Stream: Mirror: Isabelle Users Mailing List

Topic: [isabelle] Code equations for Rep in lift_definition with...

view this post on Zulip Email Gateway (Jun 12 2021 at 10:42):

From: "C.A. Watt" <>
Dear list

I am stuck trying to get an example to generate executable code. A
stripped down version is attached. I define a type "my_nat", set up as a
trivial quotient of nat. I lift a definition

definition all_zeros :: "nat list => bool"


lift_definition my_all_zeros :: "my_nat list => bool" is all_zeros .

When I attempt to export the code of the lifted function, I get the
error "No code equations for Rep_my_nat".

It looks like this is caused by the code equation for my_all_zeros
working out as

my_all_zeros ?xa ≡ all_zeros (map Rep_my_nat ?xa)

Is there a way to make code generation work with this quotient/lifting
setup? I found the "code_dt" flag to lift_definition, which seems to be
documented in isar-ref as dealing with something vaguely related, but it
doesn't affect the behaviour here.

Best wishes
Conrad Watt

view this post on Zulip Email Gateway (Jun 13 2021 at 17:56):

From: "C.A. Watt" <>
To follow up, Mark Wassell pointed out to me that changing the
definition of my_nat to

typedef my_nat = "{ n :: nat . True }" by auto

causes code generation to work as expected. It seems that, as part of
the above definition, a lemma

Rep_my_nat: "Rep_my_nat (Abs_my_nat ?x) ≡ ?x"

is generated and used as a code equation, allowing extraction to work.

The declaration in my original example

typedef my_nat = "UNIV :: (nat) set" ..

also causes a lemma of the same name to be generated, but of a very
different form, which presumably can't be used as a code equation, hence
my issues:

Rep_my_nat: "Rep_my_nat ?x \in UNIV"

If I prove the lemma generated by Mark's definition myself and declare
it as [code], extraction works as desired. Does anyone have any insight
as to why these two typedef forms have different behaviour here?

Best wishes

Last updated: Jul 15 2022 at 23:21 UTC