The built-in function If behaves strangely in a procedure/function [closed]

Question

Inside a procedure or user-defined function, If doesn't do as it should. Long ago, I found out that I should use === instead of == in a procedure in order to make the decision appear at real time. But what should I do with If? Thanks a lot.

=== edit ====

This is my program to generate sequences of "1", "2" and "3" with no equal consecutive pairs. "If" doesn't seem to work properly, or I really miss something. (allow at most 3 copies of each number.)

add[seq_, n1_, n2_, n3_] :=
 Do[
  Block[{nn1, nn2, nn3, vn, vv = Sort[{seq[[i]], seq[[i + 1]]}]},
   Print["between ", vv];
   If[vv == {2, 3}, If[n1 >= 3, Goto[next], nn1 = n1 + 1; vn = 1],
    If[vv == {1, 3}, If[n2 >= 3, Goto[next], nn2 = n2 + 1; vn = 2],
     If[vv == {1, 2}, If[n3 >= 3, Goto[next], nn3 = n3 + 1; vn = 3],
      Print["error"]]]];
   Print["Insert ", vn, " to ", seq];
   add[Insert[seq, vn, i + 1], nn1, nn2, nn3];
   Label[next]], {i, Length[seq] - 1}]
add[{1, 2, 3}, 1, 1, 1]

At first step, it inserts 3 but the next step it couldn't say vn=2

between {1,2} Insert 3 to {1,2,3} between {1,3} Insert vn to {1,3,2,3}

Strange! Replace "==" by "===" make it better but still error.

(ps. At first, "Switch" didn't work)

==== edit to be better but same error =====

Replace Goto&Label by Continue and sequential If by Switch.

add[seq_, n1_, n2_, n3_] :=
 Do[
  Block[{nn1, nn2, nn3, vn, vv = Sort[{seq[[i]], seq[[i + 1]]}]},
   Print["Between ", vv];
   Switch[vv,
    {2, 3}, If[n1 >= 3, Continue[], nn1 = n1 + 1; vn = 1],
    {1, 3}, If[n2 >= 3, Continue[], nn2 = n2 + 1; vn = 2],
    {1, 2}, If[n3 >= 3, Continue[], nn3 = n3 + 1; vn = 3],
    _, Print["error"]];
   Print["insert ", vn, " to ", seq];
   add[Insert[seq, vn, i + 1], nn1, nn2, nn3]]
  , {i, Length[seq] - 1}]

add[{1, 2, 3}, 1, 1, 1]

I expect the following output.

Between {1,2}

insert 3 to {1,2,3}

Between {1,3}

insert 2 to {1,3,2,3}

Answer 1

It's not the If that is causing your problems, but simply the errors in your program logic. In many passes of your loop nn1, nn2, nn3 and/or vn never receive a numeric value. You then call your function with variables that aren't always defined. The If statement then fails, for instance because you get a test like

{1,2}=={1,vn}

for which Mathematica can not determine the corresponding Boolean value. It returns unevaluated, causing your problems. Using === instead of == forces a definite return of the test (note that that may not be correct in your case). Anything that isn't explicitly True is determined as False.

The same problem occurs with the three n1 >= 3 tests.

---

By the way, may I congratulate you with the first occurrence of Goto and Label in Mathematica in my experience? Ever since Edsger Dijkstra's famous article Goto Considered Harmful the use of this construction is frowned upon in CS circles and it takes some courage (or perhaps ignorance) to use it.