iOS applications will not appear outside of the iTunes library on a computer and can't be run on a computer. Purchases from the iTunes App Store also won't carry over to the Mac App Store; the developer needs to write and maintain them separately, and can charge separately if they so desire.
I was under the impression that all of the apps that I purchased from the app library would be available on all of my apple devices Ipad, phone and mac. That is what was told to me...or I should say implied. It is great to have a document come up on another device, but if you cant do anything with it, it is kind of useless.