Re: [isabelle] Nominal2 fails on Datatypes with Lists



A small theory that produces the error is

theory SmallLang
  imports Nominal2.Nominal2
begin

nominal_datatype ty = TRecord ‹ty list›

end

the typevar was just an

atom_decl typevar

but this seems to be unrelated to the error.

I'm using the AFP Isabelle2019 version of Nominal2, if that helps.

Thanks,
Vincent

On Tue, 2019-10-15 at 10:46 +0000, Urban, Christian wrote:
Dear Vincent,

I have to check what is going on. Would you be able top send me a slimmed-down theory where I can see what the problem is?

Also what is typevar in the TVar constructor?

Thanks,
Christian
________________________________
From: cl-isabelle-users-bounces at lists.cam.ac.uk<mailto:cl-isabelle-users-bounces at lists.cam.ac.uk> <cl-isabelle-users-bounces at lists.cam.ac.uk<mailto:cl-isabelle-users-bounces at lists.cam.ac.uk>> on behalf of Jackson, Vincent (Data61, Kensington NSW) <Vincent.Jackson at data61.csiro.au<mailto:Vincent.Jackson at data61.csiro.au>>
Sent: 15 October 2019 03:20
To: cl-isabelle-users at lists.cam.ac.uk<mailto:cl-isabelle-users at lists.cam.ac.uk> <cl-isabelle-users at lists.cam.ac.uk<mailto:cl-isabelle-users at lists.cam.ac.uk>>
Subject: [isabelle] Nominal2 fails on Datatypes with Lists

Hello All,

I have been recently experimenting with Nominal2<https://eur03.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.isa-afp.org%2Fentries%2FNominal2.html&amp;data=01%7C01%7Cchristian.urban%40kcl.ac.uk%7C55cfee605fd64ec8e07408d7515bbf66%7C8370cf1416f34c16b83c724071654356%7C0&amp;sdata=8dL9LedsVKotsVQVSNab%2F2vu6ekR%2BDTHC%2BEnhZ%2BRC7U%3D&amp;reserved=0>;, but have run into a problem with lists in datatypes.

The datatype


nominal_datatype ty

  = TRecord ‹ty list›

  | TVar typevar

fails with


Proof failed.

 1. ⋀x. TRecord_raw (map (permute p_) (- p_ ∙ x)) = TRecord_raw x

The error(s) above occurred for the goal statement⌂:

p_ ∙ TRecord_raw = TRecord_raw

presumably because the automation does not know (or use) the fact that ‹map (permute p) xs = p ∙ xs›.
Further, although I can prove the lemma, I am unsure how (or if it is possible) to 'inject' the fact into the automation.

Any advice on how to proceed would be appreciated.

Thank you,
Vincent Jackson


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