With MLton and mlprof, you can profile your program to find out how many times each function is called and how many times each branch is taken. To do so, compile your program with -profile count -profile-branch true. For example, suppose that tak.sml contains the following.

structure Tak =
   struct
      fun tak1 (x, y, z) =
         let
            fun tak2 (x, y, z) =
               if y >= x
                  then z
               else
                  tak1 (tak2 (x - 1, y, z),
                        tak2 (y - 1, z, x),
                        tak2 (z - 1, x, y))
         in
            if y >= x
               then z
            else
               tak1 (tak2 (x - 1, y, z),
                     tak2 (y - 1, z, x),
                     tak2 (z - 1, x, y))
         end
   end

val rec f =
   fn 0 => ()
    | ~1 => print "this branch is not taken\n"
    | n => (Tak.tak1 (18, 12, 6) ; f (n-1))

val _ = f 5000

fun uncalled () = ()

Compile with count profiling and run the program.

% mlton -profile count -profile-branch true tak.sml
% ./tak

Display the profiling data, along with raw counts and file positions.

% mlprof -raw true -show-line true tak mlmon.out
623,610,002 ticks
            function               cur       raw     
--------------------------------- ----- -------------
Tak.tak1.tak2  tak.sml: 5         38.2% (238,530,000)
Tak.tak1.tak2.<true>  tak.sml: 7  27.5% (171,510,000)
Tak.tak1  tak.sml: 3              10.7%  (67,025,000)
Tak.tak1.<true>  tak.sml: 14      10.7%  (67,025,000)
Tak.tak1.tak2.<false>  tak.sml: 9 10.7%  (67,020,000)
Tak.tak1.<false>  tak.sml: 16      2.0%  (12,490,000)
f  tak.sml: 23                     0.0%       (5,001)
f.<branch>  tak.sml: 25            0.0%       (5,000)
f.<branch>  tak.sml: 23            0.0%           (1)
uncalled  tak.sml: 29              0.0%           (0)
f.<branch>  tak.sml: 24            0.0%           (0)

Branches are displayed with lexical nesting followed by <branch> where the function name would normally be, or <true> or <false> for if-expressions. It is best to run mlprof with -show-line true to help identify the branch.

One use of -profile count is as a code-coverage tool, to help find code in your program that hasn't been tested. For this reason, mlprof displays functions and branches even if they have a count of zero. As the above output shows, the branch on line 24 was never taken and the function defined on line 29 was never called. To see zero counts, it is best to run mlprof with -raw true, since some code (e.g. the branch on line 23 above) will show up with 0.0% but may still have been executed and hence have a nonzero raw count.