'Point free' is standard mathematical terminology for nothing more than the style of defining functions without making direct reference to the elements the functions act on. This style is exemplified by category theory and the reason it's called 'point free' rather than 'element free' is that category theory arose from algebraic topology where many of the functions under discussion act on sets of points in a topological space. 'Point' certainly doesn't refer to anything to do with CPOs and relating this use of the word point to arrows from terminal objects doesn't work too well if you consider vector spaces where maps from terminal objects don't correspond to (the usual notion of) points. -- Dan (Apologies if you received this message twice.)