Difference between + and :intersection

The + prefix should be thought of as an "AND" in formal logic, e.g. "give me all titles that satisfy condition A and condition B". But it's not suitable for all cases; if condition B uses a filter operator that replaces its input, then it will be difficult to use the + prefix. For example, if you wanted to find out what tags two tiddlers have in common, you might try to write a filter expression like:

• [[field Operator]tags[]] +[[compare Operator]tags[]]

But that won't work, because the second filter run will end up throwing away its input and replacing it with an input consisting of the single title [[compare Operator]]. So the result you'd get from that filter expression would be just the tags of the compare Operator tiddler.

For cases like this, the :intersection prefix is what you need. It takes the filter output so far, sets it aside, and starts the next filter run with all tiddler titles as input. Then once the latest filter run has completed, it takes the latest output, compares it to the set-aside output, and produces a new output that contains only titles that appeared in both the set-aside output and the latest output. So to get only the tags that the field Operator and compare Operator tiddlers have in common, you would write a filter expression like this:

• [[field Operator]tags[]] :intersection[[compare Operator]tags[]]

The following examples use the field Operator and compare Operator tiddlers and their respective tags.