Now LuaRocks complains because “lua51.dll” is missing from my computer.
Having experimented with that 'make install' I can say that it will never work for Windows, even with MSYS. Doesn't know it should be copying .exes, doesn't know it needs to copy the .dll, and creates lib and share directories which are useless - the package.path is <bindir>\lua and the package.cpath is <bindir>
