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Passing a CompiledFunction to mathlink C function

I have a mathlink C function f that accepts a mathematica function g
as an argument.

When defining f in the mprep .tm file, I use _Symbol in :Pattern: and
Symbol in :ArgumentTypes:. f can then call g fine with MLPutFunction.

I then made a Compile'd version of g to improve speed, but can no
longer pass it to f as CompiledFunction is not a Symbol.

How should I define f so that it can accept both regular and compiled
functions? Should I pass the function name as a String instead? Or
handle it with Manual somehow.

Thanks for any pointers,

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