I think this is a relatively straightforward problem, conceptually anyway. One would wish to collect the frequencies in the codebase with which Tᵢ typed objects are fed to mⱼ methods. Then, when autocompleting methods for a Tᵢ object, simply sort the methods by order of call frequency.
I think this would probably be an optional mode: for example, one mode of autocomplete might be to sort based on type specialization; another mode might be to sort by frequency of use in your personal codebase; another mode might be to sort by frequency of use in all GitHub repos.
I think it’s probably decent to use the GitHub repo method use frequencies as a starting point, and then do some sort of weighted average with the frequencies they’re used in personal use. That way you don’t overfit to your own codebase.
It’s also possible to find the frequencies associated with certain packages being loaded (e.g., somebody who has loaded LinearAlgebra is more likely to call qr), and do a weighted average of the frequencies associated with the packages you’ve loaded in your project to get an autocomplete that’s more likely to be perfect for your specific use case. The possibilities are endless.