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As I said in the comment you were commenting on, there is a JVM and a Mono VM. The IDE is running as two processes, one on the JVM (running the IntelliJ shell) and one on, currently, a Mono VM (running the ReSharper engine). They use IPC with a custom protocol to send UI events and ViewModel updates between the processes.

Frontend is in Java (and Kotlin), indeed, as it's a part of the IntelliJ platform. However, the backend that actually provides IDE features for C# is written in .NET. The backend is actually the same ReSharper logic that runs in Visual Studio but in headless mode.

Wondering how much code in Intellij Ultimate is already written in Kotlin. Parts of Kotlin Code in Intellij Community Edition is still kinda low:

https://github.com/JetBrains/intellij-community/search?l=kot...

MonoDevelop is far from decent IMO. See my other comment for detailed complaints.

The UI is in the JVM, the back end is hosted on Mono when on non-windows platforms at the moment.