Why is there no error issued by strict:
use strict;
$a = $a + 1;
Why is there no error issued by strict:
use strict;
$a = $a + 1;
$a and $b are special globals used by sort, so they're always defined.  Try it with $c instead and you will get an error.
$a is a special global variable. It doesn't need to be declared. See perldoc perlvar.
In Perl there are some global variables. Here $a and $b are used in the sort function. 
I think you might have noticed, like in this statement:
sort { $a <=> $b } @array_name ; 
Although strict does not complain about the special $a and $b variables, 
perlcritic will detect their usage:
Magic variables should be assigned as "local"... (Severity: 4)