The task

The following declarations are given: 
exception MinF;
datatype 'a F = A of 'a F list | B of 'a | C

Write a function called minF to return the minimal value of type 'a in a data structure of type 'a F, using the function min passed as a parameter to minF. min has to be used to choose the smaller one out of two values. minF should return the exception MinF if f contains no value of type 'a at all. 

(* minF : ('a * 'a -> 'a) -> 'a F -> 'a
   minF min f = the smallest value of type 'a in f, according
                to min, or the exception MinF, if f has no value
                of type 'a at all
*)
You are allowed to define auxiliary functions.

Examples:

(minF Int.min C handle MinF => 999) = 999;
minF Int.min (B 3) = 3;
(minF Int.min (A[]) handle MinF => 0) = 0;
(minF Int.min (A[A[],C,A[],A[],C]) handle MinF => ~999) = ~999;
minF Real.min (A[B 5.4,A[],C,B ~13.6,B 7.7]) = ~13.6;
minF Int.min (A[B 5,A[B ~5,B 765,B ~875],A[],A[B 7,A[],B 76,C]]) = ~875;
minF (fn (x,y) => chr(Int.min(ord x, ord y))) (A[B#"c",C,A[],B#"k",B#"i"]) = #"c";