Stream: Archive Mirror: Isabelle Users Mailing List

Topic: [isabelle] Changing axiom names in a locale

Email Gateway (Aug 19 2022 at 15:22):

From: Eddy Westbrook <westbrook@kestrel.edu>
Thanks, this lemmas command is very helpful.

-Eddy

Email Gateway (Aug 19 2022 at 15:22):

From: Eddy Westbrook <westbrook@kestrel.edu>
Btw, is there a similar command for declaring alias names for definitions in the imported locale as well?

Thanks,
-Eddy

Email Gateway (Aug 19 2022 at 15:22):

From: Andreas Lochbihler <andreas.lochbihler@inf.ethz.ch>
How about using abbreviations?

locale l begin
definition foo ...
end

locale l2 = l begin
abbreviation bar where "bar == foo"
end

Best,
Andreas

Email Gateway (Aug 19 2022 at 15:49):

From: Eddy Westbrook <westbrook@kestrel.edu>
Hi,

I was wondering, is there any way to import a locale in a way that changes the names it uses for the axioms, without having to write the whole locale over again? As an example of what I mean, consider the following locale for monoids:

locale monoid =
fixes zero :: "'a"
fixes plus :: "'a \<times> 'a => 'a"
assumes left_zero: "plus (zero, x) = x"
assumes right_zero: "plus (x, zero) = x"
assumes plus_assoc: "plus (plus (x,y),z) = plus (x,plus (y,z))”

Is there a way to change this to use the names “one”, “times”, “left_one”, “right_one”, and “times_assoc” without writing the whole locale over again? I was thinking something like the following, which already does what I want (if the last three lines are dropped) for changing “zero” to “one” and “plus” to “times”:

locale monoid_times = monoid
where zero = one
and plus = times
and left_zero = left_one
and right_zero = right_one
and plus_assoc = times_assoc
for one times left_one right_one times_assoc

I know that, in this particular case, what I wrote above is actually just as long as if I had re-defined monoid_times from scratch, but the context is that we often only want to change a few names, rather than all of them, so some sort of notation like this would be helpful.

Similarly, is there a way to change the type variable used, e.g., from ‘a to in monoid to ‘b in monoid_times? I know that in this case I could annotate “one” with the type variable ‘b, but in general a locale might only have elements with more complex types involving ‘a, so it might be annoying to have to write out the whole type just to change one type variable.

Thanks,
-Eddy

Email Gateway (Aug 19 2022 at 15:49):

From: Andreas Lochbihler <andreas.lochbihler@inf.ethz.ch>
Hi Eddy,

AFAIK the names of the assumption only show up as theorem names that can be used in the
locale. Therefore, instead of renaming the assumptions, you can declare alias names with
lemmas. For example:

locale monoid_times = monoid one times
for one times
begin
lemmas left_one = left_zero
lemmas right_one = right_zero
end

Unfortunately, there is no way to specify the names of type variables other than
mentioning them in the type of one of the fixed parameters.

Best,
Andreas

Last updated: Apr 24 2024 at 16:18 UTC