To Lower

The Ada example code does not append to the array as the algorithms. Instead we create an empty array of the desired length and then replace the characters inside.

  function To_Lower (C : Character) return Character renames
     Ada.Characters.Handling.To_Lower;

  --  tolower - translates all alphabetic, uppercase characters—in str to lowercase
  function To_Lower (Str : String) return String is
     Result : String (Str'Range);
  begin
     for C in  Str'Range loop
        Result (C) := To_Lower (Str (C));
     end loop;
     return Result;
  end To_Lower;

Would the append approach be impossible with Ada? No, but it would be significantly more complex and slower.

Equal Ignore Case

—equal-ignore-case—returns true if s or t are equal,

  --  ignoring case
  function Equal_Ignore_Case
    (S    : String;
     T    : String)
     return Boolean
  is
     O : constant Integer := S'First - T'First;
  begin
     if T'Length /= S'Length then
        return False;  --  if they aren't the same length, they—aren't equal
     else
        for I in  S'Range loop
           if To_Lower (S (I)) /=
              To_Lower (T (I + O))
           then
              return False;
           end if;
        end loop;
     end if;
     return True;
  end Equal_Ignore_Case;