I'd like to point out that Zed's answer creates an interpreted fun. When the fun is called it enters the evaluator which starts to evaluates the abstract syntax tree returned by erl_parse:parse_exprs/1
that it has captured. Looking at the fun created:
11> erlang:fun_info(Fun, env).
{env,[[],none,none,
[{clause,1,
[{var,1,'X'}],
[],
[{op,1,'+',{var,1,'X'},{integer,1,1}}]}]]}
12> erlang:fun_info(Fun, module).
{module,erl_eval}
One can see that it has closed over the parsed abstract syntax tree as seen in the env
info, and it is a fun created inside erlang_eval as seen in the module
info.
It is possible to use the erlang compiler to create a compiled module at runtime, and a pointer toward that is compile:forms/2 and code:load_binary/3. But the details of that should probably go into another stackoverflow question.