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Since a C "char" is not a Lua "character", consider using
"byte" instead of "character" at the following places:

under Lexical Conventions, in "a character in a literal string"
under lua_pushfstring
under lua_tolstring
under luaL_addchar
under String Manipulation, first paragraph (twice)
under string.byte
under string.char
under file:read()   (twice)

Also, under string.char, consider changing the last sentence to:
"Note that the characters corresponding to numerical codes are 
not necessarily portable across platforms. "