Generating Random SQL Queries from SQL Grammar

I am trying to automatically generate SQL queries that are only syntactically correct. I have seen the PostgreSQL grammar file, I am wondering is there a way to generate random SQL queries based on SQL grammar? There can be unlimited number of SQL queries generated but we can put a limit on the length of SQL query strings.

For example to get something like this in results:

SELECT X FROM X WHERE X BETWEEN X AND X ;