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Using mod_perl had some benefits over plain CGI.pm. You got some sort of persistence and a tight integration with Apache. Unfortunately you got a tight integration with Apache. This makes mod_perl have some obscure quirks and can make mod_perl applications hard to test and debug.
Today Plack/PSGI provides a nice layer between the web server and your code. This is great for new projects, but what about old legacy code tightly integrated with mod_perl's request object?
On way would be to fake the request object on top of Plack. This provides the ability to run your mod_perl application with any Plack capable webserver together with generic Plack::Middleware layers.