If I recall correctly, Haskell is compiled, and Yi probably is (an interpreter does exist, but there is not much of a point).

It probably has a system like XMonad, where the code is compiled, but you can hot-recompile, which is effectively the same thing.

There is a Haskell REPL. ghci.

Yes, but I am not aware of any program running in it. c.f. XMonad. It seems that the style is for complied code (and thus low-profile) with dynamic recompilation. This is effectively a REPL, but you technically do recompile. So more of a RCPL?