numerals are not atoms of primitive syntax, but for illustrative purposes it suffices to treat 5 as an atom in this example.

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Author information

Authors and Affiliations

  1. Proof Technologies Ltd, Worcester, UK

    Mark Adams

  2. Radboud University, Nijmegen, The Netherlands

    Mark Adams

Authors
  1. Mark Adams
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Correspondence to Mark Adams .

Editor information

Editors and Affiliations

  1. Inria Nancy – Grand Est, Villers-lès-Nancy, France

    Jasmin Christian Blanchette

  2. Inria Nancy – Grand Est, Villers-lès-Nancy, France

    Stephan Merz

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Adams, M. (2016). HOL Zero’s Solutions for Pollack-Inconsistency. In: Blanchette, J., Merz, S. (eds) Interactive Theorem Proving. ITP 2016. Lecture Notes in Computer Science(), vol 9807. Springer, Cham. https://doi.org/10.1007/978-3-319-43144-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-43144-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-43143-7

  • Online ISBN: 978-3-319-43144-4

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