How to use procedure pointers for subroutines with

I'm developing a Fortran program for scientific computing. I want to use procedure pointers to assign the boundary conditions in the problem, shown in the following main program

program main
use boundary
implicit none

  bc1 => boundaryA
  bc2 => boundaryB
  bc3 => boundaryC

  call comp_boundary

end program

I define all the boundary operations "boundaryA/B/C" in a "boundary" module

module boundary
implicit none

procedure(boundary_type), pointer :: bc1,bc2,bc3

abstract interface
  subroutine boundary_type(i)
    integer :: i
  end subroutine
end interface

contains

subroutine boundaryA(i)
integer :: i
  print*, 'Boundary A at ',i
end subroutine

subroutine boundaryB(i)
integer :: i
  print*, 'Boundary B at ',i
end subroutine

subroutine boundaryC(i)
integer :: i
  print*, 'Boundary C at',i
end subroutine

subroutine comp_boundary
  call bc1(1)
  call bc2(2)
  call bc3(3)
end subroutine

end module

This works well.

But my question is that if, say, boundaryC has not one input argument, but two, then my definition for the abstract interface boundary_type doesn't work now.

Is that possible to use the procedure pointer to deal with this case? Or any other way around?

You could achieve this with an OPTIONAL argument. This is more an academic solution as there is always conservation of misery. As the comment of High Performance Mark states, your decision to use one or two arguments will need to be made somewhere.

Nonetheless, the OPTIONAL argument would require to add this too all subroutines and could therefore be not really the solution you request as all subroutines are essentially changed. It is essentially the same solution you gave, with just different set of procedure arguments.

MODULE boundary
  IMPLICIT NONE

  PROCEDURE(boundary_type), POINTER :: bc1,bc2

  ABSTRACT INTERFACE
     SUBROUTINE boundary_type(i,j)
       INTEGER           :: i
       INTEGER, OPTIONAL :: j
     END SUBROUTINE boundary_type
  END INTERFACE

CONTAINS

  SUBROUTINE boundaryA(i,j)
    INTEGER           :: i
    INTEGER, OPTIONAL :: j
    PRINT *, 'Boundary A at ',i
  END SUBROUTINE boundaryA

  SUBROUTINE boundaryB(i,j)
    INTEGER           :: i
    INTEGER, OPTIONAL :: j
    PRINT *, 'Boundary B at ',i,j
  END SUBROUTINE boundaryB

  SUBROUTINE comp_boundary
    CALL bc1(1)
    CALL bc2(2,3)
  END SUBROUTINE comp_boundary

END MODULE boundary

Note: the subroutine boundaryB must always be called with both arguments as no check is done for the availability of j (using PRESENT)