You have no choice. Named subroutines are always global. You're lying to yourself when you said "local f".

You are right. I meant "define all subroutines at the same global level."

Why do you think that creating a variable somewhere should replace a variable in some unrelated sub?

It is not clear to me when a lexical variable is used and when is lost during the program execution, as in my last example, where I'd expect an uninitialized $a in all "local f"'s messages.

Ok, I can understand that confusion. Lexicals are actually allocated very early on (compile-time?) and on scope exit. This allows for the creation of private variables:

package Foo;

my $x;

sub set_x { validate($_[0]); $x = $_[0]; }
sub get_x { die("uninitialized") if !defined($x); $x }

1;
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or

{
    my $x;
    sub set_x { validate($_[0]); $x = $_[0]; }
    sub get_x { die("uninitialized") if !defined($x); $x }
}
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Lexicals are actually allocated very early on (compile-time?)

I think that it must be true that lexicals are allocated at compile time—at least, if my timeline in Re^4: closure clarity, please is anything near the correct one. I can't see any other reason why the call to f on line 27 of Re^3: closure clarity, please (which I called step 9) would be affected by the call to g on line 23 (which I called step 7). (In fact, I thought that I stole this observation from a post of yours that I read long ago ….)