There is no separate database of all the Moodle core functions - but there is the code itself, most of which has appropriate PHPDocs to explain what each function is used for.
Most IDEs will allow you to quickly search the code for functions based on words appearing in their name. Any attempt to create a separate database of Moodle functions would likely take a very long time to create and would be out of date again within a very short space of time.