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The transcript below and the attached file fortran-submodule-support.tar.gz demonstrate a skeleton Fortran 2008 submodule implementation that is currently supported by the GNU, Cray, IBM, and Intel compilers. As discussed on the CMake users list in March 2016, the CMake parser apparently cannot handle this syntax.

$ cat CMakeLists.txt 
cmake_minimum_required(VERSION 3.6)
project (fortran-submodule-issue Fortran)
add_executable(submodule-issue-reproducer fortran-submodule.F90)
rouson@localhost:~/Code/AdHoc/src/cmake/bug-xxxxy$ cat fortran-submodule.f90 
module foo_interface
  implicit none
  interface 
    module subroutine foo() 
    end subroutine 
  end interface 
end module 

submodule (foo_interface) foo_implementation
  implicit none
contains
  module subroutine foo() 
  end subroutine 
end submodule 
 
end  ! Dummy main program to produce an executable file

$ mkdir build

$ cd build

$ FC=gfortran cmake ..
-- The Fortran compiler identification is GNU 6.1.0
-- Checking whether Fortran compiler has -isysroot
-- Checking whether Fortran compiler has -isysroot - yes
-- Checking whether Fortran compiler supports OSX deployment target flag
-- Checking whether Fortran compiler supports OSX deployment target flag - yes
-- Check for working Fortran compiler: /opt/local/bin/gfortran
-- Check for working Fortran compiler: /opt/local/bin/gfortran  -- works
-- Detecting Fortran compiler ABI info
-- Detecting Fortran compiler ABI info - done
-- Checking whether /opt/local/bin/gfortran supports Fortran 90
-- Checking whether /opt/local/bin/gfortran supports Fortran 90 -- yes
-- Configuring done
-- Generating done
-- Build files have been written to: /Users/rouson/Code/AdHoc/src/cmake/bug-xxxxy/build
rouson@localhost:~/Code/AdHoc/src/cmake/bug-xxxxy/build$ make
Scanning dependencies of target submodule-issue-reproducer
[ 50%] Building Fortran object CMakeFiles/submodule-issue-reproducer.dir/fortran-submodule.F90.o
Error copying Fortran module "subroutine".  Tried "SUBROUTINE.mod" and "subroutine.mod".
make[2]: *** [CMakeFiles/submodule-issue-reproducer.dir/fortran-submodule.F90.o.provides.build] Error 1
make[1]: *** [CMakeFiles/submodule-issue-reproducer.dir/all] Error 2
make: *** [all] Error 2

$ gfortran --version
GNU Fortran (MacPorts gcc6 6.1.0_0) 6.1.0

$ cmake --version
cmake version 3.6.1