Dear List Members,
Through Mark Adams' paper "HOL Zero's Solutions for Pollack-Inconsistency"
(2016) linked at the HOL Zero homepage, I became aware of the notion of
Pollack-consistency coined by Freek Wiedijk for the property of "a system being
able to correctly parse formulas that it printed itself":
Freek Wiedijk: Pollack-inconsistency
http://doi.org/10.1016/j.entcs.2012.06.008
http://www.cs.kun.nl/~freek/pubs/rap.pdf
It is amusing to see how the parsing and printing functions of John's HOL Light
are put on the rack and stretched quite a bit.
Also Isabelle and other systems are examined.
The interesting point for me was to see that somebody had the same idea. In the
R0 implementation, not only a formula, but whole printed proofs can be parsed
again. In fact, if it is compiled and started with "make check", R0 loops
through all proofs, and this is done twice, with the output of the first run as
the input of the second, stopping immediately with an error message if a proof
fails or if the output of the two runs differ. This was implemented quite
early, so the system was designed from the very beginning to comply with a
notion of Pollack-consistency not only in terms of formulae, but in terms of
whole proofs. Like for HOL Zero, this was done in order "to achieve the highest
levels of reliability and trustworthiness through careful design and
implementation of its core components" - quoted from:
Mark Adams: HOL Zero's Solutions for Pollack-Inconsistency
http://doi.org/10.1007/978-3-319-43144-4_2
http://www.proof-technologies.com/holzero/hzsyntax_itp2016.pdf
Concerning HOL4 and HOL Zero, I am looking for introductions to them in the
literature. The appropriate candidates seem to be, at the first glance (without
having read them already):
Mark Adams: Introducing HOL Zero (Extended Abstract)
http://doi.org/10.1007/978-3-642-15582-6_25
Konrad Slind, Michael Norrish: A Brief Overview of HOL4
http://doi.org/10.1007/978-3-540-71067-7_6
The latter I found as reference no. 14 of Mark's 2016 paper.
Please let me know if you have other suggestions.
Kind regards,
Ken Kubota
____________________
Ken Kubota
http://doi.org/10.4444/100
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