main.f90

module testmod
    implicit none

    integer, parameter :: i4b = SELECTED_INT_KIND(9)
    integer, parameter :: dp = KIND(1.0D0)

    type t1
        integer :: i
    end type t1

    type t2
        real :: j
    end type t2

   type, public :: dlength
       real(dp),allocatable :: dat(:)
   endtype dlength

   type, public :: ilength
       integer(i4b),allocatable :: dat(:)
   endtype ilength
  
   type, public :: var_dlength
       type(dlength),allocatable :: var(:)
   endtype var_dlength

   type, public :: var_ilength
       type(ilength),allocatable :: var(:)
   endtype var_ilength

contains
    subroutine selectTest(thing)
        class(*), intent(in) :: thing
        select type(thing)
          type is (real)
              print*, "Type is real"
          type is (integer)
              print*, "Type is integer"
          type is (t1)
              print*, "Type is wrapped integer"
          type is (t2)
              print*, "Type is wrapped real"
          type is (dlength)
              print*, "Type is dlength"
          type is (ilength)
              print*, "Type is ilength"
          type is (var_ilength)
              print*, "Type is var_ilength"
          type is (var_dlength)
              print*, "Type is var_dlength"
          class default
              print*, "Type is undetermined"
        end select
    end subroutine selectTest
    
end module testmod

program test
    use testmod
    implicit none
    integer :: i
    real :: j
    character(len=4) :: k
    type(t1) :: i2
    type(t2) :: j2

    type(dlength) :: dl
    type(ilength) :: il
    type(var_dlength) :: vdl 
    type(var_ilength) :: vil

    call selectTest(i)
    call selectTest(j)
    call selectTest(k)
    call selectTest(i2)
    call selectTest(j2)
    
    call selectTest(dl)
    call selectTest(il)
    call selectTest(vdl)
    call selectTest(vil)
end program test

Output gives:

 Type is integer                             
 Type is real                                
 Type is undetermined                        
 Type is wrapped integer                     
 Type is wrapped real                        
 Type is dlength                             
 Type is ilength                             
 Type is var_dlength                         
 Type is var_ilength