Declaration of dummy argument explicit shape arrays in Fortran - arrays

Question

I thought that the specification of an explicit shape dummy argument array in a subroutine can involve any integer variables, including other dummy variables (usual cases), module variables, and local variables of the present subroutine. But it turns out that local variables (which are not dummy variables) can not be used in the specification.
An example is as follows:
module mp
implicit none
contains
subroutine p(b)
integer :: m=4, n=4 !not integer,parameter :: m=4, n=4
integer :: b(m,n)
end subroutine p
end module mp
gfortran will raise Error: Variable 'm' cannot appear in the expression at (1)
For this example, I can use integer,parameter :: m=4, n=4 to avoid this, but I do not understand why the original case does not work, considering the fact that the bounds/extents of explicit shape arrays do not need to be known at compile time. A modified version of the above example works:
module mp
implicit none
integer :: m=4, n=4
contains
subroutine p(b)
integer :: b(m,n)
end subroutine p
end module mp
Considering the slight difference between the two examples, I expect both of them work, but in fact the former does not. Could someone explain the reason?
Update: I found out that this is a very subtle issue because it depends on whether the subroutine is contained in a module or is standalone, it also depends on the version of gfortran. I have posted examples in the answer region.

Answer 1

Formally, there are requirements on what the bounds in such an explicit shape array are. These don't simply map to "don't have to be known at compile time".
For an array explicit shape, the array bounds must be specification expressions. Often, such bounds must be constant expressions, but this is not the case for dummy arguments. This partly gives rise to the (erroneous) thought that they needn't be known at compile time.
However, the constraints for a specification expression must still be met. These can be found in Fortran 2018 10.1.11. In particular, a local variable (even a saved one) may not appear in a specification expression.
For the examples of the question, using named constants such as with
integer, parameter :: m=4, n=4
is allowed in a specification expression. Indeed, the specification expressions m and n are even constant expressions in this case.
If we had
function p(b,m,n)
integer m, n, b(m,n)
end function
then we have valid specification expressions for the array bounds, even though m and n are not constants.

Answer 2

The right workaround is to put the procedure body in a BLOCK construct:
module mp3
contains
subroutine p(b)
implicit none
integer :: m=4, n=4
BLOCK
integer :: b(m,n)
END BLOCK
end subroutine p
end module mp3
The fact that it works in gfortran-8 as a standalone subroutine should be reported on bugzilla. You've got a nice minimal example there.
EDIT: I hadn't noticed that b was a dummy argument. I was thinking more in terms of something like
module mp3
contains
subroutine p(x)
implicit none
real x
integer :: m=4, n=4
BLOCK
integer :: b(m,n)
END BLOCK
end subroutine p
end module mp3
But as the example stands the BLOCK approach just can't work. Also gfortran 8.1.0 rejects the form with the standalone subroutine:
subroutine p(x)
implicit none
real x
integer :: m=4, n=4
integer :: b(m,n)
end subroutine p
Error: Variable 'm' cannot appear in the expression at (1)
(As it should)

Answer 3

Finally, I found out that this is a very subtle issue because it depends on the version of gfortran and also depends on whether the subroutine is contained in a module or is standalone.
Neither gfortran-4.8 or gfortran-8 can compile successfully the following code:
module mp3
contains
subroutine p(b)
implicit none
integer :: m=4, n=4
integer :: b(m,n)
end subroutine p
end module mp3
But if we consider a standalone subroutine as follows:
subroutine p(b)
implicit none
integer :: m=4, n=4
integer :: b(m,n)
end subroutine p
Then gfortran-4.8 still reject this form, but gfortran-8 accepts this, which may be just a bug in gfortran-8 because further testing (by user5713492) indicates that gfortran-8.1.0 also rejects this form.
In summary, local variables of a subroutine are not allowed in the specification expression of dummy argument arrays.
Using local non-constant variables in specification expressions is not very often needed. So it is not a terrible idea to forbid this usage.