Automatic imports using inference (like `goimports`)

Would it be possible to have something similar to goimports, such that relevant imports are added on saving/formatting a file?

For example, if inference concludes that only one import is valid, then that is imported.
Or, if there are multiple candidates (e.g. for Url or Request), it could derive the types from called functions' parameter types, and infer from those additional facts?

And similarly auto-remove of unused imports.

The issue names saving/formatting, inference, candidate imports, and unused-import removal but no files or tests. Start by locating the import-handling entry points used during saving or formatting and determine how inferred types could resolve candidates. Done would mean a decided, tested design for adding uniquely inferred imports and removing unused ones.