Change text-format through the theme
First of all you should be aware that if you were to display the input of a input like is was full HTML, it would be the same thing as giving the user who created the content access to using the full HTML filter. The only difference is that you wont tell the user that he can type full HTML. This could potentially open your site to exploits, if people write harmful HTML. You should instead give users access to the filters that you want to use for their input.

Now if you want to display any text through any filter, you can do that by using check_markup. You simply pass the text and filter id to the function and it will return a text you can use on your site.