This is due to closures. With the braces, your first sub, do_a is defined within the lexical scope that sets $var to 'first var'. In other words: 

{  
  my $var = 'first var';  # sets $var for this block

  # defines a sub IN this block, so gets this $var
  sub do_a {
      print "In 'aaa' var is set to '$var'\n";
  }
}

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Because subroutine names are available globally, do_a can be called from anywhere, but gets the $var defined in its lexical block.

Similarly, do_b is defined in a block where $var is set to nothing, and do_c is in a block with no $var at all.

In reply to Re^3: Scope, package, and 'my' variables by friedo
in thread Scope, package, and 'my' variables by ff

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