Are there any tools to set up an automated IMAP client?

By which I mean I want to set up some software on a headless Linux box
which connects to an account on an IMAP server elsewhere. It could
then be configured to perform actions on received email, such as
filter it, move it to folders, forward it to people based on various
criteria, etc.

It seems like the sort of thing that must exist but I'm clearly
picking the wrong things to Google for...

Mark