How to understand why MainEvaluate is used in Compile'd function?

Question

Given

lyapexp[n_] := (Hold[Compile[{{kMin, _Integer}, tol, r, u0, u1},
      Module[{
        relErr, ohs,
        res = {0., 0.},
        hs = Table[.0, {n}],
        k = 0,
        nzs = Table[.0, {n}],
        ss = Table[.0, {n}],
        ws = IdentityMatrix[n]/2,
        zs = IdentityMatrix[n]/2,
        success = 1.0,
        uPrev = u0,
        uCurr = u1
        },
       While[True,
        k++;
        zs = Dnn[r, uCurr, uPrev].ws;
        Do[
         (Module[{nzi},
            Do[(
               zi -= zi.zj/Norm[zj, 2] zj) /. zj :> zs[[1 ;; n, j]]
             , {j, i - 1}];
            nzi = Norm[zi];
            nzs[[i]] = nzi;
            ws[[1 ;; n, i]] = zi/nzi]) /. zi :> zs[[1 ;; n, i]]
         , {i, n}];
        ohs = hs;
        ss += Log[nzs];
        hs = ss/k;
        relErr = Norm && relErr < tol,
         res = {hs, 1.0};
         Break[];
         ];
        {uCurr, uPrev, success} = nn[r, uCurr, uPrev, success];
        If[success == 0,
         res = {0., 0.};
         Break[];
         ];
        ];
       res
       ], CompilationOptions -> {"InlineExternalDefinitions" -> True},
       RuntimeOptions -> "Speed", 
      CompilationTarget -> "C"]] //. {Pattern[p, _IdentityMatrix] :> 
      Block[{}, p /; True], 
     HoldPattern[e_ /. (p_ :> r_)] :> 
      Block[{}, (Hold[e] /. p :> r) /; True]}) //. 
  HoldPattern[Hold[expr_]] :> expr

why is MainEvaluate used in CompilePrint[lyapexp[2]]?

EDIT

Now (after SetSystemOptions["CompileOptions" -> "CompileReportExternal" -> True]) it's

lyapexp[n_] := (Hold[Compile[{{kMin, _Integer}, tol, r, u0, u1},
      Module[{
        relErr, ohs,
        res = {0., 0.},
        hs = Table[.0, {n}],
        k = 0,
        nzs = Table[.0, {n}],
        ss = Table[.0, {n}],
        ws = {{1., 0.}, {0., 1.}},
        zs,
        success = 1.0,
        uPrev = u0,
        uCurr = u1
        },
       While[True,
        k++;
        zs = Dnn[r, uCurr, uPrev].ws;
        Do[
         (Module[{nzi},
            Do[(
               zi -= zi.zj/Norm[zj, 2] zj) /. zj :> zs[[1 ;; n, j]]
             , {j, i - 1}];
            nzi = Norm[zi];
            nzs[[i]] = nzi;
            ws[[1 ;; n, i]] = zi/nzi]) /. zi :> zs[[1 ;; n, i]]
         , {i, n}];
        ohs = hs;
        ss += Log[nzs];
        hs = ss/k;
        relErr = Norm[1 - ohs/hs, 2];
        If[k >= kMin && relErr < tol,
         res = Prepend[hs, 1.0];
         Break[];
         ];
        {uCurr, uPrev, success} = nn[r, uCurr, uPrev, success];
        If[success == 0,
         res = Prepend[Table[0., {n}], 0.];
         Break[];
         ];
        ];
       res
       ], CompilationOptions -> {"InlineExternalDefinitions" -> True},
       RuntimeOptions -> "Speed", 
      CompilationTarget -> "C"]] //. {Pattern[p, _IdentityMatrix] :> 
      Block[{}, p /; True], 
     HoldPattern[e_ /. (p_ :> r_)] :> 
      Block[{}, (Hold[e] /. p :> r) /; True]}) //. 
  HoldPattern[Hold[expr_]] :> expr

So, how do I do replacements in my Compile'd code correctly?

Answer 1

The correct code is:

lyapexp[n_] := 
 ReleaseHold[Replace[Hold[Compile[{{kMin, _Integer}, tol, r, u0, u1},
      Module[{
        relErr, ohs,
        res = {0., 0.},
        hs = Table[.0, {n}],
        k = 0,
        nzs = Table[.0, {n}],
        ss = Table[.0, {n}],
        ws = {{1., 0.}, {0., 1.}},
        zs,
        success = 1.0,
        uPrev = u0,
        uCurr = u1
        },
       While[True,
        k++;
        zs = Dnn[r, uCurr, uPrev].ws;
        Do[
         (Module[{nzi},
            Do[(
               zi -= zi.zj/Norm[zj, 2] zj) /. zj :> zs[[1 ;; n, j]]
             , {j, i - 1}];
            nzi = Norm[zi];
            nzs[[i]] = nzi;
            ws[[1 ;; n, i]] = zi/nzi]) /. zi :> zs[[1 ;; n, i]]
         , {i, n}];
        ohs = hs;
        ss += Log[nzs];
        hs = ss/k;
        relErr = Norm[1 - ohs/hs, 2];
        If[k >= kMin && relErr < tol,
         res = Prepend[hs, 1.0];
         Break[]
         ];
        {uCurr, uPrev, success} = nn[r, uCurr, uPrev, success];
        If[success == 0,
         res = Prepend[Table[0., {n}], 0.];
         Break[]
         ];
        ];
       res
       ], CompilationOptions -> {"InlineExternalDefinitions" -> True},
       RuntimeOptions -> "Speed", 
      CompilationTarget -> "C"]] //. {Pattern[p, _IdentityMatrix] :> 
      Block[{}, p /; True], 
     HoldPattern[e_ /. (p_ :> r_)] :> 
      Block[{}, (Hold[e] /. p :> r) /; True]}, 
   HoldPattern[Hold[expr_]] :> expr, Infinity]]