Question: Is there a list or method to determine a list of the lua functions available/installed?

Sofar I could only find the lua source files. Maybe I should write something that search through all the installed lua files for lines starting with "function". Then I will have a list, but it would still not give me the rest of detail of the functions.

Any better ideas or suggestions?

Answer: 
You know the [LuaTeX functions short reference](http://www.luatex.org/svn/trunk/manual/old/functionref.pdf)? That together with the [Lua reference](http://www.lua.org/manual/5.1/) should cover all available functions if I am correct.
This is hard to answer, as you are asking the lua equivalent of 'what are the names of all defined macros?'. The answer is: it depends.

The core luatex functions are documented in the reference manual, as Patrick wrote in his answer. Everything else is loaded from lua source files on your hard-disk, but only if you (possibly indirectly) asked for it, just as would be the case for macros/packages.

If you are only interested in a list of defined lua functions in your current luatex source file, you can try this inside a lua code block:

```
function dump (prefix, a) 
  for i,v in pairs (a) do
    if type(v) == "table" then
      dump(prefix .. '.' .. i,v)
    elseif type(v) == "function" then
      print (prefix .. '.' .. i .. '()')
    end 
  end
end
dump('_G',_G)

```

but there are two caveats: 

* you only get to know function names, not their calling conventions. This is about as useful as only knowing macro names (meaning: not very useful at all)
* circular references to tables will confuse this bit of lua code, it needs to be made smarter to allow for that