The editor I had to write for Full Metal Jacket (my visual dataflow language) infers types by a mechanism similar to Prolog unification when you draw edges to connect vertices/function calls, and won't let you draw edges where the types at each end are incompatible. I imagine it would be a lot harder to do this in an editor for a text-based language, so it would probably be left to the compiler to check, which would have to build its own graph connecting function calls.
Incidentally, things have moved on in the functional programming world from vanilla Hindley-Milner types, and there's a lot of interest now in dependent types, which depend on values returned at run time, e.g. if you're drawing on a window, the x-coordinate's type is a number from 0 to the window's width, which might change while the program is running. This adds an extra layer of type safety, eliminates a further class of errors, and allows the compiler to safely remove some run-time checks.
Incidentally, things have moved on in the functional programming world from vanilla Hindley-Milner types, and there's a lot of interest now in dependent types, which depend on values returned at run time, e.g. if you're drawing on a window, the x-coordinate's type is a number from 0 to the window's width, which might change while the program is running. This adds an extra layer of type safety, eliminates a further class of errors, and allows the compiler to safely remove some run-time checks.