wrote a library in BASIC for screen / window applications in DOS. (you know, pop-up text-windows and so on). How do I do that on linux (in C)?
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I know there exist things like QT and ncurses

So it's graphical interface we are after or text based?

For text, I agree with others, ncurses

For graphical

• pyGTK
  basically everything you need, some learnig curve as it's big and versatile. But to be honest, when trying to achieve something I'd suggest to start from GTK reference to me it somehow conveys the logic better than the PyGTK reference
• Kivy
  haven't used it, but might be fun to use
• wxWidgets
  very cross-platform. Not only you can use it to write UI that will require minor fixes to have the same code for Windows and Linux at the same time, you can also tell it whether the toolkit used under the hood on Linux should be QT or GTK
• Tk
  old, simple (more fancy things need some gymnastics) but simple (easy to use) and supported in Python out of the box (you don't even need to install anything)
• QT
  I'm putting it here just for fairness. I don't like it, don't like its signal-slot design, I think it's hogging up too much resources. But last time I used it was ~10 years ago and in the end, it does in fact work