Functions and triggers allow users to insert code into the backend server that other users may execute without knowing it. Hence, both mechanisms permit users to "Trojan horse" others with relative impunity. The only real protection is tight control over who can define functions.
Functions written in any language except SQL run inside the backend server process with the operating systems permissions of the database server daemon process. It is possible to change the server's internal data structures from inside of trusted functions. Hence, among many other things, such functions can circumvent any system access controls. This is an inherent problem with user-defined C functions.
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