i'm not an expert, but: once value of thunk is evaluated, it's written
back by code called mutator

Whilst that is indeed mutation, it is not what is usually referred to as the "mutator" in the context of garbage collection. Quite simply, the "mutator" is the actual running program, as opposed to the GC, which is part of the underlying runtime system. Conceptually, the mutator and GC are the two mutually-exclusive threads of control that modify the heap. Usually one must halt while the other runs.

Regards,
    Malcolm

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