For an optional integer parameter I can write "y_Integer:4711":

Clear[f];
f[x_Integer,y_Integer:4711]:=x+y;
{f[1],f[1,2]}
{4712,3}

1. Unfortunately boolean expressions don't have head "Boolean" but "Symbol". Hence I cannot write "b_Boolean:True" for an optional boolean parameter with default True.

   Clear[f];
   f[x_Integer,b_Boolean:True]:=If[b,x,-x];
   {f[1],f[1,False]}
   {1,f[1,False]}
   

2. I can write "b?BooleanQ" or "b/;BooleanQ[b]". Then at least b has to be boolean, but then it is no longer optional:

   Clear[f];
   f[x_Integer,b_?BooleanQ]:=If[b,x,-x];
   {f[1],f[1,False]}
   {f[1],-1}
   

3. I would like to write something like "b_?BooleanQ:True". But this does not work:

   Clear[f];
   f[x_Integer,b_?BooleanQ:True]:=If[b,x,-x];
   {f[1],f[1,False]}
   {f[1],f[1,False]}
   

4. One solution I found is with two definitions. But this is intricately and not easy to understand:

   Clear[f];
   f[x_Integer,b_?BooleanQ]:=If[b,x,-x];
   f[x_Integer,b_:True]:=f[x,b];
   {f[1],f[1,False]}
   {1,-1}
   

5. Another solution is with "Optional". This works, which is strange since it should be the same as within Point 3 above:

   Clear[f];
   f[x_Integer,Optional[b_?BooleanQ,True]]:=If[b,x,-x];
   {f[1],f[1,False]}
   {1,-1}
   

6. Of course I could use "Options", "OptionPatterns" and "OptionValue". But this seems to be overkill to me.

7. What is the simplest way to specify an optional boolean parameter with a default value?