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Please note that most developers prefer to only bind to the few library calls they actually need. E.g. an rmdir() binding is just a single line with the LuaJIT FFI. And a simple binding to e.g. zlib takes only two dozen lines, see the FFI Tutorial. You can find many examples for this floating around on the net.
The following list only shows larger or somewhat comprehensive library bindings:
ljsyscall: Linux system calls.
luapower/winapi: Win32 API
luapower/objc: Objective-C & Cocoa bridge
LJIT2Win32: Core Windows libraries.
ljf-com: Microsoft COM.
LJIT2RPi: VideoCore of Raspberry Pi.
TINN: Windows API Sets, includes a shell.
luajit-mysql: MySQL.
luapower/mysql: MySQL.
LJIT2Sophia: Sophia.
lsqlite3-ffi: SQLite.
LJIT2SQLite: SQLite.
LJSQLite3: SQLite3.
mongolua: MongoDB and BSON library.
luajit-unqlite: UnQLite.
glua: OpenGL/GLUT.
luajit-glfw: OpenGL and GLFW.
LJIT2Khronos: Khronos (OpenGL, EGL, OpenCL, OpenVG)
luapower/cairo: cairo.
luapower/clipper: clipper.
luapower/giflib: giflib.
luapower/nanojpeg: nanojpeg.
luapower/freetype: freetype.
openal-lua-ffi: OpenAL.
wavpack-lua-ffi: Wavpack.
libsndfile-lua-ffi: libsndfile.
mad-lua-ffi: MAD (MPEG Audio Decoder).
ffmpeg-lua-ffi: ffmpeg.
LJIT2X264: X264
luajit-msgpack-pure: MessagePack.
iconv-lua-ffi: iconv.
LJIT2Http_Parser: HTTP parser.
luapower/expat: expat XML parser.
luapower/genx: genx XML generator.
lua-libssh: libssh (OpenSSH).
LJIT2WinCNG: WinCNG.
luapower/md5: MD5.
luapower/sha2: SHA-256, SHA-384, SHA-512.
luapower/zlib: zlib.
luapower/minizip: minizip.
ufo: Precompiled binaries for OSX/Windows and other platforms. Bindings for: Cairo, Pixman, SDL 1.3, zlib, libpng, libbz2, ZeroMQ, Expat, Freetype, GLFW, APR, AntTweakBar, OpenGL, OpenCL.
luapower/hunspell - hunspell (spell checking)