Type bound procedure as arguments - fortran

Question

I want to pass a type bound procedures (as an external function) to another function as follows:
module mod1
implicit none
type type1
real :: a
contains
procedure,pass :: f
end type
contains
real function f(y,e)
class(type1), intent(in) :: y
real,intent(in) :: e
f=y%a+e
end function
end module
program test
use mod1
type(type1) :: t
t%a=3e0
write(*,*) s(t%f)
contains
real function s(g)
real,external :: g
s=g(5e0)+2e0
end function
end program
gfortran produces gives this error :
write(*,*) s(t%f)
1
Error: Expected argument list at (1)
But what I can do is:
program test
t%a=3e0
write(*,*) s(k)
contains
real function s(g)
real,external :: g
s=g(5e0)+2e0
end function
real function k(e)
real,intent(in) :: e
k=3e0+e
end function
end program
I think the problem is related to Passing type bound procedures as arguments, but I don't see at the moment how the answers there can help me.
EDIT:
A better example which (hopefully) shows the difficulty:
module mod2
implicit none
contains
real function s(g)
interface
real function g(x)
real, intent(in) :: x
end function
end interface
s=g(5e0)+2e0
end function
end module
module mod1
use mod2
type type1
real :: a
contains
procedure,pass :: f
procedure,pass :: h
end type
contains
real function f(y,e)
class(type1), intent(in) :: y
real,intent(in) :: e
f=y%a+e
end function
real function h(y)
class(type1), intent(inout) :: y
h=s(y%f)
end function
end module
program test
use mod1
type(type1) :: t
t%a=3e0
write(*,*) t%h
end program
EDIT II:
Ok, the wrappers still work in combination with a pointer:
module mod2
implicit none
contains
real function s(g)
interface
real function g(x)
real, intent(in) :: x
end function
end interface
s=g(5e0)+2e0
end function
end module
module mod1
use mod2
type type1
real :: a
contains
procedure,pass :: f
procedure,pass :: h
end type
class(type1),pointer :: help_w
contains
real function f(y,e)
class(type1), intent(in) :: y
real,intent(in) :: e
f=y%a+e
end function
real function h(y)
class(type1), intent(inout),target :: y
help_w => y
h=s(wrap)
end function
function wrap(x)
real,intent(in) :: x
wrap=help_w%f(x)
end function
end module
program test
use mod1
type(type1) :: t
t%a=3e0
write(*,*) t%h()
end program
This is certainly not a beautiful solution but at least it works.

Answer 1

You can write a wrapper. This is the most straightforward version. Requires passing internal function as a dummy argument (F2008), but you could declare the wrapper in a module too, if the t can bee there.
Note I changed the declaration of the procedure argument in s to something more modern - the interface block.
program test
use mod1
type(type1) :: t
t%a=3e0
write(*,*) s(wrap)
contains
real function s(g)
interface
real function g(x)
real, intent(in) :: x
end function
end interface
s=g(5e0)+2e0
end function
function wrap(x)
real, intent(in) :: x
wrap = t%f(x)
end function
end program
The reason for your error is well described in the answers to the linked question, you cannot pass type bound procedures the way you tried.